Parallel Domain Decomposition Formulation and Software for Large-Scale Sparse Symmetrical/Unsymmetrical Aeroacoustic Applications

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Watson, Willie R. (Technical Monitor)

2005-01-01

The overall objectives of this research work are to formulate and validate efficient parallel algorithms, and to efficiently design/implement computer software for solving large-scale acoustic problems, arised from the unified frameworks of the finite element procedures. The adopted parallel Finite Element (FE) Domain Decomposition (DD) procedures should fully take advantages of multiple processing capabilities offered by most modern high performance computing platforms for efficient parallel computation. To achieve this objective. the formulation needs to integrate efficient sparse (and dense) assembly techniques, hybrid (or mixed) direct and iterative equation solvers, proper pre-conditioned strategies, unrolling strategies, and effective processors' communicating schemes. Finally, the numerical performance of the developed parallel finite element procedures will be evaluated by solving series of structural, and acoustic (symmetrical and un-symmetrical) problems (in different computing platforms). Comparisons with existing "commercialized" and/or "public domain" software are also included, whenever possible.

Parallel iterative methods for sparse linear and nonlinear equations

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Domain decomposition methods for the parallel computation of reacting flows

NASA Technical Reports Server (NTRS)

Keyes, David E.

1988-01-01

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turner, A.; Davis, A.; University of Wisconsin-Madison, Madison, WI 53706

CCFE perform Monte-Carlo transport simulations on large and complex tokamak models such as ITER. Such simulations are challenging since streaming and deep penetration effects are equally important. In order to make such simulations tractable, both variance reduction (VR) techniques and parallel computing are used. It has been found that the application of VR techniques in such models significantly reduces the efficiency of parallel computation due to 'long histories'. VR in MCNP can be accomplished using energy-dependent weight windows. The weight window represents an 'average behaviour' of particles, and large deviations in the arriving weight of a particle give rise tomore » extreme amounts of splitting being performed and a long history. When running on parallel clusters, a long history can have a detrimental effect on the parallel efficiency - if one process is computing the long history, the other CPUs complete their batch of histories and wait idle. Furthermore some long histories have been found to be effectively intractable. To combat this effect, CCFE has developed an adaptation of MCNP which dynamically adjusts the WW where a large weight deviation is encountered. The method effectively 'de-optimises' the WW, reducing the VR performance but this is offset by a significant increase in parallel efficiency. Testing with a simple geometry has shown the method does not bias the result. This 'long history method' has enabled CCFE to significantly improve the performance of MCNP calculations for ITER on parallel clusters, and will be beneficial for any geometry combining streaming and deep penetration effects. (authors)« less

Parallel Preconditioning for CFD Problems on the CM-5

NASA Technical Reports Server (NTRS)

Simon, Horst D.; Kremenetsky, Mark D.; Richardson, John; Lasinski, T. A. (Technical Monitor)

1994-01-01

Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.

Efficient ICCG on a shared memory multiprocessor

NASA Technical Reports Server (NTRS)

Hammond, Steven W.; Schreiber, Robert

1989-01-01

Different approaches are discussed for exploiting parallelism in the ICCG (Incomplete Cholesky Conjugate Gradient) method for solving large sparse symmetric positive definite systems of equations on a shared memory parallel computer. Techniques for efficiently solving triangular systems and computing sparse matrix-vector products are explored. Three methods for scheduling the tasks in solving triangular systems are implemented on the Sequent Balance 21000. Sample problems that are representative of a large class of problems solved using iterative methods are used. We show that a static analysis to determine data dependences in the triangular solve can greatly improve its parallel efficiency. We also show that ignoring symmetry and storing the whole matrix can reduce solution time substantially.

Hierarchical Parallelism in Finite Difference Analysis of Heat Conduction

NASA Technical Reports Server (NTRS)

Padovan, Joseph; Krishna, Lala; Gute, Douglas

1997-01-01

Based on the concept of hierarchical parallelism, this research effort resulted in highly efficient parallel solution strategies for very large scale heat conduction problems. Overall, the method of hierarchical parallelism involves the partitioning of thermal models into several substructured levels wherein an optimal balance into various associated bandwidths is achieved. The details are described in this report. Overall, the report is organized into two parts. Part 1 describes the parallel modelling methodology and associated multilevel direct, iterative and mixed solution schemes. Part 2 establishes both the formal and computational properties of the scheme.

On nonlinear finite element analysis in single-, multi- and parallel-processors

NASA Technical Reports Server (NTRS)

Utku, S.; Melosh, R.; Islam, M.; Salama, M.

1982-01-01

Numerical solution of nonlinear equilibrium problems of structures by means of Newton-Raphson type iterations is reviewed. Each step of the iteration is shown to correspond to the solution of a linear problem, therefore the feasibility of the finite element method for nonlinear analysis is established. Organization and flow of data for various types of digital computers, such as single-processor/single-level memory, single-processor/two-level-memory, vector-processor/two-level-memory, and parallel-processors, with and without sub-structuring (i.e. partitioning) are given. The effect of the relative costs of computation, memory and data transfer on substructuring is shown. The idea of assigning comparable size substructures to parallel processors is exploited. Under Cholesky type factorization schemes, the efficiency of parallel processing is shown to decrease due to the occasional shared data, just as that due to the shared facilities.

Parallelization of implicit finite difference schemes in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel

1990-01-01

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

Vectorized and multitasked solution of the few-group neutron diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zee, S.K.; Turinsky, P.J.; Shayer, Z.

1989-03-01

A numerical algorithm with parallelism was used to solve the two-group, multidimensional neutron diffusion equations on computers characterized by shared memory, vector pipeline, and multi-CPU architecture features. Specifically, solutions were obtained on the Cray X/MP-48, the IBM-3090 with vector facilities, and the FPS-164. The material-centered mesh finite difference method approximation and outer-inner iteration method were employed. Parallelism was introduced in the inner iterations using the cyclic line successive overrelaxation iterative method and solving in parallel across lines. The outer iterations were completed using the Chebyshev semi-iterative method that allows parallelism to be introduced in both space and energy groups. Formore » the three-dimensional model, power, soluble boron, and transient fission product feedbacks were included. Concentrating on the pressurized water reactor (PWR), the thermal-hydraulic calculation of moderator density assumed single-phase flow and a closed flow channel, allowing parallelism to be introduced in the solution across the radial plane. Using a pinwise detail, quarter-core model of a typical PWR in cycle 1, for the two-dimensional model without feedback the measured million floating point operations per second (MFLOPS)/vector speedups were 83/11.7. 18/2.2, and 2.4/5.6 on the Cray, IBM, and FPS without multitasking, respectively. Lower performance was observed with a coarser mesh, i.e., shorter vector length, due to vector pipeline start-up. For an 18 x 18 x 30 (x-y-z) three-dimensional model with feedback of the same core, MFLOPS/vector speedups of --61/6.7 and an execution time of 0.8 CPU seconds on the Cray without multitasking were measured. Finally, using two CPUs and the vector pipelines of the Cray, a multitasking efficiency of 81% was noted for the three-dimensional model.« less

Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

NASA Astrophysics Data System (ADS)

Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

2013-09-01

Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are presented to compare the output from the MCPI library to current state-of-practice numerical integration methods. It is shown that MCPI is capable of out-performing the state-of-practice in terms of computational cost and accuracy.

Parallel Reconstruction Using Null Operations (PRUNO)

PubMed Central

Zhang, Jian; Liu, Chunlei; Moseley, Michael E.

2011-01-01

A novel iterative k-space data-driven technique, namely Parallel Reconstruction Using Null Operations (PRUNO), is presented for parallel imaging reconstruction. In PRUNO, both data calibration and image reconstruction are formulated into linear algebra problems based on a generalized system model. An optimal data calibration strategy is demonstrated by using Singular Value Decomposition (SVD). And an iterative conjugate- gradient approach is proposed to efficiently solve missing k-space samples during reconstruction. With its generalized formulation and precise mathematical model, PRUNO reconstruction yields good accuracy, flexibility, stability. Both computer simulation and in vivo studies have shown that PRUNO produces much better reconstruction quality than autocalibrating partially parallel acquisition (GRAPPA), especially under high accelerating rates. With the aid of PRUO reconstruction, ultra high accelerating parallel imaging can be performed with decent image quality. For example, we have done successful PRUNO reconstruction at a reduction factor of 6 (effective factor of 4.44) with 8 coils and only a few autocalibration signal (ACS) lines. PMID:21604290

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1991-01-01

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

Efficient parallel resolution of the simplified transport equations in mixed-dual formulation

NASA Astrophysics Data System (ADS)

Barrault, M.; Lathuilière, B.; Ramet, P.; Roman, J.

2011-03-01

A reactivity computation consists of computing the highest eigenvalue of a generalized eigenvalue problem, for which an inverse power algorithm is commonly used. Very fine modelizations are difficult to treat for our sequential solver, based on the simplified transport equations, in terms of memory consumption and computational time. A first implementation of a Lagrangian based domain decomposition method brings to a poor parallel efficiency because of an increase in the power iterations [1]. In order to obtain a high parallel efficiency, we improve the parallelization scheme by changing the location of the loop over the subdomains in the overall algorithm and by benefiting from the characteristics of the Raviart-Thomas finite element. The new parallel algorithm still allows us to locally adapt the numerical scheme (mesh, finite element order). However, it can be significantly optimized for the matching grid case. The good behavior of the new parallelization scheme is demonstrated for the matching grid case on several hundreds of nodes for computations based on a pin-by-pin discretization.

PRIM: An Efficient Preconditioning Iterative Reweighted Least Squares Method for Parallel Brain MRI Reconstruction.

PubMed

Xu, Zheng; Wang, Sheng; Li, Yeqing; Zhu, Feiyun; Huang, Junzhou

2018-02-08

The most recent history of parallel Magnetic Resonance Imaging (pMRI) has in large part been devoted to finding ways to reduce acquisition time. While joint total variation (JTV) regularized model has been demonstrated as a powerful tool in increasing sampling speed for pMRI, however, the major bottleneck is the inefficiency of the optimization method. While all present state-of-the-art optimizations for the JTV model could only reach a sublinear convergence rate, in this paper, we squeeze the performance by proposing a linear-convergent optimization method for the JTV model. The proposed method is based on the Iterative Reweighted Least Squares algorithm. Due to the complexity of the tangled JTV objective, we design a novel preconditioner to further accelerate the proposed method. Extensive experiments demonstrate the superior performance of the proposed algorithm for pMRI regarding both accuracy and efficiency compared with state-of-the-art methods.

New Parallel Algorithms for Structural Analysis and Design of Aerospace Structures

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.

1998-01-01

Subspace and Lanczos iterations have been developed, well documented, and widely accepted as efficient methods for obtaining p-lowest eigen-pair solutions of large-scale, practical engineering problems. The focus of this paper is to incorporate recent developments in vectorized sparse technologies in conjunction with Subspace and Lanczos iterative algorithms for computational enhancements. Numerical performance, in terms of accuracy and efficiency of the proposed sparse strategies for Subspace and Lanczos algorithm, is demonstrated by solving for the lowest frequencies and mode shapes of structural problems on the IBM-R6000/590 and SunSparc 20 workstations.

Parallel computation of multigroup reactivity coefficient using iterative method

NASA Astrophysics Data System (ADS)

Susmikanti, Mike; Dewayatna, Winter

2013-09-01

One of the research activities to support the commercial radioisotope production program is a safety research target irradiation FPM (Fission Product Molybdenum). FPM targets form a tube made of stainless steel in which the nuclear degrees of superimposed high-enriched uranium. FPM irradiation tube is intended to obtain fission. The fission material widely used in the form of kits in the world of nuclear medicine. Irradiation FPM tube reactor core would interfere with performance. One of the disorders comes from changes in flux or reactivity. It is necessary to study a method for calculating safety terrace ongoing configuration changes during the life of the reactor, making the code faster became an absolute necessity. Neutron safety margin for the research reactor can be reused without modification to the calculation of the reactivity of the reactor, so that is an advantage of using perturbation method. The criticality and flux in multigroup diffusion model was calculate at various irradiation positions in some uranium content. This model has a complex computation. Several parallel algorithms with iterative method have been developed for the sparse and big matrix solution. The Black-Red Gauss Seidel Iteration and the power iteration parallel method can be used to solve multigroup diffusion equation system and calculated the criticality and reactivity coeficient. This research was developed code for reactivity calculation which used one of safety analysis with parallel processing. It can be done more quickly and efficiently by utilizing the parallel processing in the multicore computer. This code was applied for the safety limits calculation of irradiated targets FPM with increment Uranium.

Computational Issues in Damping Identification for Large Scale Problems

NASA Technical Reports Server (NTRS)

Pilkey, Deborah L.; Roe, Kevin P.; Inman, Daniel J.

1997-01-01

Two damping identification methods are tested for efficiency in large-scale applications. One is an iterative routine, and the other a least squares method. Numerical simulations have been performed on multiple degree-of-freedom models to test the effectiveness of the algorithm and the usefulness of parallel computation for the problems. High Performance Fortran is used to parallelize the algorithm. Tests were performed using the IBM-SP2 at NASA Ames Research Center. The least squares method tested incurs high communication costs, which reduces the benefit of high performance computing. This method's memory requirement grows at a very rapid rate meaning that larger problems can quickly exceed available computer memory. The iterative method's memory requirement grows at a much slower pace and is able to handle problems with 500+ degrees of freedom on a single processor. This method benefits from parallelization, and significant speedup can he seen for problems of 100+ degrees-of-freedom.

Efficient parallel implicit methods for rotary-wing aerodynamics calculations

NASA Astrophysics Data System (ADS)

Wissink, Andrew M.

Euler/Navier-Stokes Computational Fluid Dynamics (CFD) methods are commonly used for prediction of the aerodynamics and aeroacoustics of modern rotary-wing aircraft. However, their widespread application to large complex problems is limited lack of adequate computing power. Parallel processing offers the potential for dramatic increases in computing power, but most conventional implicit solution methods are inefficient in parallel and new techniques must be adopted to realize its potential. This work proposes alternative implicit schemes for Euler/Navier-Stokes rotary-wing calculations which are robust and efficient in parallel. The first part of this work proposes an efficient parallelizable modification of the Lower Upper-Symmetric Gauss Seidel (LU-SGS) implicit operator used in the well-known Transonic Unsteady Rotor Navier Stokes (TURNS) code. The new hybrid LU-SGS scheme couples a point-relaxation approach of the Data Parallel-Lower Upper Relaxation (DP-LUR) algorithm for inter-processor communication with the Symmetric Gauss Seidel algorithm of LU-SGS for on-processor computations. With the modified operator, TURNS is implemented in parallel using Message Passing Interface (MPI) for communication. Numerical performance and parallel efficiency are evaluated on the IBM SP2 and Thinking Machines CM-5 multi-processors for a variety of steady-state and unsteady test cases. The hybrid LU-SGS scheme maintains the numerical performance of the original LU-SGS algorithm in all cases and shows a good degree of parallel efficiency. It experiences a higher degree of robustness than DP-LUR for third-order upwind solutions. The second part of this work examines use of Krylov subspace iterative solvers for the nonlinear CFD solutions. The hybrid LU-SGS scheme is used as a parallelizable preconditioner. Two iterative methods are tested, Generalized Minimum Residual (GMRES) and Orthogonal s-Step Generalized Conjugate Residual (OSGCR). The Newton method demonstrates good parallel performance on the IBM SP2, with OS-GCR giving slightly better performance than GMRES on large numbers of processors. For steady and quasi-steady calculations, the convergence rate is accelerated but the overall solution time remains about the same as the standard hybrid LU-SGS scheme. For unsteady calculations, however, the Newton method maintains a higher degree of time-accuracy which allows tbe use of larger timesteps and results in CPU savings of 20-35%.

Fault Tolerant Parallel Implementations of Iterative Algorithms for Optimal Control Problems

DTIC Science & Technology

1988-01-21

p/.V)] steps, but did not discuss any specific parallel implementation. Gajski [51 improved upon this result by performing the SIMD computation in...N = p2. our approach reduces to that of [51, except that Gajski presents the coefficient computation and partial solution phases as a single...8217>. the SIMD algo- rithm presented by Gajski [5] can be most efficiently mapped to a unidirec- tional ring network with broadcasting capability. Based

Parallel Implementation of 3-D Iterative Reconstruction With Intra-Thread Update for the jPET-D4

NASA Astrophysics Data System (ADS)

Lam, Chih Fung; Yamaya, Taiga; Obi, Takashi; Yoshida, Eiji; Inadama, Naoko; Shibuya, Kengo; Nishikido, Fumihiko; Murayama, Hideo

2009-02-01

One way to speed-up iterative image reconstruction is by parallel computing with a computer cluster. However, as the number of computing threads increases, parallel efficiency decreases due to network transfer delay. In this paper, we proposed a method to reduce data transfer between computing threads by introducing an intra-thread update. The update factor is collected from each slave thread and a global image is updated as usual in the first K sub-iteration. In the rest of the sub-iterations, the global image is only updated at an interval which is controlled by a parameter L. In between that interval, the intra-thread update is carried out whereby an image update is performed in each slave thread locally. We investigated combinations of K and L parameters based on parallel implementation of RAMLA for the jPET-D4 scanner. Our evaluation used four workstations with a total of 16 slave threads. Each slave thread calculated a different set of LORs which are divided according to ring difference numbers. We assessed image quality of the proposed method with a hotspot simulation phantom. The figure of merit was the full-width-half-maximum of hotspots and the background normalized standard deviation. At an optimum K and L setting, we did not find significant change in the output images. We also applied the proposed method to a Hoffman phantom experiment and found the difference due to intra-thread update was negligible. With the intra-thread update, computation time could be reduced by about 23%.

Multiprocessor smalltalk: Implementation, performance, and analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pallas, J.I.

1990-01-01

Multiprocessor Smalltalk demonstrates the value of object-oriented programming on a multiprocessor. Its implementation and analysis shed light on three areas: concurrent programming in an object oriented language without special extensions, implementation techniques for adapting to multiprocessors, and performance factors in the resulting system. Adding parallelism to Smalltalk code is easy, because programs already use control abstractions like iterators. Smalltalk's basic control and concurrency primitives (lambda expressions, processes and semaphores) can be used to build parallel control abstractions, including parallel iterators, parallel objects, atomic objects, and futures. Language extensions for concurrency are not required. This implementation demonstrates that it is possiblemore » to build an efficient parallel object-oriented programming system and illustrates techniques for doing so. Three modification tools-serialization, replication, and reorganization-adapted the Berkeley Smalltalk interpreter to the Firefly multiprocessor. Multiprocessor Smalltalk's performance shows that the combination of multiprocessing and object-oriented programming can be effective: speedups (relative to the original serial version) exceed 2.0 for five processors on all the benchmarks; the median efficiency is 48%. Analysis shows both where performance is lost and how to improve and generalize the experimental results. Changes in the interpreter to support concurrency add at most 12% overhead; better access to per-process variables could eliminate much of that. Changes in the user code to express concurrency add as much as 70% overhead; this overhead could be reduced to 54% if blocks (lambda expressions) were reentrant. Performance is also lost when the program cannot keep all five processors busy.« less

AZTEC. Parallel Iterative method Software for Solving Linear Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hutchinson, S.; Shadid, J.; Tuminaro, R.

1995-07-01

AZTEC is an interactive library that greatly simplifies the parrallelization process when solving the linear systems of equations Ax=b where A is a user supplied n X n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. AZTEC is intended as a software tool for users who want to avoid cumbersome parallel programming details but who have large sparse linear systems which require an efficiently utilized parallel processing system. A collection of data transformation tools are provided that allow for easy creation of distributed sparse unstructured matricesmore » for parallel solutions.« less

Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging

NASA Astrophysics Data System (ADS)

Wu, Ping; Liu, Kai; Zhang, Qian; Xue, Zhenwen; Li, Yongbao; Ning, Nannan; Yang, Xin; Li, Xingde; Tian, Jie

2012-12-01

Liver cancer is one of the most common malignant tumors worldwide. In order to enable the noninvasive detection of small liver tumors in mice, we present a parallel iterative shrinkage (PIS) algorithm for dual-modality tomography. It takes advantage of microcomputed tomography and multiview bioluminescence imaging, providing anatomical structure and bioluminescence intensity information to reconstruct the size and location of tumors. By incorporating prior knowledge of signal sparsity, we associate some mathematical strategies including specific smooth convex approximation, an iterative shrinkage operator, and affine subspace with the PIS method, which guarantees the accuracy, efficiency, and reliability for three-dimensional reconstruction. Then an in vivo experiment on the bead-implanted mouse has been performed to validate the feasibility of this method. The findings indicate that a tiny lesion less than 3 mm in diameter can be localized with a position bias no more than 1 mm the computational efficiency is one to three orders of magnitude faster than the existing algorithms; this approach is robust to the different regularization parameters and the lp norms. Finally, we have applied this algorithm to another in vivo experiment on an HCCLM3 orthotopic xenograft mouse model, which suggests the PIS method holds the promise for practical applications of whole-body cancer detection.

Solution of the within-group multidimensional discrete ordinates transport equations on massively parallel architectures

NASA Astrophysics Data System (ADS)

Zerr, Robert Joseph

2011-12-01

The integral transport matrix method (ITMM) has been used as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells and between the cells and boundary surfaces. The main goals of this work were to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and performance of the developed methods for increasing number of processes. This project compares the effectiveness of the ITMM with the SI scheme parallelized with the Koch-Baker-Alcouffe (KBA) method. The primary parallel solution method involves a decomposition of the domain into smaller spatial sub-domains, each with their own transport matrices, and coupled together via interface boundary angular fluxes. Each sub-domain has its own set of ITMM operators and represents an independent transport problem. Multiple iterative parallel solution methods have investigated, including parallel block Jacobi (PBJ), parallel red/black Gauss-Seidel (PGS), and parallel GMRES (PGMRES). The fastest observed parallel solution method, PGS, was used in a weak scaling comparison with the PARTISN code. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method without acceleration/preconditioning is not competitive for any problem parameters considered. The best comparisons occur for problems that are difficult for SI DSA, namely highly scattering and optically thick. SI DSA execution time curves are generally steeper than the PGS ones. However, until further testing is performed it cannot be concluded that SI DSA does not outperform the ITMM with PGS even on several thousand or tens of thousands of processors. The PGS method does outperform SI DSA for the periodic heterogeneous layers (PHL) configuration problems. Although this demonstrates a relative strength/weakness between the two methods, the practicality of these problems is much less, further limiting instances where it would be beneficial to select ITMM over SI DSA. The results strongly indicate a need for a robust, stable, and efficient acceleration method (or preconditioner for PGMRES). The spatial multigrid (SMG) method is currently incomplete in that it does not work for all cases considered and does not effectively improve the convergence rate for all values of scattering ratio c or cell dimension h. Nevertheless, it does display the desired trend for highly scattering, optically thin problems. That is, it tends to lower the rate of growth of number of iterations with increasing number of processes, P, while not increasing the number of additional operations per iteration to the extent that the total execution time of the rapidly converging accelerated iterations exceeds that of the slower unaccelerated iterations. A predictive parallel performance model has been developed for the PBJ method. Timing tests were performed such that trend lines could be fitted to the data for the different components and used to estimate the execution times. Applied to the weak scaling results, the model notably underestimates construction time, but combined with a slight overestimation in iterative solution time, the model predicts total execution time very well for large P. It also does a decent job with the strong scaling results, closely predicting the construction time and time per iteration, especially as P increases. Although not shown to be competitive up to 1,024 processing elements with the current state of the art, the parallelized ITMM exhibits promising scaling trends. Ultimately, compared to the KBA method, the parallelized ITMM may be found to be a very attractive option for transport calculations spatially decomposed over several tens of thousands of processes. Acceleration/preconditioning of the parallelized ITMM once developed will improve the convergence rate and improve its competitiveness. (Abstract shortened by UMI.)

Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Tungkahotara, Siroj; Watson, Willie R.; Rajan, Subramaniam D.

2005-01-01

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

Krylov subspace methods on supercomputers

NASA Technical Reports Server (NTRS)

Saad, Youcef

1988-01-01

A short survey of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers is presented. Conjugate gradient methods have proven very useful on traditional scalar computers, and their popularity is likely to increase as three-dimensional models gain importance. A conservative approach to derive effective iterative techniques for supercomputers has been to find efficient parallel/vector implementations of the standard algorithms. The main source of difficulty in the incomplete factorization preconditionings is in the solution of the triangular systems at each step. A few approaches consisting of implementing efficient forward and backward triangular solutions are described in detail. Polynomial preconditioning as an alternative to standard incomplete factorization techniques is also discussed. Another efficient approach is to reorder the equations so as to improve the structure of the matrix to achieve better parallelism or vectorization. An overview of these and other ideas and their effectiveness or potential for different types of architectures is given.

Parallel heuristics for scalable community detection

DOE PAGES

Lu, Hao; Halappanavar, Mahantesh; Kalyanaraman, Ananth

2015-08-14

Community detection has become a fundamental operation in numerous graph-theoretic applications. Despite its potential for application, there is only limited support for community detection on large-scale parallel computers, largely owing to the irregular and inherently sequential nature of the underlying heuristics. In this paper, we present parallelization heuristics for fast community detection using the Louvain method as the serial template. The Louvain method is an iterative heuristic for modularity optimization. Originally developed in 2008, the method has become increasingly popular owing to its ability to detect high modularity community partitions in a fast and memory-efficient manner. However, the method ismore » also inherently sequential, thereby limiting its scalability. Here, we observe certain key properties of this method that present challenges for its parallelization, and consequently propose heuristics that are designed to break the sequential barrier. For evaluation purposes, we implemented our heuristics using OpenMP multithreading, and tested them over real world graphs derived from multiple application domains. Compared to the serial Louvain implementation, our parallel implementation is able to produce community outputs with a higher modularity for most of the inputs tested, in comparable number or fewer iterations, while providing real speedups of up to 16x using 32 threads.« less

LDRD final report on massively-parallel linear programming : the parPCx system.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parekh, Ojas; Phillips, Cynthia Ann; Boman, Erik Gunnar

2005-02-01

This report summarizes the research and development performed from October 2002 to September 2004 at Sandia National Laboratories under the Laboratory-Directed Research and Development (LDRD) project ''Massively-Parallel Linear Programming''. We developed a linear programming (LP) solver designed to use a large number of processors. LP is the optimization of a linear objective function subject to linear constraints. Companies and universities have expended huge efforts over decades to produce fast, stable serial LP solvers. Previous parallel codes run on shared-memory systems and have little or no distribution of the constraint matrix. We have seen no reports of general LP solver runsmore » on large numbers of processors. Our parallel LP code is based on an efficient serial implementation of Mehrotra's interior-point predictor-corrector algorithm (PCx). The computational core of this algorithm is the assembly and solution of a sparse linear system. We have substantially rewritten the PCx code and based it on Trilinos, the parallel linear algebra library developed at Sandia. Our interior-point method can use either direct or iterative solvers for the linear system. To achieve a good parallel data distribution of the constraint matrix, we use a (pre-release) version of a hypergraph partitioner from the Zoltan partitioning library. We describe the design and implementation of our new LP solver called parPCx and give preliminary computational results. We summarize a number of issues related to efficient parallel solution of LPs with interior-point methods including data distribution, numerical stability, and solving the core linear system using both direct and iterative methods. We describe a number of applications of LP specific to US Department of Energy mission areas and we summarize our efforts to integrate parPCx (and parallel LP solvers in general) into Sandia's massively-parallel integer programming solver PICO (Parallel Interger and Combinatorial Optimizer). We conclude with directions for long-term future algorithmic research and for near-term development that could improve the performance of parPCx.« less

Iterative load-balancing method with multigrid level relaxation for particle simulation with short-range interactions

NASA Astrophysics Data System (ADS)

Furuichi, Mikito; Nishiura, Daisuke

2017-10-01

We developed dynamic load-balancing algorithms for Particle Simulation Methods (PSM) involving short-range interactions, such as Smoothed Particle Hydrodynamics (SPH), Moving Particle Semi-implicit method (MPS), and Discrete Element method (DEM). These are needed to handle billions of particles modeled in large distributed-memory computer systems. Our method utilizes flexible orthogonal domain decomposition, allowing the sub-domain boundaries in the column to be different for each row. The imbalances in the execution time between parallel logical processes are treated as a nonlinear residual. Load-balancing is achieved by minimizing the residual within the framework of an iterative nonlinear solver, combined with a multigrid technique in the local smoother. Our iterative method is suitable for adjusting the sub-domain frequently by monitoring the performance of each computational process because it is computationally cheaper in terms of communication and memory costs than non-iterative methods. Numerical tests demonstrated the ability of our approach to handle workload imbalances arising from a non-uniform particle distribution, differences in particle types, or heterogeneous computer architecture which was difficult with previously proposed methods. We analyzed the parallel efficiency and scalability of our method using Earth simulator and K-computer supercomputer systems.

Parallel medicinal chemistry approaches to selective HDAC1/HDAC2 inhibitor (SHI-1:2) optimization.

PubMed

Kattar, Solomon D; Surdi, Laura M; Zabierek, Anna; Methot, Joey L; Middleton, Richard E; Hughes, Bethany; Szewczak, Alexander A; Dahlberg, William K; Kral, Astrid M; Ozerova, Nicole; Fleming, Judith C; Wang, Hongmei; Secrist, Paul; Harsch, Andreas; Hamill, Julie E; Cruz, Jonathan C; Kenific, Candia M; Chenard, Melissa; Miller, Thomas A; Berk, Scott C; Tempest, Paul

2009-02-15

The successful application of both solid and solution phase library synthesis, combined with tight integration into the medicinal chemistry effort, resulted in the efficient optimization of a novel structural series of selective HDAC1/HDAC2 inhibitors by the MRL-Boston Parallel Medicinal Chemistry group. An initial lead from a small parallel library was found to be potent and selective in biochemical assays. Advanced compounds were the culmination of iterative library design and possess excellent biochemical and cellular potency, as well as acceptable PK and efficacy in animal models.

The multigrid preconditioned conjugate gradient method

NASA Technical Reports Server (NTRS)

Tatebe, Osamu

1993-01-01

A multigrid preconditioned conjugate gradient method (MGCG method), which uses the multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wavelength components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an efficient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition of the multigrid preconditioner in order to satisfy requirements of a preconditioner of the PCG method. Next numerical experiments show a behavior of the MGCG method and that the MGCG method is superior to both the ICCG method and the multigrid method in point of fast convergence and high parallelism. This fast convergence is understood in terms of the eigenvalue analysis of the preconditioned matrix. From this observation of the multigrid preconditioner, it is realized that the MGCG method converges in very few iterations and the multigrid preconditioner is a desirable preconditioner of the conjugate gradient method.

Development Of A Parallel Performance Model For The THOR Neutral Particle Transport Code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yessayan, Raffi; Azmy, Yousry; Schunert, Sebastian

The THOR neutral particle transport code enables simulation of complex geometries for various problems from reactor simulations to nuclear non-proliferation. It is undergoing a thorough V&V requiring computational efficiency. This has motivated various improvements including angular parallelization, outer iteration acceleration, and development of peripheral tools. For guiding future improvements to the code’s efficiency, better characterization of its parallel performance is useful. A parallel performance model (PPM) can be used to evaluate the benefits of modifications and to identify performance bottlenecks. Using INL’s Falcon HPC, the PPM development incorporates an evaluation of network communication behavior over heterogeneous links and a functionalmore » characterization of the per-cell/angle/group runtime of each major code component. After evaluating several possible sources of variability, this resulted in a communication model and a parallel portion model. The former’s accuracy is bounded by the variability of communication on Falcon while the latter has an error on the order of 1%.« less

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

DOE PAGES

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

2015-12-01

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-upsmore » that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.« less

Gauss-Seidel Iterative Method as a Real-Time Pile-Up Solver of Scintillation Pulses

NASA Astrophysics Data System (ADS)

Novak, Roman; Vencelj, Matja¿

2009-12-01

The pile-up rejection in nuclear spectroscopy has been confronted recently by several pile-up correction schemes that compensate for distortions of the signal and subsequent energy spectra artifacts as the counting rate increases. We study here a real-time capability of the event-by-event correction method, which at the core translates to solving many sets of linear equations. Tight time limits and constrained front-end electronics resources make well-known direct solvers inappropriate. We propose a novel approach based on the Gauss-Seidel iterative method, which turns out to be a stable and cost-efficient solution to improve spectroscopic resolution in the front-end electronics. We show the method convergence properties for a class of matrices that emerge in calorimetric processing of scintillation detector signals and demonstrate the ability of the method to support the relevant resolutions. The sole iteration-based error component can be brought below the sliding window induced errors in a reasonable number of iteration steps, thus allowing real-time operation. An area-efficient hardware implementation is proposed that fully utilizes the method's inherent parallelism.

Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy.

PubMed

Zelyak, O; Fallone, B G; St-Aubin, J

2017-12-14

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.

Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy

NASA Astrophysics Data System (ADS)

Zelyak, O.; Fallone, B. G.; St-Aubin, J.

2018-01-01

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.

Corrigendum to "Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy".

PubMed

Zelyak, Oleksandr; Fallone, B Gino; St-Aubin, Joel

2018-03-12

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation. © 2018 Institute of Physics and Engineering in Medicine.

Parallel Conjugate Gradient: Effects of Ordering Strategies, Programming Paradigms, and Architectural Platforms

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Heber, Gerd; Biswas, Rupak

2000-01-01

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. A sparse matrix-vector multiply (SPMV) usually accounts for most of the floating-point operations within a CG iteration. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and SPMV using different programming paradigms and architectures. Results show that for this class of applications, ordering significantly improves overall performance, that cache reuse may be more important than reducing communication, and that it is possible to achieve message passing performance using shared memory constructs through careful data ordering and distribution. However, a multi-threaded implementation of CG on the Tera MTA does not require special ordering or partitioning to obtain high efficiency and scalability.

Non-iterative Voltage Stability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makarov, Yuri V.; Vyakaranam, Bharat; Hou, Zhangshuan

2014-09-30

This report demonstrates promising capabilities and performance characteristics of the proposed method using several power systems models. The new method will help to develop a new generation of highly efficient tools suitable for real-time parallel implementation. The ultimate benefit obtained will be early detection of system instability and prevention of system blackouts in real time.

Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations

DOE PAGES

Banerjee, Amartya S.; Lin, Lin; Hu, Wei; ...

2016-10-21

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) canmore » be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale twodimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. In conclusion, employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.« less

Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics: II.Towards Massively Parallel Computations using Smooth Particle Mesh Ewald.

PubMed

Lagardère, Louis; Lipparini, Filippo; Polack, Étienne; Stamm, Benjamin; Cancès, Éric; Schnieders, Michael; Ren, Pengyu; Maday, Yvon; Piquemal, Jean-Philip

2014-02-28

In this paper, we present a scalable and efficient implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The Smooth Particle-Mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the Direct Inversion in the Iterative Subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy-force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package which is the first implementation for a polarizable model making large scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of spme and a noticeable improvement of the memory management giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to non-optimized, sequential implementations giving new directions for polarizable molecular dynamics in periodic boundary conditions using massively parallel implementations.

Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics: II.Towards Massively Parallel Computations using Smooth Particle Mesh Ewald

PubMed Central

Lagardère, Louis; Lipparini, Filippo; Polack, Étienne; Stamm, Benjamin; Cancès, Éric; Schnieders, Michael; Ren, Pengyu; Maday, Yvon; Piquemal, Jean-Philip

2015-01-01

In this paper, we present a scalable and efficient implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The Smooth Particle-Mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the Direct Inversion in the Iterative Subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy-force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package which is the first implementation for a polarizable model making large scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of spme and a noticeable improvement of the memory management giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to non-optimized, sequential implementations giving new directions for polarizable molecular dynamics in periodic boundary conditions using massively parallel implementations. PMID:26512230

State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Read, Julie L.; Younes, Ahmad Bani; Macomber, Brent; Turner, James; Junkins, John L.

2015-06-01

The Modified Chebyshev Picard Iteration (MCPI) method has recently proven to be highly efficient for a given accuracy compared to several commonly adopted numerical integration methods, as a means to solve for perturbed orbital motion. This method utilizes Picard iteration, which generates a sequence of path approximations, and Chebyshev Polynomials, which are orthogonal and also enable both efficient and accurate function approximation. The nodes consistent with discrete Chebyshev orthogonality are generated using cosine sampling; this strategy also reduces the Runge effect and as a consequence of orthogonality, there is no matrix inversion required to find the basis function coefficients. The MCPI algorithms considered herein are parallel-structured so that they are immediately well-suited for massively parallel implementation with additional speedup. MCPI has a wide range of applications beyond ephemeris propagation, including the propagation of the State Transition Matrix (STM) for perturbed two-body motion. A solution is achieved for a spherical harmonic series representation of earth gravity (EGM2008), although the methodology is suitable for application to any gravity model. Included in this representation the normalized, Associated Legendre Functions are given and verified numerically. Modifications of the classical algorithm techniques, such as rewriting the STM equations in a second-order cascade formulation, gives rise to additional speedup. Timing results for the baseline formulation and this second-order formulation are given.

Fast iterative censoring CFAR algorithm for ship detection from SAR images

NASA Astrophysics Data System (ADS)

Gu, Dandan; Yue, Hui; Zhang, Yuan; Gao, Pengcheng

2017-11-01

Ship detection is one of the essential techniques for ship recognition from synthetic aperture radar (SAR) images. This paper presents a fast iterative detection procedure to eliminate the influence of target returns on the estimation of local sea clutter distributions for constant false alarm rate (CFAR) detectors. A fast block detector is first employed to extract potential target sub-images; and then, an iterative censoring CFAR algorithm is used to detect ship candidates from each target blocks adaptively and efficiently, where parallel detection is available, and statistical parameters of G0 distribution fitting local sea clutter well can be quickly estimated based on an integral image operator. Experimental results of TerraSAR-X images demonstrate the effectiveness of the proposed technique.

A Framework for Load Balancing of Tensor Contraction Expressions via Dynamic Task Partitioning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lai, Pai-Wei; Stock, Kevin; Rajbhandari, Samyam

In this paper, we introduce the Dynamic Load-balanced Tensor Contractions (DLTC), a domain-specific library for efficient task parallel execution of tensor contraction expressions, a class of computation encountered in quantum chemistry and physics. Our framework decomposes each contraction into smaller unit of tasks, represented by an abstraction referred to as iterators. We exploit an extra level of parallelism by having tasks across independent contractions executed concurrently through a dynamic load balancing run- time. We demonstrate the improved performance, scalability, and flexibility for the computation of tensor contraction expressions on parallel computers using examples from coupled cluster methods.

Single-step reinitialization and extending algorithms for level-set based multi-phase flow simulations

NASA Astrophysics Data System (ADS)

Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-12-01

We propose efficient single-step formulations for reinitialization and extending algorithms, which are critical components of level-set based interface-tracking methods. The level-set field is reinitialized with a single-step (non iterative) "forward tracing" algorithm. A minimum set of cells is defined that describes the interface, and reinitialization employs only data from these cells. Fluid states are extrapolated or extended across the interface by a single-step "backward tracing" algorithm. Both algorithms, which are motivated by analogy to ray-tracing, avoid multiple block-boundary data exchanges that are inevitable for iterative reinitialization and extending approaches within a parallel-computing environment. The single-step algorithms are combined with a multi-resolution conservative sharp-interface method and validated by a wide range of benchmark test cases. We demonstrate that the proposed reinitialization method achieves second-order accuracy in conserving the volume of each phase. The interface location is invariant to reapplication of the single-step reinitialization. Generally, we observe smaller absolute errors than for standard iterative reinitialization on the same grid. The computational efficiency is higher than for the standard and typical high-order iterative reinitialization methods. We observe a 2- to 6-times efficiency improvement over the standard method for serial execution. The proposed single-step extending algorithm, which is commonly employed for assigning data to ghost cells with ghost-fluid or conservative interface interaction methods, shows about 10-times efficiency improvement over the standard method while maintaining same accuracy. Despite their simplicity, the proposed algorithms offer an efficient and robust alternative to iterative reinitialization and extending methods for level-set based multi-phase simulations.

Single-agent parallel window search

NASA Technical Reports Server (NTRS)

Powley, Curt; Korf, Richard E.

1991-01-01

Parallel window search is applied to single-agent problems by having different processes simultaneously perform iterations of Iterative-Deepening-A(asterisk) (IDA-asterisk) on the same problem but with different cost thresholds. This approach is limited by the time to perform the goal iteration. To overcome this disadvantage, the authors consider node ordering. They discuss how global node ordering by minimum h among nodes with equal f = g + h values can reduce the time complexity of serial IDA-asterisk by reducing the time to perform the iterations prior to the goal iteration. Finally, the two ideas of parallel window search and node ordering are combined to eliminate the weaknesses of each approach while retaining the strengths. The resulting approach, called simply parallel window search, can be used to find a near-optimal solution quickly, improve the solution until it is optimal, and then finally guarantee optimality, depending on the amount of time available.

SPIRiT: Iterative Self-consistent Parallel Imaging Reconstruction from Arbitrary k-Space

PubMed Central

Lustig, Michael; Pauly, John M.

2010-01-01

A new approach to autocalibrating, coil-by-coil parallel imaging reconstruction is presented. It is a generalized reconstruction framework based on self consistency. The reconstruction problem is formulated as an optimization that yields the most consistent solution with the calibration and acquisition data. The approach is general and can accurately reconstruct images from arbitrary k-space sampling patterns. The formulation can flexibly incorporate additional image priors such as off-resonance correction and regularization terms that appear in compressed sensing. Several iterative strategies to solve the posed reconstruction problem in both image and k-space domain are presented. These are based on a projection over convex sets (POCS) and a conjugate gradient (CG) algorithms. Phantom and in-vivo studies demonstrate efficient reconstructions from undersampled Cartesian and spiral trajectories. Reconstructions that include off-resonance correction and nonlinear ℓ1-wavelet regularization are also demonstrated. PMID:20665790

Efficient relaxed-Jacobi smoothers for multigrid on parallel computers

NASA Astrophysics Data System (ADS)

Yang, Xiang; Mittal, Rajat

2017-03-01

In this Technical Note, we present a family of Jacobi-based multigrid smoothers suitable for the solution of discretized elliptic equations. These smoothers are based on the idea of scheduled-relaxation Jacobi proposed recently by Yang & Mittal (2014) [18] and employ two or three successive relaxed Jacobi iterations with relaxation factors derived so as to maximize the smoothing property of these iterations. The performance of these new smoothers measured in terms of convergence acceleration and computational workload, is assessed for multi-domain implementations typical of parallelized solvers, and compared to the lexicographic point Gauss-Seidel smoother. The tests include the geometric multigrid method on structured grids as well as the algebraic grid method on unstructured grids. The tests demonstrate that unlike Gauss-Seidel, the convergence of these Jacobi-based smoothers is unaffected by domain decomposition, and furthermore, they outperform the lexicographic Gauss-Seidel by factors that increase with domain partition count.

Aerodynamic optimization by simultaneously updating flow variables and design parameters

NASA Technical Reports Server (NTRS)

Rizk, M. H.

1990-01-01

The application of conventional optimization schemes to aerodynamic design problems leads to inner-outer iterative procedures that are very costly. An alternative approach is presented based on the idea of updating the flow variable iterative solutions and the design parameter iterative solutions simultaneously. Two schemes based on this idea are applied to problems of correcting wind tunnel wall interference and optimizing advanced propeller designs. The first of these schemes is applicable to a limited class of two-design-parameter problems with an equality constraint. It requires the computation of a single flow solution. The second scheme is suitable for application to general aerodynamic problems. It requires the computation of several flow solutions in parallel. In both schemes, the design parameters are updated as the iterative flow solutions evolve. Computations are performed to test the schemes' efficiency, accuracy, and sensitivity to variations in the computational parameters.

Unified Lambert Tool for Massively Parallel Applications in Space Situational Awareness

NASA Astrophysics Data System (ADS)

Woollands, Robyn M.; Read, Julie; Hernandez, Kevin; Probe, Austin; Junkins, John L.

2018-03-01

This paper introduces a parallel-compiled tool that combines several of our recently developed methods for solving the perturbed Lambert problem using modified Chebyshev-Picard iteration. This tool (unified Lambert tool) consists of four individual algorithms, each of which is unique and better suited for solving a particular type of orbit transfer. The first is a Keplerian Lambert solver, which is used to provide a good initial guess (warm start) for solving the perturbed problem. It is also used to determine the appropriate algorithm to call for solving the perturbed problem. The arc length or true anomaly angle spanned by the transfer trajectory is the parameter that governs the automated selection of the appropriate perturbed algorithm, and is based on the respective algorithm convergence characteristics. The second algorithm solves the perturbed Lambert problem using the modified Chebyshev-Picard iteration two-point boundary value solver. This algorithm does not require a Newton-like shooting method and is the most efficient of the perturbed solvers presented herein, however the domain of convergence is limited to about a third of an orbit and is dependent on eccentricity. The third algorithm extends the domain of convergence of the modified Chebyshev-Picard iteration two-point boundary value solver to about 90% of an orbit, through regularization with the Kustaanheimo-Stiefel transformation. This is the second most efficient of the perturbed set of algorithms. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver for solving multiple revolution perturbed transfers. This method does require "shooting" but differs from Newton-like shooting methods in that it does not require propagation of a state transition matrix. The unified Lambert tool makes use of the General Mission Analysis Tool and we use it to compute thousands of perturbed Lambert trajectories in parallel on the Space Situational Awareness computer cluster at the LASR Lab, Texas A&M University. We demonstrate the power of our tool by solving a highly parallel example problem, that is the generation of extremal field maps for optimal spacecraft rendezvous (and eventual orbit debris removal). In addition we demonstrate the need for including perturbative effects in simulations for satellite tracking or data association. The unified Lambert tool is ideal for but not limited to space situational awareness applications.

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

NASA Astrophysics Data System (ADS)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-07-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

Solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators.

PubMed

Zhao, Jing; Zong, Haili

2018-01-01

In this paper, we propose parallel and cyclic iterative algorithms for solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators. We also combine the process of cyclic and parallel iterative methods and propose two mixed iterative algorithms. Our several algorithms do not need any prior information about the operator norms. Under mild assumptions, we prove weak convergence of the proposed iterative sequences in Hilbert spaces. As applications, we obtain several iterative algorithms to solve the multiple-set split equality problem.

Parallelized implicit propagators for the finite-difference Schrödinger equation

NASA Astrophysics Data System (ADS)

Parker, Jonathan; Taylor, K. T.

1995-08-01

We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.

Improving the iterative Linear Interaction Energy approach using automated recognition of configurational transitions.

PubMed

Vosmeer, C Ruben; Kooi, Derk P; Capoferri, Luigi; Terpstra, Margreet M; Vermeulen, Nico P E; Geerke, Daan P

2016-01-01

Recently an iterative method was proposed to enhance the accuracy and efficiency of ligand-protein binding affinity prediction through linear interaction energy (LIE) theory. For ligand binding to flexible Cytochrome P450s (CYPs), this method was shown to decrease the root-mean-square error and standard deviation of error prediction by combining interaction energies of simulations starting from different conformations. Thereby, different parts of protein-ligand conformational space are sampled in parallel simulations. The iterative LIE framework relies on the assumption that separate simulations explore different local parts of phase space, and do not show transitions to other parts of configurational space that are already covered in parallel simulations. In this work, a method is proposed to (automatically) detect such transitions during the simulations that are performed to construct LIE models and to predict binding affinities. Using noise-canceling techniques and splines to fit time series of the raw data for the interaction energies, transitions during simulation between different parts of phase space are identified. Boolean selection criteria are then applied to determine which parts of the interaction energy trajectories are to be used as input for the LIE calculations. Here we show that this filtering approach benefits the predictive quality of our previous CYP 2D6-aryloxypropanolamine LIE model. In addition, an analysis is performed of the gain in computational efficiency that can be obtained from monitoring simulations using the proposed filtering method and by prematurely terminating simulations accordingly.

A parallel computing engine for a class of time critical processes.

PubMed

Nabhan, T M; Zomaya, A Y

1997-01-01

This paper focuses on the efficient parallel implementation of systems of numerically intensive nature over loosely coupled multiprocessor architectures. These analytical models are of significant importance to many real-time systems that have to meet severe time constants. A parallel computing engine (PCE) has been developed in this work for the efficient simplification and the near optimal scheduling of numerical models over the different cooperating processors of the parallel computer. First, the analytical system is efficiently coded in its general form. The model is then simplified by using any available information (e.g., constant parameters). A task graph representing the interconnections among the different components (or equations) is generated. The graph can then be compressed to control the computation/communication requirements. The task scheduler employs a graph-based iterative scheme, based on the simulated annealing algorithm, to map the vertices of the task graph onto a Multiple-Instruction-stream Multiple-Data-stream (MIMD) type of architecture. The algorithm uses a nonanalytical cost function that properly considers the computation capability of the processors, the network topology, the communication time, and congestion possibilities. Moreover, the proposed technique is simple, flexible, and computationally viable. The efficiency of the algorithm is demonstrated by two case studies with good results.

Extending substructure based iterative solvers to multiple load and repeated analyses

NASA Technical Reports Server (NTRS)

Farhat, Charbel

1993-01-01

Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.

Scalable splitting algorithms for big-data interferometric imaging in the SKA era

NASA Astrophysics Data System (ADS)

Onose, Alexandru; Carrillo, Rafael E.; Repetti, Audrey; McEwen, Jason D.; Thiran, Jean-Philippe; Pesquet, Jean-Christophe; Wiaux, Yves

2016-11-01

In the context of next-generation radio telescopes, like the Square Kilometre Array (SKA), the efficient processing of large-scale data sets is extremely important. Convex optimization tasks under the compressive sensing framework have recently emerged and provide both enhanced image reconstruction quality and scalability to increasingly larger data sets. We focus herein mainly on scalability and propose two new convex optimization algorithmic structures able to solve the convex optimization tasks arising in radio-interferometric imaging. They rely on proximal splitting and forward-backward iterations and can be seen, by analogy, with the CLEAN major-minor cycle, as running sophisticated CLEAN-like iterations in parallel in multiple data, prior, and image spaces. Both methods support any convex regularization function, in particular, the well-studied ℓ1 priors promoting image sparsity in an adequate domain. Tailored for big-data, they employ parallel and distributed computations to achieve scalability, in terms of memory and computational requirements. One of them also exploits randomization, over data blocks at each iteration, offering further flexibility. We present simulation results showing the feasibility of the proposed methods as well as their advantages compared to state-of-the-art algorithmic solvers. Our MATLAB code is available online on GitHub.

Aztec user`s guide. Version 1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S.

1995-10-01

Aztec is an iterative library that greatly simplifies the parallelization process when solving the linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. Aztec is intended as a software tool for users who want to avoid cumbersome parallel programming details but who have large sparse linear systems which require an efficiently utilized parallel processing system. A collection of data transformation tools are provided that allow for easy creation of distributed sparsemore » unstructured matrices for parallel solution. Once the distributed matrix is created, computation can be performed on any of the parallel machines running Aztec: nCUBE 2, IBM SP2 and Intel Paragon, MPI platforms as well as standard serial and vector platforms. Aztec includes a number of Krylov iterative methods such as conjugate gradient (CG), generalized minimum residual (GMRES) and stabilized biconjugate gradient (BICGSTAB) to solve systems of equations. These Krylov methods are used in conjunction with various preconditioners such as polynomial or domain decomposition methods using LU or incomplete LU factorizations within subdomains. Although the matrix A can be general, the package has been designed for matrices arising from the approximation of partial differential equations (PDEs). In particular, the Aztec package is oriented toward systems arising from PDE applications.« less

Iterative algorithms for large sparse linear systems on parallel computers

NASA Technical Reports Server (NTRS)

Adams, L. M.

1982-01-01

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

LSRN: A PARALLEL ITERATIVE SOLVER FOR STRONGLY OVER- OR UNDERDETERMINED SYSTEMS*

PubMed Central

Meng, Xiangrui; Saunders, Michael A.; Mahoney, Michael W.

2014-01-01

We describe a parallel iterative least squares solver named LSRN that is based on random normal projection. LSRN computes the min-length solution to minx∈ℝn ‖Ax − b‖2, where A ∈ ℝm × n with m ≫ n or m ≪ n, and where A may be rank-deficient. Tikhonov regularization may also be included. Since A is involved only in matrix-matrix and matrix-vector multiplications, it can be a dense or sparse matrix or a linear operator, and LSRN automatically speeds up when A is sparse or a fast linear operator. The preconditioning phase consists of a random normal projection, which is embarrassingly parallel, and a singular value decomposition of size ⌈γ min(m, n)⌉ × min(m, n), where γ is moderately larger than 1, e.g., γ = 2. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predictable when we apply LSQR or the Chebyshev semi-iterative method. As we demonstrate, the Chebyshev method is particularly efficient for solving large problems on clusters with high communication cost. Numerical results show that on a shared-memory machine, LSRN is very competitive with LAPACK’s DGELSD and a fast randomized least squares solver called Blendenpik on large dense problems, and it outperforms the least squares solver from SuiteSparseQR on sparse problems without sparsity patterns that can be exploited to reduce fill-in. Further experiments show that LSRN scales well on an Amazon Elastic Compute Cloud cluster. PMID:25419094

An Efficient Algorithm for Perturbed Orbit Integration Combining Analytical Continuation and Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Elgohary, T.; Kim, D.; Turner, J.; Junkins, J.

2014-09-01

Several methods exist for integrating the motion in high order gravity fields. Some recent methods use an approximate starting orbit, and an efficient method is needed for generating warm starts that account for specific low order gravity approximations. By introducing two scalar Lagrange-like invariants and employing Leibniz product rule, the perturbed motion is integrated by a novel recursive formulation. The Lagrange-like invariants allow exact arbitrary order time derivatives. Restricting attention to the perturbations due to the zonal harmonics J2 through J6, we illustrate an idea. The recursively generated vector-valued time derivatives for the trajectory are used to develop a continuation series-based solution for propagating position and velocity. Numerical comparisons indicate performance improvements of ~ 70X over existing explicit Runge-Kutta methods while maintaining mm accuracy for the orbit predictions. The Modified Chebyshev Picard Iteration (MCPI) is an iterative path approximation method to solve nonlinear ordinary differential equations. The MCPI utilizes Picard iteration with orthogonal Chebyshev polynomial basis functions to recursively update the states. The key advantages of the MCPI are as follows: 1) Large segments of a trajectory can be approximated by evaluating the forcing function at multiple nodes along the current approximation during each iteration. 2) It can readily handle general gravity perturbations as well as non-conservative forces. 3) Parallel applications are possible. The Picard sequence converges to the solution over large time intervals when the forces are continuous and differentiable. According to the accuracy of the starting solutions, however, the MCPI may require significant number of iterations and function evaluations compared to other integrators. In this work, we provide an efficient methodology to establish good starting solutions from the continuation series method; this warm start improves the performance of the MCPI significantly and will likely be useful for other applications where efficiently computed approximate orbit solutions are needed.

Fully Parallel MHD Stability Analysis Tool

NASA Astrophysics Data System (ADS)

Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang

2014-10-01

Progress on full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. It is a powerful tool for studying MHD and MHD-kinetic instabilities and it is widely used by fusion community. Parallel version of MARS is intended for simulations on local parallel clusters. It will be an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, already implemented in MARS. Parallelization of the code includes parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the present MARS algorithm using parallel libraries and procedures. Initial results of the code parallelization will be reported. Work is supported by the U.S. DOE SBIR program.

Study of noise propagation and the effects of insufficient numbers of projection angles and detector samplings for iterative reconstruction using planar-integral data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, B.; Zeng, G. L.

2006-09-15

A rotating slat collimator can be used to acquire planar-integral data. It achieves higher geometric efficiency than a parallel-hole collimator by accepting more photons, but the planar-integral data contain less tomographic information that may result in larger noise amplification in the reconstruction. Lodge evaluated the rotating slat system and the parallel-hole system based on noise behavior for an FBP reconstruction. Here, we evaluate the noise propagation properties of the two collimation systems for iterative reconstruction. We extend Huesman's noise propagation analysis of the line-integral system to the planar-integral case, and show that approximately 2.0(D/dp) SPECT angles, 2.5(D/dp) self-spinning angles atmore » each detector position, and a 0.5dp detector sampling interval are required in order for the planar-integral data to be efficiently utilized. Here, D is the diameter of the object and dp is the linear dimension of the voxels that subdivide the object. The noise propagation behaviors of the two systems are then compared based on a least-square reconstruction using the ratio of the SNR in the image reconstructed using a planar-integral system to that reconstructed using a line-integral system. The ratio is found to be proportional to {radical}(F/D), where F is a geometric efficiency factor. This result has been verified by computer simulations. It confirms that for an iterative reconstruction, the noise tradeoff of the two systems is not only dependent on the increase of the geometric efficiency afforded by the planar projection method, but also dependent on the size of the object. The planar-integral system works better for small objects, while the line-integral system performs better for large ones. This result is consistent with Lodge's results based on the FBP method.« less

Segmentation of remotely sensed data using parallel region growing

NASA Technical Reports Server (NTRS)

Tilton, J. C.; Cox, S. C.

1983-01-01

The improved spatial resolution of the new earth resources satellites will increase the need for effective utilization of spatial information in machine processing of remotely sensed data. One promising technique is scene segmentation by region growing. Region growing can use spatial information in two ways: only spatially adjacent regions merge together, and merging criteria can be based on region-wide spatial features. A simple region growing approach is described in which the similarity criterion is based on region mean and variance (a simple spatial feature). An effective way to implement region growing for remote sensing is as an iterative parallel process on a large parallel processor. A straightforward parallel pixel-based implementation of the algorithm is explored and its efficiency is compared with sequential pixel-based, sequential region-based, and parallel region-based implementations. Experimental results from on aircraft scanner data set are presented, as is a discussioon of proposed improvements to the segmentation algorithm.

A parallel algorithm for the two-dimensional time fractional diffusion equation with implicit difference method.

PubMed

Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen; Liu, Jie

2014-01-01

It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M(x)M(y)N(2)). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.

A Bootstrap Metropolis-Hastings Algorithm for Bayesian Analysis of Big Data.

PubMed

Liang, Faming; Kim, Jinsu; Song, Qifan

2016-01-01

Markov chain Monte Carlo (MCMC) methods have proven to be a very powerful tool for analyzing data of complex structures. However, their computer-intensive nature, which typically require a large number of iterations and a complete scan of the full dataset for each iteration, precludes their use for big data analysis. In this paper, we propose the so-called bootstrap Metropolis-Hastings (BMH) algorithm, which provides a general framework for how to tame powerful MCMC methods to be used for big data analysis; that is to replace the full data log-likelihood by a Monte Carlo average of the log-likelihoods that are calculated in parallel from multiple bootstrap samples. The BMH algorithm possesses an embarrassingly parallel structure and avoids repeated scans of the full dataset in iterations, and is thus feasible for big data problems. Compared to the popular divide-and-combine method, BMH can be generally more efficient as it can asymptotically integrate the whole data information into a single simulation run. The BMH algorithm is very flexible. Like the Metropolis-Hastings algorithm, it can serve as a basic building block for developing advanced MCMC algorithms that are feasible for big data problems. This is illustrated in the paper by the tempering BMH algorithm, which can be viewed as a combination of parallel tempering and the BMH algorithm. BMH can also be used for model selection and optimization by combining with reversible jump MCMC and simulated annealing, respectively.

A Bootstrap Metropolis–Hastings Algorithm for Bayesian Analysis of Big Data

PubMed Central

Kim, Jinsu; Song, Qifan

2016-01-01

Markov chain Monte Carlo (MCMC) methods have proven to be a very powerful tool for analyzing data of complex structures. However, their computer-intensive nature, which typically require a large number of iterations and a complete scan of the full dataset for each iteration, precludes their use for big data analysis. In this paper, we propose the so-called bootstrap Metropolis-Hastings (BMH) algorithm, which provides a general framework for how to tame powerful MCMC methods to be used for big data analysis; that is to replace the full data log-likelihood by a Monte Carlo average of the log-likelihoods that are calculated in parallel from multiple bootstrap samples. The BMH algorithm possesses an embarrassingly parallel structure and avoids repeated scans of the full dataset in iterations, and is thus feasible for big data problems. Compared to the popular divide-and-combine method, BMH can be generally more efficient as it can asymptotically integrate the whole data information into a single simulation run. The BMH algorithm is very flexible. Like the Metropolis-Hastings algorithm, it can serve as a basic building block for developing advanced MCMC algorithms that are feasible for big data problems. This is illustrated in the paper by the tempering BMH algorithm, which can be viewed as a combination of parallel tempering and the BMH algorithm. BMH can also be used for model selection and optimization by combining with reversible jump MCMC and simulated annealing, respectively. PMID:29033469

Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Xujun; Li, Jiyuan; Jiang, Xikai

An efficient parallel Stokes’s solver is developed towards the complete inclusion of hydrodynamic interactions of Brownian particles in any geometry. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green’s function formalism. We present a scalable parallel computational approach, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the General geometry Ewald-like method. Our approach employs a highly-efficient iterative finite element Stokes’ solver for the accurate treatment of long-range hydrodynamic interactions within arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallelmore » Stokes’ solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem result in an O(N) parallel algorithm. We also illustrate the new algorithm in the context of the dynamics of confined polymer solutions in equilibrium and non-equilibrium conditions. Our method is extended to treat suspended finite size particles of arbitrary shape in any geometry using an Immersed Boundary approach.« less

Parallel O(N) Stokes’ solver towards scalable Brownian dynamics of hydrodynamically interacting objects in general geometries

DOE PAGES

Zhao, Xujun; Li, Jiyuan; Jiang, Xikai; ...

2017-06-29

An efficient parallel Stokes’s solver is developed towards the complete inclusion of hydrodynamic interactions of Brownian particles in any geometry. A Langevin description of the particle dynamics is adopted, where the long-range interactions are included using a Green’s function formalism. We present a scalable parallel computational approach, where the general geometry Stokeslet is calculated following a matrix-free algorithm using the General geometry Ewald-like method. Our approach employs a highly-efficient iterative finite element Stokes’ solver for the accurate treatment of long-range hydrodynamic interactions within arbitrary confined geometries. A combination of mid-point time integration of the Brownian stochastic differential equation, the parallelmore » Stokes’ solver, and a Chebyshev polynomial approximation for the fluctuation-dissipation theorem result in an O(N) parallel algorithm. We also illustrate the new algorithm in the context of the dynamics of confined polymer solutions in equilibrium and non-equilibrium conditions. Our method is extended to treat suspended finite size particles of arbitrary shape in any geometry using an Immersed Boundary approach.« less

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Crivelli, Luis; Roux, Francois-Xavier

1992-01-01

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallelize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet -- and perhaps will never -- be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

HPC-NMF: A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kannan, Ramakrishnan; Sukumar, Sreenivas R.; Ballard, Grey M.

NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient distributed algorithms to solve the problem for big data sets. We propose a high-performance distributed-memory parallel algorithm that computes the factorization by iteratively solving alternating non-negative least squares (NLS) subproblems formore » $$\\WW$$ and $$\\HH$$. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). As opposed to previous implementation, our algorithm is also flexible: It performs well for both dense and sparse matrices, and allows the user to choose any one of the multiple algorithms for solving the updates to low rank factors $$\\WW$$ and $$\\HH$$ within the alternating iterations.« less

Real-Time Compressive Sensing MRI Reconstruction Using GPU Computing and Split Bregman Methods

PubMed Central

Smith, David S.; Gore, John C.; Yankeelov, Thomas E.; Welch, E. Brian

2012-01-01

Compressive sensing (CS) has been shown to enable dramatic acceleration of MRI acquisition in some applications. Being an iterative reconstruction technique, CS MRI reconstructions can be more time-consuming than traditional inverse Fourier reconstruction. We have accelerated our CS MRI reconstruction by factors of up to 27 by using a split Bregman solver combined with a graphics processing unit (GPU) computing platform. The increases in speed we find are similar to those we measure for matrix multiplication on this platform, suggesting that the split Bregman methods parallelize efficiently. We demonstrate that the combination of the rapid convergence of the split Bregman algorithm and the massively parallel strategy of GPU computing can enable real-time CS reconstruction of even acquisition data matrices of dimension 40962 or more, depending on available GPU VRAM. Reconstruction of two-dimensional data matrices of dimension 10242 and smaller took ~0.3 s or less, showing that this platform also provides very fast iterative reconstruction for small-to-moderate size images. PMID:22481908

Real-Time Compressive Sensing MRI Reconstruction Using GPU Computing and Split Bregman Methods.

PubMed

Smith, David S; Gore, John C; Yankeelov, Thomas E; Welch, E Brian

2012-01-01

Compressive sensing (CS) has been shown to enable dramatic acceleration of MRI acquisition in some applications. Being an iterative reconstruction technique, CS MRI reconstructions can be more time-consuming than traditional inverse Fourier reconstruction. We have accelerated our CS MRI reconstruction by factors of up to 27 by using a split Bregman solver combined with a graphics processing unit (GPU) computing platform. The increases in speed we find are similar to those we measure for matrix multiplication on this platform, suggesting that the split Bregman methods parallelize efficiently. We demonstrate that the combination of the rapid convergence of the split Bregman algorithm and the massively parallel strategy of GPU computing can enable real-time CS reconstruction of even acquisition data matrices of dimension 4096(2) or more, depending on available GPU VRAM. Reconstruction of two-dimensional data matrices of dimension 1024(2) and smaller took ~0.3 s or less, showing that this platform also provides very fast iterative reconstruction for small-to-moderate size images.

Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P.

1996-01-01

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

Scaling Optimization of the SIESTA MHD Code

NASA Astrophysics Data System (ADS)

Seal, Sudip; Hirshman, Steven; Perumalla, Kalyan

2013-10-01

SIESTA is a parallel three-dimensional plasma equilibrium code capable of resolving magnetic islands at high spatial resolutions for toroidal plasmas. Originally designed to exploit small-scale parallelism, SIESTA has now been scaled to execute efficiently over several thousands of processors P. This scaling improvement was accomplished with minimal intrusion to the execution flow of the original version. First, the efficiency of the iterative solutions was improved by integrating the parallel tridiagonal block solver code BCYCLIC. Krylov-space generation in GMRES was then accelerated using a customized parallel matrix-vector multiplication algorithm. Novel parallel Hessian generation algorithms were integrated and memory access latencies were dramatically reduced through loop nest optimizations and data layout rearrangement. These optimizations sped up equilibria calculations by factors of 30-50. It is possible to compute solutions with granularity N/P near unity on extremely fine radial meshes (N > 1024 points). Grid separation in SIESTA, which manifests itself primarily in the resonant components of the pressure far from rational surfaces, is strongly suppressed by finer meshes. Large problem sizes of up to 300 K simultaneous non-linear coupled equations have been solved on the NERSC supercomputers. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

DGDFT: A massively parallel method for large scale density functional theory calculations.

PubMed

Hu, Wei; Lin, Lin; Yang, Chao

2015-09-28

We describe a massively parallel implementation of the recently developed discontinuous Galerkin density functional theory (DGDFT) method, for efficient large-scale Kohn-Sham DFT based electronic structure calculations. The DGDFT method uses adaptive local basis (ALB) functions generated on-the-fly during the self-consistent field iteration to represent the solution to the Kohn-Sham equations. The use of the ALB set provides a systematic way to improve the accuracy of the approximation. By using the pole expansion and selected inversion technique to compute electron density, energy, and atomic forces, we can make the computational complexity of DGDFT scale at most quadratically with respect to the number of electrons for both insulating and metallic systems. We show that for the two-dimensional (2D) phosphorene systems studied here, using 37 basis functions per atom allows us to reach an accuracy level of 1.3 × 10(-4) Hartree/atom in terms of the error of energy and 6.2 × 10(-4) Hartree/bohr in terms of the error of atomic force, respectively. DGDFT can achieve 80% parallel efficiency on 128,000 high performance computing cores when it is used to study the electronic structure of 2D phosphorene systems with 3500-14 000 atoms. This high parallel efficiency results from a two-level parallelization scheme that we will describe in detail.

A fast iterative scheme for the linearized Boltzmann equation

NASA Astrophysics Data System (ADS)

Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

2017-06-01

Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference between these results and those using the hard-sphere potential is discussed.

Non-Cartesian Parallel Imaging Reconstruction

PubMed Central

Wright, Katherine L.; Hamilton, Jesse I.; Griswold, Mark A.; Gulani, Vikas; Seiberlich, Nicole

2014-01-01

Non-Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non-Cartesian trajectories can enable more efficient coverage of k-space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be employed to reconstruct images from undersampled Cartesian data, non-Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the non-homogeneous sensitivities of multi-coil phased arrays. This review will begin with an overview of non-Cartesian k-space trajectories and their sampling properties, followed by an in-depth discussion of several selected non-Cartesian parallel imaging algorithms. Three representative non-Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non-Cartesian GRAPPA, and Iterative Self-Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non-Cartesian parallel imaging will be covered. PMID:24408499

Solutions of large-scale electromagnetics problems involving dielectric objects with the parallel multilevel fast multipole algorithm.

PubMed

Ergül, Özgür

2011-11-01

Fast and accurate solutions of large-scale electromagnetics problems involving homogeneous dielectric objects are considered. Problems are formulated with the electric and magnetic current combined-field integral equation and discretized with the Rao-Wilton-Glisson functions. Solutions are performed iteratively by using the multilevel fast multipole algorithm (MLFMA). For the solution of large-scale problems discretized with millions of unknowns, MLFMA is parallelized on distributed-memory architectures using a rigorous technique, namely, the hierarchical partitioning strategy. Efficiency and accuracy of the developed implementation are demonstrated on very large problems involving as many as 100 million unknowns.

Linear scaling computation of the Fock matrix. VI. Data parallel computation of the exchange-correlation matrix

NASA Astrophysics Data System (ADS)

Gan, Chee Kwan; Challacombe, Matt

2003-05-01

Recently, early onset linear scaling computation of the exchange-correlation matrix has been achieved using hierarchical cubature [J. Chem. Phys. 113, 10037 (2000)]. Hierarchical cubature differs from other methods in that the integration grid is adaptive and purely Cartesian, which allows for a straightforward domain decomposition in parallel computations; the volume enclosing the entire grid may be simply divided into a number of nonoverlapping boxes. In our data parallel approach, each box requires only a fraction of the total density to perform the necessary numerical integrations due to the finite extent of Gaussian-orbital basis sets. This inherent data locality may be exploited to reduce communications between processors as well as to avoid memory and copy overheads associated with data replication. Although the hierarchical cubature grid is Cartesian, naive boxing leads to irregular work loads due to strong spatial variations of the grid and the electron density. In this paper we describe equal time partitioning, which employs time measurement of the smallest sub-volumes (corresponding to the primitive cubature rule) to load balance grid-work for the next self-consistent-field iteration. After start-up from a heuristic center of mass partitioning, equal time partitioning exploits smooth variation of the density and grid between iterations to achieve load balance. With the 3-21G basis set and a medium quality grid, equal time partitioning applied to taxol (62 heavy atoms) attained a speedup of 61 out of 64 processors, while for a 110 molecule water cluster at standard density it achieved a speedup of 113 out of 128. The efficiency of equal time partitioning applied to hierarchical cubature improves as the grid work per processor increases. With a fine grid and the 6-311G(df,p) basis set, calculations on the 26 atom molecule α-pinene achieved a parallel efficiency better than 99% with 64 processors. For more coarse grained calculations, superlinear speedups are found to result from reduced computational complexity associated with data parallelism.

Capabilities of Fully Parallelized MHD Stability Code MARS

NASA Astrophysics Data System (ADS)

Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang

2016-10-01

Results of full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. Parallel version of MARS, named PMARS, has been recently developed at FAR-TECH. Parallelized MARS is an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, implemented in MARS. Parallelization of the code included parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse vector iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the MARS algorithm using parallel libraries and procedures. Parallelized MARS is capable of calculating eigenmodes with significantly increased spatial resolution: up to 5,000 adapted radial grid points with up to 500 poloidal harmonics. Such resolution is sufficient for simulation of kink, tearing and peeling-ballooning instabilities with physically relevant parameters. Work is supported by the U.S. DOE SBIR program.

Fully Parallel MHD Stability Analysis Tool

NASA Astrophysics Data System (ADS)

Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang

2015-11-01

Progress on full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. It is a powerful tool for studying MHD and MHD-kinetic instabilities and it is widely used by fusion community. Parallel version of MARS is intended for simulations on local parallel clusters. It will be an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, already implemented in MARS. Parallelization of the code includes parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the present MARS algorithm using parallel libraries and procedures. Results of MARS parallelization and of the development of a new fix boundary equilibrium code adapted for MARS input will be reported. Work is supported by the U.S. DOE SBIR program.

Parallelization of the preconditioned IDR solver for modern multicore computer systems

NASA Astrophysics Data System (ADS)

Bessonov, O. A.; Fedoseyev, A. I.

2012-10-01

This paper present the analysis, parallelization and optimization approach for the large sparse matrix solver CNSPACK for modern multicore microprocessors. CNSPACK is an advanced solver successfully used for coupled solution of stiff problems arising in multiphysics applications such as CFD, semiconductor transport, kinetic and quantum problems. It employs iterative IDR algorithm with ILU preconditioning (user chosen ILU preconditioning order). CNSPACK has been successfully used during last decade for solving problems in several application areas, including fluid dynamics and semiconductor device simulation. However, there was a dramatic change in processor architectures and computer system organization in recent years. Due to this, performance criteria and methods have been revisited, together with involving the parallelization of the solver and preconditioner using Open MP environment. Results of the successful implementation for efficient parallelization are presented for the most advances computer system (Intel Core i7-9xx or two-processor Xeon 55xx/56xx).

AZTEC: A parallel iterative package for the solving linear systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S.

1996-12-31

We describe a parallel linear system package, AZTEC. The package incorporates a number of parallel iterative methods (e.g. GMRES, biCGSTAB, CGS, TFQMR) and preconditioners (e.g. Jacobi, Gauss-Seidel, polynomial, domain decomposition with LU or ILU within subdomains). Additionally, AZTEC allows for the reuse of previous preconditioning factorizations within Newton schemes for nonlinear methods. Currently, a number of different users are using this package to solve a variety of PDE applications.

Efficient iteration in data-parallel programs with irregular and dynamically distributed data structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Littlefield, R.J.

1990-02-01

To implement an efficient data-parallel program on a non-shared memory MIMD multicomputer, data and computations must be properly partitioned to achieve good load balance and locality of reference. Programs with irregular data reference patterns often require irregular partitions. Although good partitions may be easy to determine, they can be difficult or impossible to implement in programming languages that provide only regular data distributions, such as blocked or cyclic arrays. We are developing Onyx, a programming system that provides a shared memory model of distributed data structures and extends the concept of data distribution to include irregular and dynamic distributions. Thismore » provides a powerful means to specify irregular partitions. Perhaps surprisingly, programs using it can also execute efficiently. In this paper, we describe and evaluate the Onyx implementation of a model problem that repeatedly executes an irregular but fixed data reference pattern. On an NCUBE hypercube, the speed of the Onyx implementation is comparable to that of carefully handwritten message-passing code.« less

Parallel computing techniques for rotorcraft aerodynamics

NASA Astrophysics Data System (ADS)

Ekici, Kivanc

The modification of unsteady three-dimensional Navier-Stokes codes for application on massively parallel and distributed computing environments is investigated. The Euler/Navier-Stokes code TURNS (Transonic Unsteady Rotor Navier-Stokes) was chosen as a test bed because of its wide use by universities and industry. For the efficient implementation of TURNS on parallel computing systems, two algorithmic changes are developed. First, main modifications to the implicit operator, Lower-Upper Symmetric Gauss Seidel (LU-SGS) originally used in TURNS, is performed. Second, application of an inexact Newton method, coupled with a Krylov subspace iterative method (Newton-Krylov method) is carried out. Both techniques have been tried previously for the Euler equations mode of the code. In this work, we have extended the methods to the Navier-Stokes mode. Several new implicit operators were tried because of convergence problems of traditional operators with the high cell aspect ratio (CAR) grids needed for viscous calculations on structured grids. Promising results for both Euler and Navier-Stokes cases are presented for these operators. For the efficient implementation of Newton-Krylov methods to the Navier-Stokes mode of TURNS, efficient preconditioners must be used. The parallel implicit operators used in the previous step are employed as preconditioners and the results are compared. The Message Passing Interface (MPI) protocol has been used because of its portability to various parallel architectures. It should be noted that the proposed methodology is general and can be applied to several other CFD codes (e.g. OVERFLOW).

Scalable Nonlinear Solvers for Fully Implicit Coupled Nuclear Fuel Modeling. Final Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Xiao-Chuan; Keyes, David; Yang, Chao

2014-09-29

The focus of the project is on the development and customization of some highly scalable domain decomposition based preconditioning techniques for the numerical solution of nonlinear, coupled systems of partial differential equations (PDEs) arising from nuclear fuel simulations. These high-order PDEs represent multiple interacting physical fields (for example, heat conduction, oxygen transport, solid deformation), each is modeled by a certain type of Cahn-Hilliard and/or Allen-Cahn equations. Most existing approaches involve a careful splitting of the fields and the use of field-by-field iterations to obtain a solution of the coupled problem. Such approaches have many advantages such as ease of implementationmore » since only single field solvers are needed, but also exhibit disadvantages. For example, certain nonlinear interactions between the fields may not be fully captured, and for unsteady problems, stable time integration schemes are difficult to design. In addition, when implemented on large scale parallel computers, the sequential nature of the field-by-field iterations substantially reduces the parallel efficiency. To overcome the disadvantages, fully coupled approaches have been investigated in order to obtain full physics simulations.« less

Scalable load balancing for massively parallel distributed Monte Carlo particle transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Brien, M. J.; Brantley, P. S.; Joy, K. I.

2013-07-01

In order to run computer simulations efficiently on massively parallel computers with hundreds of thousands or millions of processors, care must be taken that the calculation is load balanced across the processors. Examining the workload of every processor leads to an unscalable algorithm, with run time at least as large as O(N), where N is the number of processors. We present a scalable load balancing algorithm, with run time 0(log(N)), that involves iterated processor-pair-wise balancing steps, ultimately leading to a globally balanced workload. We demonstrate scalability of the algorithm up to 2 million processors on the Sequoia supercomputer at Lawrencemore » Livermore National Laboratory. (authors)« less

Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

NASA Astrophysics Data System (ADS)

Xing, F.; Masson, R.; Lopez, S.

2017-09-01

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non-immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is discretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence.

Agile parallel bioinformatics workflow management using Pwrake.

PubMed

Mishima, Hiroyuki; Sasaki, Kensaku; Tanaka, Masahiro; Tatebe, Osamu; Yoshiura, Koh-Ichiro

2011-09-08

In bioinformatics projects, scientific workflow systems are widely used to manage computational procedures. Full-featured workflow systems have been proposed to fulfil the demand for workflow management. However, such systems tend to be over-weighted for actual bioinformatics practices. We realize that quick deployment of cutting-edge software implementing advanced algorithms and data formats, and continuous adaptation to changes in computational resources and the environment are often prioritized in scientific workflow management. These features have a greater affinity with the agile software development method through iterative development phases after trial and error.Here, we show the application of a scientific workflow system Pwrake to bioinformatics workflows. Pwrake is a parallel workflow extension of Ruby's standard build tool Rake, the flexibility of which has been demonstrated in the astronomy domain. Therefore, we hypothesize that Pwrake also has advantages in actual bioinformatics workflows. We implemented the Pwrake workflows to process next generation sequencing data using the Genomic Analysis Toolkit (GATK) and Dindel. GATK and Dindel workflows are typical examples of sequential and parallel workflows, respectively. We found that in practice, actual scientific workflow development iterates over two phases, the workflow definition phase and the parameter adjustment phase. We introduced separate workflow definitions to help focus on each of the two developmental phases, as well as helper methods to simplify the descriptions. This approach increased iterative development efficiency. Moreover, we implemented combined workflows to demonstrate modularity of the GATK and Dindel workflows. Pwrake enables agile management of scientific workflows in the bioinformatics domain. The internal domain specific language design built on Ruby gives the flexibility of rakefiles for writing scientific workflows. Furthermore, readability and maintainability of rakefiles may facilitate sharing workflows among the scientific community. Workflows for GATK and Dindel are available at http://github.com/misshie/Workflows.

Agile parallel bioinformatics workflow management using Pwrake

PubMed Central

2011-01-01

Background In bioinformatics projects, scientific workflow systems are widely used to manage computational procedures. Full-featured workflow systems have been proposed to fulfil the demand for workflow management. However, such systems tend to be over-weighted for actual bioinformatics practices. We realize that quick deployment of cutting-edge software implementing advanced algorithms and data formats, and continuous adaptation to changes in computational resources and the environment are often prioritized in scientific workflow management. These features have a greater affinity with the agile software development method through iterative development phases after trial and error. Here, we show the application of a scientific workflow system Pwrake to bioinformatics workflows. Pwrake is a parallel workflow extension of Ruby's standard build tool Rake, the flexibility of which has been demonstrated in the astronomy domain. Therefore, we hypothesize that Pwrake also has advantages in actual bioinformatics workflows. Findings We implemented the Pwrake workflows to process next generation sequencing data using the Genomic Analysis Toolkit (GATK) and Dindel. GATK and Dindel workflows are typical examples of sequential and parallel workflows, respectively. We found that in practice, actual scientific workflow development iterates over two phases, the workflow definition phase and the parameter adjustment phase. We introduced separate workflow definitions to help focus on each of the two developmental phases, as well as helper methods to simplify the descriptions. This approach increased iterative development efficiency. Moreover, we implemented combined workflows to demonstrate modularity of the GATK and Dindel workflows. Conclusions Pwrake enables agile management of scientific workflows in the bioinformatics domain. The internal domain specific language design built on Ruby gives the flexibility of rakefiles for writing scientific workflows. Furthermore, readability and maintainability of rakefiles may facilitate sharing workflows among the scientific community. Workflows for GATK and Dindel are available at http://github.com/misshie/Workflows. PMID:21899774

Data consistency-driven scatter kernel optimization for x-ray cone-beam CT

NASA Astrophysics Data System (ADS)

Kim, Changhwan; Park, Miran; Sung, Younghun; Lee, Jaehak; Choi, Jiyoung; Cho, Seungryong

2015-08-01

Accurate and efficient scatter correction is essential for acquisition of high-quality x-ray cone-beam CT (CBCT) images for various applications. This study was conducted to demonstrate the feasibility of using the data consistency condition (DCC) as a criterion for scatter kernel optimization in scatter deconvolution methods in CBCT. As in CBCT, data consistency in the mid-plane is primarily challenged by scatter, we utilized data consistency to confirm the degree of scatter correction and to steer the update in iterative kernel optimization. By means of the parallel-beam DCC via fan-parallel rebinning, we iteratively optimized the scatter kernel parameters, using a particle swarm optimization algorithm for its computational efficiency and excellent convergence. The proposed method was validated by a simulation study using the XCAT numerical phantom and also by experimental studies using the ACS head phantom and the pelvic part of the Rando phantom. The results showed that the proposed method can effectively improve the accuracy of deconvolution-based scatter correction. Quantitative assessments of image quality parameters such as contrast and structure similarity (SSIM) revealed that the optimally selected scatter kernel improves the contrast of scatter-free images by up to 99.5%, 94.4%, and 84.4%, and of the SSIM in an XCAT study, an ACS head phantom study, and a pelvis phantom study by up to 96.7%, 90.5%, and 87.8%, respectively. The proposed method can achieve accurate and efficient scatter correction from a single cone-beam scan without need of any auxiliary hardware or additional experimentation.

On the inversion of geodetic integrals defined over the sphere using 1-D FFT

NASA Astrophysics Data System (ADS)

García, R. V.; Alejo, C. A.

2005-08-01

An iterative method is presented which performs inversion of integrals defined over the sphere. The method is based on one-dimensional fast Fourier transform (1-D FFT) inversion and is implemented with the projected Landweber technique, which is used to solve constrained least-squares problems reducing the associated 1-D cyclic-convolution error. The results obtained are as precise as the direct matrix inversion approach, but with better computational efficiency. A case study uses the inversion of Hotine’s integral to obtain gravity disturbances from geoid undulations. Numerical convergence is also analyzed and comparisons with respect to the direct matrix inversion method using conjugate gradient (CG) iteration are presented. Like the CG method, the number of iterations needed to get the optimum (i.e., small) error decreases as the measurement noise increases. Nevertheless, for discrete data given over a whole parallel band, the method can be applied directly without implementing the projected Landweber method, since no cyclic convolution error exists.

Computational aspects of helicopter trim analysis and damping levels from Floquet theory

NASA Technical Reports Server (NTRS)

Gaonkar, Gopal H.; Achar, N. S.

1992-01-01

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Application of microarray analysis on computer cluster and cloud platforms.

PubMed

Bernau, C; Boulesteix, A-L; Knaus, J

2013-01-01

Analysis of recent high-dimensional biological data tends to be computationally intensive as many common approaches such as resampling or permutation tests require the basic statistical analysis to be repeated many times. A crucial advantage of these methods is that they can be easily parallelized due to the computational independence of the resampling or permutation iterations, which has induced many statistics departments to establish their own computer clusters. An alternative is to rent computing resources in the cloud, e.g. at Amazon Web Services. In this article we analyze whether a selection of statistical projects, recently implemented at our department, can be efficiently realized on these cloud resources. Moreover, we illustrate an opportunity to combine computer cluster and cloud resources. In order to compare the efficiency of computer cluster and cloud implementations and their respective parallelizations we use microarray analysis procedures and compare their runtimes on the different platforms. Amazon Web Services provide various instance types which meet the particular needs of the different statistical projects we analyzed in this paper. Moreover, the network capacity is sufficient and the parallelization is comparable in efficiency to standard computer cluster implementations. Our results suggest that many statistical projects can be efficiently realized on cloud resources. It is important to mention, however, that workflows can change substantially as a result of a shift from computer cluster to cloud computing.

Run-time parallelization and scheduling of loops

NASA Technical Reports Server (NTRS)

Saltz, Joel H.; Mirchandaney, Ravi; Crowley, Kay

1991-01-01

Run-time methods are studied to automatically parallelize and schedule iterations of a do loop in certain cases where compile-time information is inadequate. The methods presented involve execution time preprocessing of the loop. At compile-time, these methods set up the framework for performing a loop dependency analysis. At run-time, wavefronts of concurrently executable loop iterations are identified. Using this wavefront information, loop iterations are reordered for increased parallelism. Symbolic transformation rules are used to produce: inspector procedures that perform execution time preprocessing, and executors or transformed versions of source code loop structures. These transformed loop structures carry out the calculations planned in the inspector procedures. Performance results are presented from experiments conducted on the Encore Multimax. These results illustrate that run-time reordering of loop indexes can have a significant impact on performance.

Exploiting parallel computing with limited program changes using a network of microcomputers

NASA Technical Reports Server (NTRS)

Rogers, J. L., Jr.; Sobieszczanski-Sobieski, J.

1985-01-01

Network computing and multiprocessor computers are two discernible trends in parallel processing. The computational behavior of an iterative distributed process in which some subtasks are completed later than others because of an imbalance in computational requirements is of significant interest. The effects of asynchronus processing was studied. A small existing program was converted to perform finite element analysis by distributing substructure analysis over a network of four Apple IIe microcomputers connected to a shared disk, simulating a parallel computer. The substructure analysis uses an iterative, fully stressed, structural resizing procedure. A framework of beams divided into three substructures is used as the finite element model. The effects of asynchronous processing on the convergence of the design variables are determined by not resizing particular substructures on various iterations.

Density-matrix-based algorithm for solving eigenvalue problems

NASA Astrophysics Data System (ADS)

Polizzi, Eric

2009-03-01

A fast and stable numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques and takes its inspiration from the contour integration and density-matrix representation in quantum mechanics. It will be shown that this algorithm—named FEAST—exhibits high efficiency, robustness, accuracy, and scalability on parallel architectures. Examples from electronic structure calculations of carbon nanotubes are presented, and numerical performances and capabilities are discussed.

Limits on the Efficiency of Event-Based Algorithms for Monte Carlo Neutron Transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romano, Paul K.; Siegel, Andrew R.

The traditional form of parallelism in Monte Carlo particle transport simulations, wherein each individual particle history is considered a unit of work, does not lend itself well to data-level parallelism. Event-based algorithms, which were originally used for simulations on vector processors, may offer a path toward better utilizing data-level parallelism in modern computer architectures. In this study, a simple model is developed for estimating the efficiency of the event-based particle transport algorithm under two sets of assumptions. Data collected from simulations of four reactor problems using OpenMC was then used in conjunction with the models to calculate the speedup duemore » to vectorization as a function of the size of the particle bank and the vector width. When each event type is assumed to have constant execution time, the achievable speedup is directly related to the particle bank size. We observed that the bank size generally needs to be at least 20 times greater than vector size to achieve vector efficiency greater than 90%. Lastly, when the execution times for events are allowed to vary, the vector speedup is also limited by differences in execution time for events being carried out in a single event-iteration.« less

Limits on the Efficiency of Event-Based Algorithms for Monte Carlo Neutron Transport

DOE PAGES

Romano, Paul K.; Siegel, Andrew R.

2017-07-01

The traditional form of parallelism in Monte Carlo particle transport simulations, wherein each individual particle history is considered a unit of work, does not lend itself well to data-level parallelism. Event-based algorithms, which were originally used for simulations on vector processors, may offer a path toward better utilizing data-level parallelism in modern computer architectures. In this study, a simple model is developed for estimating the efficiency of the event-based particle transport algorithm under two sets of assumptions. Data collected from simulations of four reactor problems using OpenMC was then used in conjunction with the models to calculate the speedup duemore » to vectorization as a function of the size of the particle bank and the vector width. When each event type is assumed to have constant execution time, the achievable speedup is directly related to the particle bank size. We observed that the bank size generally needs to be at least 20 times greater than vector size to achieve vector efficiency greater than 90%. Lastly, when the execution times for events are allowed to vary, the vector speedup is also limited by differences in execution time for events being carried out in a single event-iteration.« less

An iterative reduced field-of-view reconstruction for periodically rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) MRI.

PubMed

Lin, Jyh-Miin; Patterson, Andrew J; Chang, Hing-Chiu; Gillard, Jonathan H; Graves, Martin J

2015-10-01

To propose a new reduced field-of-view (rFOV) strategy for iterative reconstructions in a clinical environment. Iterative reconstructions can incorporate regularization terms to improve the image quality of periodically rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) MRI. However, the large amount of calculations required for full FOV iterative reconstructions has posed a huge computational challenge for clinical usage. By subdividing the entire problem into smaller rFOVs, the iterative reconstruction can be accelerated on a desktop with a single graphic processing unit (GPU). This rFOV strategy divides the iterative reconstruction into blocks, based on the block-diagonal dominant structure. A near real-time reconstruction system was developed for the clinical MR unit, and parallel computing was implemented using the object-oriented model. In addition, the Toeplitz method was implemented on the GPU to reduce the time required for full interpolation. Using the data acquired from the PROPELLER MRI, the reconstructed images were then saved in the digital imaging and communications in medicine format. The proposed rFOV reconstruction reduced the gridding time by 97%, as the total iteration time was 3 s even with multiple processes running. A phantom study showed that the structure similarity index for rFOV reconstruction was statistically superior to conventional density compensation (p < 0.001). In vivo study validated the increased signal-to-noise ratio, which is over four times higher than with density compensation. Image sharpness index was improved using the regularized reconstruction implemented. The rFOV strategy permits near real-time iterative reconstruction to improve the image quality of PROPELLER images. Substantial improvements in image quality metrics were validated in the experiments. The concept of rFOV reconstruction may potentially be applied to other kinds of iterative reconstructions for shortened reconstruction duration.

Distorted Born iterative T-matrix method for inversion of CSEM data in anisotropic media

NASA Astrophysics Data System (ADS)

Jakobsen, Morten; Tveit, Svenn

2018-05-01

We present a direct iterative solutions to the nonlinear controlled-source electromagnetic (CSEM) inversion problem in the frequency domain, which is based on a volume integral equation formulation of the forward modelling problem in anisotropic conductive media. Our vectorial nonlinear inverse scattering approach effectively replaces an ill-posed nonlinear inverse problem with a series of linear ill-posed inverse problems, for which there already exist efficient (regularized) solution methods. The solution update the dyadic Green's function's from the source to the scattering-volume and from the scattering-volume to the receivers, after each iteration. The T-matrix approach of multiple scattering theory is used for efficient updating of all dyadic Green's functions after each linearized inversion step. This means that we have developed a T-matrix variant of the Distorted Born Iterative (DBI) method, which is often used in the acoustic and electromagnetic (medical) imaging communities as an alternative to contrast-source inversion. The main advantage of using the T-matrix approach in this context, is that it eliminates the need to perform a full forward simulation at each iteration of the DBI method, which is known to be consistent with the Gauss-Newton method. The T-matrix allows for a natural domain decomposition, since in the sense that a large model can be decomposed into an arbitrary number of domains that can be treated independently and in parallel. The T-matrix we use for efficient model updating is also independent of the source-receiver configuration, which could be an advantage when performing fast-repeat modelling and time-lapse inversion. The T-matrix is also compatible with the use of modern renormalization methods that can potentially help us to reduce the sensitivity of the CSEM inversion results on the starting model. To illustrate the performance and potential of our T-matrix variant of the DBI method for CSEM inversion, we performed a numerical experiments based on synthetic CSEM data associated with 2D VTI and 3D orthorombic model inversions. The results of our numerical experiment suggest that the DBIT method for inversion of CSEM data in anisotropic media is both accurate and efficient.

The novel implicit LU-SGS parallel iterative method based on the diffusion equation of a nuclear reactor on a GPU cluster

NASA Astrophysics Data System (ADS)

Zhang, Jilin; Sha, Chaoqun; Wu, Yusen; Wan, Jian; Zhou, Li; Ren, Yongjian; Si, Huayou; Yin, Yuyu; Jing, Ya

2017-02-01

GPU not only is used in the field of graphic technology but also has been widely used in areas needing a large number of numerical calculations. In the energy industry, because of low carbon, high energy density, high duration and other characteristics, the development of nuclear energy cannot easily be replaced by other energy sources. Management of core fuel is one of the major areas of concern in a nuclear power plant, and it is directly related to the economic benefits and cost of nuclear power. The large-scale reactor core expansion equation is large and complicated, so the calculation of the diffusion equation is crucial in the core fuel management process. In this paper, we use CUDA programming technology on a GPU cluster to run the LU-SGS parallel iterative calculation against the background of the diffusion equation of the reactor. We divide one-dimensional and two-dimensional mesh into a plurality of domains, with each domain evenly distributed on the GPU blocks. A parallel collision scheme is put forward that defines the virtual boundary of the grid exchange information and data transmission by non-stop collision. Compared with the serial program, the experiment shows that GPU greatly improves the efficiency of program execution and verifies that GPU is playing a much more important role in the field of numerical calculations.

A Strassen-Newton algorithm for high-speed parallelizable matrix inversion

NASA Technical Reports Server (NTRS)

Bailey, David H.; Ferguson, Helaman R. P.

1988-01-01

Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spotz, William F.

PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of themore » underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.« less

Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation

NASA Astrophysics Data System (ADS)

Costa, Carlos A. N.; Campos, Itamara S.; Costa, Jessé C.; Neto, Francisco A.; Schleicher, Jörg; Novais, Amélia

2013-08-01

Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality.

Efficient parallel simulation of CO2 geologic sequestration insaline aquifers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Keni; Doughty, Christine; Wu, Yu-Shu

2007-01-01

An efficient parallel simulator for large-scale, long-termCO2 geologic sequestration in saline aquifers has been developed. Theparallel simulator is a three-dimensional, fully implicit model thatsolves large, sparse linear systems arising from discretization of thepartial differential equations for mass and energy balance in porous andfractured media. The simulator is based on the ECO2N module of the TOUGH2code and inherits all the process capabilities of the single-CPU TOUGH2code, including a comprehensive description of the thermodynamics andthermophysical properties of H2O-NaCl- CO2 mixtures, modeling singleand/or two-phase isothermal or non-isothermal flow processes, two-phasemixtures, fluid phases appearing or disappearing, as well as saltprecipitation or dissolution. The newmore » parallel simulator uses MPI forparallel implementation, the METIS software package for simulation domainpartitioning, and the iterative parallel linear solver package Aztec forsolving linear equations by multiple processors. In addition, theparallel simulator has been implemented with an efficient communicationscheme. Test examples show that a linear or super-linear speedup can beobtained on Linux clusters as well as on supercomputers. Because of thesignificant improvement in both simulation time and memory requirement,the new simulator provides a powerful tool for tackling larger scale andmore complex problems than can be solved by single-CPU codes. Ahigh-resolution simulation example is presented that models buoyantconvection, induced by a small increase in brine density caused bydissolution of CO2.« less

Use of general purpose graphics processing units with MODFLOW

USGS Publications Warehouse

Hughes, Joseph D.; White, Jeremy T.

2013-01-01

To evaluate the use of general-purpose graphics processing units (GPGPUs) to improve the performance of MODFLOW, an unstructured preconditioned conjugate gradient (UPCG) solver has been developed. The UPCG solver uses a compressed sparse row storage scheme and includes Jacobi, zero fill-in incomplete, and modified-incomplete lower-upper (LU) factorization, and generalized least-squares polynomial preconditioners. The UPCG solver also includes options for sequential and parallel solution on the central processing unit (CPU) using OpenMP. For simulations utilizing the GPGPU, all basic linear algebra operations are performed on the GPGPU; memory copies between the central processing unit CPU and GPCPU occur prior to the first iteration of the UPCG solver and after satisfying head and flow criteria or exceeding a maximum number of iterations. The efficiency of the UPCG solver for GPGPU and CPU solutions is benchmarked using simulations of a synthetic, heterogeneous unconfined aquifer with tens of thousands to millions of active grid cells. Testing indicates GPGPU speedups on the order of 2 to 8, relative to the standard MODFLOW preconditioned conjugate gradient (PCG) solver, can be achieved when (1) memory copies between the CPU and GPGPU are optimized, (2) the percentage of time performing memory copies between the CPU and GPGPU is small relative to the calculation time, (3) high-performance GPGPU cards are utilized, and (4) CPU-GPGPU combinations are used to execute sequential operations that are difficult to parallelize. Furthermore, UPCG solver testing indicates GPGPU speedups exceed parallel CPU speedups achieved using OpenMP on multicore CPUs for preconditioners that can be easily parallelized.

On some Aitken-like acceleration of the Schwarz method

NASA Astrophysics Data System (ADS)

Garbey, M.; Tromeur-Dervout, D.

2002-12-01

In this paper we present a family of domain decomposition based on Aitken-like acceleration of the Schwarz method seen as an iterative procedure with a linear rate of convergence. We first present the so-called Aitken-Schwarz procedure for linear differential operators. The solver can be a direct solver when applied to the Helmholtz problem with five-point finite difference scheme on regular grids. We then introduce the Steffensen-Schwarz variant which is an iterative domain decomposition solver that can be applied to linear and nonlinear problems. We show that these solvers have reasonable numerical efficiency compared to classical fast solvers for the Poisson problem or multigrids for more general linear and nonlinear elliptic problems. However, the salient feature of our method is that our algorithm has high tolerance to slow network in the context of distributed parallel computing and is attractive, generally speaking, to use with computer architecture for which performance is limited by the memory bandwidth rather than the flop performance of the CPU. This is nowadays the case for most parallel. computer using the RISC processor architecture. We will illustrate this highly desirable property of our algorithm with large-scale computing experiments.

Parallel solution of the symmetric tridiagonal eigenproblem. Research report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jessup, E.R.

1989-10-01

This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed-memory Multiple Instruction, Multiple Data multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speed up, and accuracy. Experiments on an IPSC hypercube multiprocessor reveal that Cuppen's method ismore » the most accurate approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effect of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptions of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.« less

Parallel solution of the symmetric tridiagonal eigenproblem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jessup, E.R.

1989-01-01

This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed memory MIMD multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues, and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speedup, and accuracy. Experiments on an iPSC hyper-cube multiprocessor reveal that Cuppen's method is the most accuratemore » approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effects of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptations of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aliaga, José I., E-mail: aliaga@uji.es; Alonso, Pedro; Badía, José M.

We introduce a new iterative Krylov subspace-based eigensolver for the simulation of macromolecular motions on desktop multithreaded platforms equipped with multicore processors and, possibly, a graphics accelerator (GPU). The method consists of two stages, with the original problem first reduced into a simpler band-structured form by means of a high-performance compute-intensive procedure. This is followed by a memory-intensive but low-cost Krylov iteration, which is off-loaded to be computed on the GPU by means of an efficient data-parallel kernel. The experimental results reveal the performance of the new eigensolver. Concretely, when applied to the simulation of macromolecules with a few thousandsmore » degrees of freedom and the number of eigenpairs to be computed is small to moderate, the new solver outperforms other methods implemented as part of high-performance numerical linear algebra packages for multithreaded architectures.« less

A distributed-memory approximation algorithm for maximum weight perfect bipartite matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azad, Ariful; Buluc, Aydin; Li, Xiaoye S.

We design and implement an efficient parallel approximation algorithm for the problem of maximum weight perfect matching in bipartite graphs, i.e. the problem of finding a set of non-adjacent edges that covers all vertices and has maximum weight. This problem differs from the maximum weight matching problem, for which scalable approximation algorithms are known. It is primarily motivated by finding good pivots in scalable sparse direct solvers before factorization where sequential implementations of maximum weight perfect matching algorithms, such as those available in MC64, are widely used due to the lack of scalable alternatives. To overcome this limitation, we proposemore » a fully parallel distributed memory algorithm that first generates a perfect matching and then searches for weightaugmenting cycles of length four in parallel and iteratively augments the matching with a vertex disjoint set of such cycles. For most practical problems the weights of the perfect matchings generated by our algorithm are very close to the optimum. An efficient implementation of the algorithm scales up to 256 nodes (17,408 cores) on a Cray XC40 supercomputer and can solve instances that are too large to be handled by a single node using the sequential algorithm.« less

An efficient spectral crystal plasticity solver for GPU architectures

NASA Astrophysics Data System (ADS)

Malahe, Michael

2018-03-01

We present a spectral crystal plasticity (CP) solver for graphics processing unit (GPU) architectures that achieves a tenfold increase in efficiency over prior GPU solvers. The approach makes use of a database containing a spectral decomposition of CP simulations performed using a conventional iterative solver over a parameter space of crystal orientations and applied velocity gradients. The key improvements in efficiency come from reducing global memory transactions, exposing more instruction-level parallelism, reducing integer instructions and performing fast range reductions on trigonometric arguments. The scheme also makes more efficient use of memory than prior work, allowing for larger problems to be solved on a single GPU. We illustrate these improvements with a simulation of 390 million crystal grains on a consumer-grade GPU, which executes at a rate of 2.72 s per strain step.

Parallel iterative solution for h and p approximations of the shallow water equations

USGS Publications Warehouse

Barragy, E.J.; Walters, R.A.

1998-01-01

A p finite element scheme and parallel iterative solver are introduced for a modified form of the shallow water equations. The governing equations are the three-dimensional shallow water equations. After a harmonic decomposition in time and rearrangement, the resulting equations are a complex Helmholz problem for surface elevation, and a complex momentum equation for the horizontal velocity. Both equations are nonlinear and the resulting system is solved using the Picard iteration combined with a preconditioned biconjugate gradient (PBCG) method for the linearized subproblems. A subdomain-based parallel preconditioner is developed which uses incomplete LU factorization with thresholding (ILUT) methods within subdomains, overlapping ILUT factorizations for subdomain boundaries and under-relaxed iteration for the resulting block system. The method builds on techniques successfully applied to linear elements by introducing ordering and condensation techniques to handle uniform p refinement. The combined methods show good performance for a range of p (element order), h (element size), and N (number of processors). Performance and scalability results are presented for a field scale problem where up to 512 processors are used. ?? 1998 Elsevier Science Ltd. All rights reserved.

Error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems

NASA Astrophysics Data System (ADS)

Arrarás, A.; Portero, L.; Yotov, I.

2014-01-01

We study space and time discretizations for mixed formulations of parabolic problems. The spatial approximation is based on the multipoint flux mixed finite element method, which reduces to an efficient cell-centered pressure system on general grids, including triangles, quadrilaterals, tetrahedra, and hexahedra. The time integration is performed by using a domain decomposition time-splitting technique combined with multiterm fractional step diagonally implicit Runge-Kutta methods. The resulting scheme is unconditionally stable and computationally efficient, as it reduces the global system to a collection of uncoupled subdomain problems that can be solved in parallel without the need for Schwarz-type iteration. Convergence analysis for both the semidiscrete and fully discrete schemes is presented.

Handling Big Data in Medical Imaging: Iterative Reconstruction with Large-Scale Automated Parallel Computation

PubMed Central

Lee, Jae H.; Yao, Yushu; Shrestha, Uttam; Gullberg, Grant T.; Seo, Youngho

2014-01-01

The primary goal of this project is to implement the iterative statistical image reconstruction algorithm, in this case maximum likelihood expectation maximum (MLEM) used for dynamic cardiac single photon emission computed tomography, on Spark/GraphX. This involves porting the algorithm to run on large-scale parallel computing systems. Spark is an easy-to- program software platform that can handle large amounts of data in parallel. GraphX is a graph analytic system running on top of Spark to handle graph and sparse linear algebra operations in parallel. The main advantage of implementing MLEM algorithm in Spark/GraphX is that it allows users to parallelize such computation without any expertise in parallel computing or prior knowledge in computer science. In this paper we demonstrate a successful implementation of MLEM in Spark/GraphX and present the performance gains with the goal to eventually make it useable in clinical setting. PMID:27081299

Handling Big Data in Medical Imaging: Iterative Reconstruction with Large-Scale Automated Parallel Computation.

PubMed

Lee, Jae H; Yao, Yushu; Shrestha, Uttam; Gullberg, Grant T; Seo, Youngho

2014-11-01

The primary goal of this project is to implement the iterative statistical image reconstruction algorithm, in this case maximum likelihood expectation maximum (MLEM) used for dynamic cardiac single photon emission computed tomography, on Spark/GraphX. This involves porting the algorithm to run on large-scale parallel computing systems. Spark is an easy-to- program software platform that can handle large amounts of data in parallel. GraphX is a graph analytic system running on top of Spark to handle graph and sparse linear algebra operations in parallel. The main advantage of implementing MLEM algorithm in Spark/GraphX is that it allows users to parallelize such computation without any expertise in parallel computing or prior knowledge in computer science. In this paper we demonstrate a successful implementation of MLEM in Spark/GraphX and present the performance gains with the goal to eventually make it useable in clinical setting.

Run-time parallelization and scheduling of loops

NASA Technical Reports Server (NTRS)

Saltz, Joel H.; Mirchandaney, Ravi; Crowley, Kay

1990-01-01

Run time methods are studied to automatically parallelize and schedule iterations of a do loop in certain cases, where compile-time information is inadequate. The methods presented involve execution time preprocessing of the loop. At compile-time, these methods set up the framework for performing a loop dependency analysis. At run time, wave fronts of concurrently executable loop iterations are identified. Using this wavefront information, loop iterations are reordered for increased parallelism. Symbolic transformation rules are used to produce: inspector procedures that perform execution time preprocessing and executors or transformed versions of source code loop structures. These transformed loop structures carry out the calculations planned in the inspector procedures. Performance results are presented from experiments conducted on the Encore Multimax. These results illustrate that run time reordering of loop indices can have a significant impact on performance. Furthermore, the overheads associated with this type of reordering are amortized when the loop is executed several times with the same dependency structure.

Project APhiD: A Lorenz-gauged A-Φ decomposition for parallelized computation of ultra-broadband electromagnetic induction in a fully heterogeneous Earth

NASA Astrophysics Data System (ADS)

Weiss, Chester J.

2013-08-01

An essential element for computational hypothesis testing, data inversion and experiment design for electromagnetic geophysics is a robust forward solver, capable of easily and quickly evaluating the electromagnetic response of arbitrary geologic structure. The usefulness of such a solver hinges on the balance among competing desires like ease of use, speed of forward calculation, scalability to large problems or compute clusters, parsimonious use of memory access, accuracy and by necessity, the ability to faithfully accommodate a broad range of geologic scenarios over extremes in length scale and frequency content. This is indeed a tall order. The present study addresses recent progress toward the development of a forward solver with these properties. Based on the Lorenz-gauged Helmholtz decomposition, a new finite volume solution over Cartesian model domains endowed with complex-valued electrical properties is shown to be stable over the frequency range 10-2-1010 Hz and range 10-3-105 m in length scale. Benchmark examples are drawn from magnetotellurics, exploration geophysics, geotechnical mapping and laboratory-scale analysis, showing excellent agreement with reference analytic solutions. Computational efficiency is achieved through use of a matrix-free implementation of the quasi-minimum-residual (QMR) iterative solver, which eliminates explicit storage of finite volume matrix elements in favor of "on the fly" computation as needed by the iterative Krylov sequence. Further efficiency is achieved through sparse coupling matrices between the vector and scalar potentials whose non-zero elements arise only in those parts of the model domain where the conductivity gradient is non-zero. Multi-thread parallelization in the QMR solver through OpenMP pragmas is used to reduce the computational cost of its most expensive step: the single matrix-vector product at each iteration. High-level MPI communicators farm independent processes to available compute nodes for simultaneous computation of multi-frequency or multi-transmitter responses.

Parallel computation of fluid-structural interactions using high resolution upwind schemes

NASA Astrophysics Data System (ADS)

Hu, Zongjun

An efficient and accurate solver is developed to simulate the non-linear fluid-structural interactions in turbomachinery flutter flows. A new low diffusion E-CUSP scheme, Zha CUSP scheme, is developed to improve the efficiency and accuracy of the inviscid flux computation. The 3D unsteady Navier-Stokes equations with the Baldwin-Lomax turbulence model are solved using the finite volume method with the dual-time stepping scheme. The linearized equations are solved with Gauss-Seidel line iterations. The parallel computation is implemented using MPI protocol. The solver is validated with 2D cases for its turbulence modeling, parallel computation and unsteady calculation. The Zha CUSP scheme is validated with 2D cases, including a supersonic flat plate boundary layer, a transonic converging-diverging nozzle and a transonic inlet diffuser. The Zha CUSP2 scheme is tested with 3D cases, including a circular-to-rectangular nozzle, a subsonic compressor cascade and a transonic channel. The Zha CUSP schemes are proved to be accurate, robust and efficient in these tests. The steady and unsteady separation flows in a 3D stationary cascade under high incidence and three inlet Mach numbers are calculated to study the steady state separation flow patterns and their unsteady oscillation characteristics. The leading edge vortex shedding is the mechanism behind the unsteady characteristics of the high incidence separated flows. The separation flow characteristics is affected by the inlet Mach number. The blade aeroelasticity of a linear cascade with forced oscillating blades is studied using parallel computation. A simplified two-passage cascade with periodic boundary condition is first calculated under a medium frequency and a low incidence. The full scale cascade with 9 blades and two end walls is then studied more extensively under three oscillation frequencies and two incidence angles. The end wall influence and the blade stability are studied and compared under different frequencies and incidence angles. The Zha CUSP schemes are the first time to be applied in moving grid systems and 2D and 3D calculations. The implicit Gauss-Seidel iteration with dual time stepping is the first time to be used for moving grid systems. The NASA flutter cascade is the first time to be calculated in full scale.

A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TETRAHEDRAL DOMAINS

PubMed Central

Fu, Zhisong; Kirby, Robert M.; Whitaker, Ross T.

2014-01-01

Generating numerical solutions to the eikonal equation and its many variations has a broad range of applications in both the natural and computational sciences. Efficient solvers on cutting-edge, parallel architectures require new algorithms that may not be theoretically optimal, but that are designed to allow asynchronous solution updates and have limited memory access patterns. This paper presents a parallel algorithm for solving the eikonal equation on fully unstructured tetrahedral meshes. The method is appropriate for the type of fine-grained parallelism found on modern massively-SIMD architectures such as graphics processors and takes into account the particular constraints and capabilities of these computing platforms. This work builds on previous work for solving these equations on triangle meshes; in this paper we adapt and extend previous two-dimensional strategies to accommodate three-dimensional, unstructured, tetrahedralized domains. These new developments include a local update strategy with data compaction for tetrahedral meshes that provides solutions on both serial and parallel architectures, with a generalization to inhomogeneous, anisotropic speed functions. We also propose two new update schemes, specialized to mitigate the natural data increase observed when moving to three dimensions, and the data structures necessary for efficiently mapping data to parallel SIMD processors in a way that maintains computational density. Finally, we present descriptions of the implementations for a single CPU, as well as multicore CPUs with shared memory and SIMD architectures, with comparative results against state-of-the-art eikonal solvers. PMID:25221418

Trace: a high-throughput tomographic reconstruction engine for large-scale datasets.

PubMed

Bicer, Tekin; Gürsoy, Doğa; Andrade, Vincent De; Kettimuthu, Rajkumar; Scullin, William; Carlo, Francesco De; Foster, Ian T

2017-01-01

Modern synchrotron light sources and detectors produce data at such scale and complexity that large-scale computation is required to unleash their full power. One of the widely used imaging techniques that generates data at tens of gigabytes per second is computed tomography (CT). Although CT experiments result in rapid data generation, the analysis and reconstruction of the collected data may require hours or even days of computation time with a medium-sized workstation, which hinders the scientific progress that relies on the results of analysis. We present Trace, a data-intensive computing engine that we have developed to enable high-performance implementation of iterative tomographic reconstruction algorithms for parallel computers. Trace provides fine-grained reconstruction of tomography datasets using both (thread-level) shared memory and (process-level) distributed memory parallelization. Trace utilizes a special data structure called replicated reconstruction object to maximize application performance. We also present the optimizations that we apply to the replicated reconstruction objects and evaluate them using tomography datasets collected at the Advanced Photon Source. Our experimental evaluations show that our optimizations and parallelization techniques can provide 158× speedup using 32 compute nodes (384 cores) over a single-core configuration and decrease the end-to-end processing time of a large sinogram (with 4501 × 1 × 22,400 dimensions) from 12.5 h to <5 min per iteration. The proposed tomographic reconstruction engine can efficiently process large-scale tomographic data using many compute nodes and minimize reconstruction times.

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baudron, Anne-Marie, E-mail: anne-marie.baudron@cea.fr; CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex; Lautard, Jean-Jacques, E-mail: jean-jacques.lautard@cea.fr

2014-12-15

In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity ofmore » the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.« less

Design and performance evaluation of a 20-aperture multipinhole collimator for myocardial perfusion imaging applications.

PubMed

Bowen, Jason D; Huang, Qiu; Ellin, Justin R; Lee, Tzu-Cheng; Shrestha, Uttam; Gullberg, Grant T; Seo, Youngho

2013-10-21

Single photon emission computed tomography (SPECT) myocardial perfusion imaging remains a critical tool in the diagnosis of coronary artery disease. However, after more than three decades of use, photon detection efficiency remains poor and unchanged. This is due to the continued reliance on parallel-hole collimators first introduced in 1964. These collimators possess poor geometric efficiency. Here we present the performance evaluation results of a newly designed multipinhole collimator with 20 pinhole apertures (PH20) for commercial SPECT systems. Computer simulations and numerical observer studies were used to assess the noise, bias and diagnostic imaging performance of a PH20 collimator in comparison with those of a low energy high resolution (LEHR) parallel-hole collimator. Ray-driven projector/backprojector pairs were used to model SPECT imaging acquisitions, including simulation of noiseless projection data and performing MLEM/OSEM image reconstructions. Poisson noise was added to noiseless projections for realistic projection data. Noise and bias performance were investigated for five mathematical cardiac and torso (MCAT) phantom anatomies imaged at two gantry orbit positions (19.5 and 25.0 cm). PH20 and LEHR images were reconstructed with 300 MLEM iterations and 30 OSEM iterations (ten subsets), respectively. Diagnostic imaging performance was assessed by a receiver operating characteristic (ROC) analysis performed on a single MCAT phantom; however, in this case PH20 images were reconstructed with 75 pixel-based OSEM iterations (four subsets). Four PH20 projection views from two positions of a dual-head camera acquisition and 60 LEHR projections were simulated for all studies. At uniformly-imposed resolution of 12.5 mm, significant improvements in SNR and diagnostic sensitivity (represented by the area under the ROC curve, or AUC) were realized when PH20 collimators are substituted for LEHR parallel-hole collimators. SNR improves by factors of 1.94-2.34 for the five patient anatomies and two orbital positions studied. For the ROC analysis the PH20 AUC is larger than the LEHR AUC with a p-value of 0.0067. Bias performance, however, decreases with the use of PH20 collimators. Systematic analyses showed PH20 collimators present improved diagnostic imaging performance over LEHR collimators, requiring only collimator exchange on existing SPECT cameras for their use.

Design and performance evaluation of a 20-aperture multipinhole collimator for myocardial perfusion imaging applications

NASA Astrophysics Data System (ADS)

Bowen, Jason D.; Huang, Qiu; Ellin, Justin R.; Lee, Tzu-Cheng; Shrestha, Uttam; Gullberg, Grant T.; Seo, Youngho

2013-10-01

Single photon emission computed tomography (SPECT) myocardial perfusion imaging remains a critical tool in the diagnosis of coronary artery disease. However, after more than three decades of use, photon detection efficiency remains poor and unchanged. This is due to the continued reliance on parallel-hole collimators first introduced in 1964. These collimators possess poor geometric efficiency. Here we present the performance evaluation results of a newly designed multipinhole collimator with 20 pinhole apertures (PH20) for commercial SPECT systems. Computer simulations and numerical observer studies were used to assess the noise, bias and diagnostic imaging performance of a PH20 collimator in comparison with those of a low energy high resolution (LEHR) parallel-hole collimator. Ray-driven projector/backprojector pairs were used to model SPECT imaging acquisitions, including simulation of noiseless projection data and performing MLEM/OSEM image reconstructions. Poisson noise was added to noiseless projections for realistic projection data. Noise and bias performance were investigated for five mathematical cardiac and torso (MCAT) phantom anatomies imaged at two gantry orbit positions (19.5 and 25.0 cm). PH20 and LEHR images were reconstructed with 300 MLEM iterations and 30 OSEM iterations (ten subsets), respectively. Diagnostic imaging performance was assessed by a receiver operating characteristic (ROC) analysis performed on a single MCAT phantom; however, in this case PH20 images were reconstructed with 75 pixel-based OSEM iterations (four subsets). Four PH20 projection views from two positions of a dual-head camera acquisition and 60 LEHR projections were simulated for all studies. At uniformly-imposed resolution of 12.5 mm, significant improvements in SNR and diagnostic sensitivity (represented by the area under the ROC curve, or AUC) were realized when PH20 collimators are substituted for LEHR parallel-hole collimators. SNR improves by factors of 1.94-2.34 for the five patient anatomies and two orbital positions studied. For the ROC analysis the PH20 AUC is larger than the LEHR AUC with a p-value of 0.0067. Bias performance, however, decreases with the use of PH20 collimators. Systematic analyses showed PH20 collimators present improved diagnostic imaging performance over LEHR collimators, requiring only collimator exchange on existing SPECT cameras for their use.

Image segmentation by iterative parallel region growing with application to data compression and image analysis

NASA Technical Reports Server (NTRS)

Tilton, James C.

1988-01-01

Image segmentation can be a key step in data compression and image analysis. However, the segmentation results produced by most previous approaches to region growing are suspect because they depend on the order in which portions of the image are processed. An iterative parallel segmentation algorithm avoids this problem by performing globally best merges first. Such a segmentation approach, and two implementations of the approach on NASA's Massively Parallel Processor (MPP) are described. Application of the segmentation approach to data compression and image analysis is then described, and results of such application are given for a LANDSAT Thematic Mapper image.

Parallelizing flow-accumulation calculations on graphics processing units—From iterative DEM preprocessing algorithm to recursive multiple-flow-direction algorithm

NASA Astrophysics Data System (ADS)

Qin, Cheng-Zhi; Zhan, Lijun

2012-06-01

As one of the important tasks in digital terrain analysis, the calculation of flow accumulations from gridded digital elevation models (DEMs) usually involves two steps in a real application: (1) using an iterative DEM preprocessing algorithm to remove the depressions and flat areas commonly contained in real DEMs, and (2) using a recursive flow-direction algorithm to calculate the flow accumulation for every cell in the DEM. Because both algorithms are computationally intensive, quick calculation of the flow accumulations from a DEM (especially for a large area) presents a practical challenge to personal computer (PC) users. In recent years, rapid increases in hardware capacity of the graphics processing units (GPUs) provided in modern PCs have made it possible to meet this challenge in a PC environment. Parallel computing on GPUs using a compute-unified-device-architecture (CUDA) programming model has been explored to speed up the execution of the single-flow-direction algorithm (SFD). However, the parallel implementation on a GPU of the multiple-flow-direction (MFD) algorithm, which generally performs better than the SFD algorithm, has not been reported. Moreover, GPU-based parallelization of the DEM preprocessing step in the flow-accumulation calculations has not been addressed. This paper proposes a parallel approach to calculate flow accumulations (including both iterative DEM preprocessing and a recursive MFD algorithm) on a CUDA-compatible GPU. For the parallelization of an MFD algorithm (MFD-md), two different parallelization strategies using a GPU are explored. The first parallelization strategy, which has been used in the existing parallel SFD algorithm on GPU, has the problem of computing redundancy. Therefore, we designed a parallelization strategy based on graph theory. The application results show that the proposed parallel approach to calculate flow accumulations on a GPU performs much faster than either sequential algorithms or other parallel GPU-based algorithms based on existing parallelization strategies.

ICON-MIC: Implementing a CPU/MIC Collaboration Parallel Framework for ICON on Tianhe-2 Supercomputer.

PubMed

Wang, Zihao; Chen, Yu; Zhang, Jingrong; Li, Lun; Wan, Xiaohua; Liu, Zhiyong; Sun, Fei; Zhang, Fa

2018-03-01

Electron tomography (ET) is an important technique for studying the three-dimensional structures of the biological ultrastructure. Recently, ET has reached sub-nanometer resolution for investigating the native and conformational dynamics of macromolecular complexes by combining with the sub-tomogram averaging approach. Due to the limited sampling angles, ET reconstruction typically suffers from the "missing wedge" problem. Using a validation procedure, iterative compressed-sensing optimized nonuniform fast Fourier transform (NUFFT) reconstruction (ICON) demonstrates its power in restoring validated missing information for a low-signal-to-noise ratio biological ET dataset. However, the huge computational demand has become a bottleneck for the application of ICON. In this work, we implemented a parallel acceleration technology ICON-many integrated core (MIC) on Xeon Phi cards to address the huge computational demand of ICON. During this step, we parallelize the element-wise matrix operations and use the efficient summation of a matrix to reduce the cost of matrix computation. We also developed parallel versions of NUFFT on MIC to achieve a high acceleration of ICON by using more efficient fast Fourier transform (FFT) calculation. We then proposed a hybrid task allocation strategy (two-level load balancing) to improve the overall performance of ICON-MIC by making full use of the idle resources on Tianhe-2 supercomputer. Experimental results using two different datasets show that ICON-MIC has high accuracy in biological specimens under different noise levels and a significant acceleration, up to 13.3 × , compared with the CPU version. Further, ICON-MIC has good scalability efficiency and overall performance on Tianhe-2 supercomputer.

THC-MP: High performance numerical simulation of reactive transport and multiphase flow in porous media

NASA Astrophysics Data System (ADS)

Wei, Xiaohui; Li, Weishan; Tian, Hailong; Li, Hongliang; Xu, Haixiao; Xu, Tianfu

2015-07-01

The numerical simulation of multiphase flow and reactive transport in the porous media on complex subsurface problem is a computationally intensive application. To meet the increasingly computational requirements, this paper presents a parallel computing method and architecture. Derived from TOUGHREACT that is a well-established code for simulating subsurface multi-phase flow and reactive transport problems, we developed a high performance computing THC-MP based on massive parallel computer, which extends greatly on the computational capability for the original code. The domain decomposition method was applied to the coupled numerical computing procedure in the THC-MP. We designed the distributed data structure, implemented the data initialization and exchange between the computing nodes and the core solving module using the hybrid parallel iterative and direct solver. Numerical accuracy of the THC-MP was verified through a CO2 injection-induced reactive transport problem by comparing the results obtained from the parallel computing and sequential computing (original code). Execution efficiency and code scalability were examined through field scale carbon sequestration applications on the multicore cluster. The results demonstrate successfully the enhanced performance using the THC-MP on parallel computing facilities.

A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.

PubMed

Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D

2014-01-01

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.

A Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations

NASA Technical Reports Server (NTRS)

Venter, Gerhard; Sobieszczanski-Sobieski, Jaroslaw

2005-01-01

A parallel Particle Swarm Optimization (PSO) algorithm is presented. Particle swarm optimization is a fairly recent addition to the family of non-gradient based, probabilistic search algorithms that is based on a simplified social model and is closely tied to swarming theory. Although PSO algorithms present several attractive properties to the designer, they are plagued by high computational cost as measured by elapsed time. One approach to reduce the elapsed time is to make use of coarse-grained parallelization to evaluate the design points. Previous parallel PSO algorithms were mostly implemented in a synchronous manner, where all design points within a design iteration are evaluated before the next iteration is started. This approach leads to poor parallel speedup in cases where a heterogeneous parallel environment is used and/or where the analysis time depends on the design point being analyzed. This paper introduces an asynchronous parallel PSO algorithm that greatly improves the parallel e ciency. The asynchronous algorithm is benchmarked on a cluster assembled of Apple Macintosh G5 desktop computers, using the multi-disciplinary optimization of a typical transport aircraft wing as an example.

Data preprocessing for determining outer/inner parallelization in the nested loop problem using OpenMP

NASA Astrophysics Data System (ADS)

Handhika, T.; Bustamam, A.; Ernastuti, Kerami, D.

2017-07-01

Multi-thread programming using OpenMP on the shared-memory architecture with hyperthreading technology allows the resource to be accessed by multiple processors simultaneously. Each processor can execute more than one thread for a certain period of time. However, its speedup depends on the ability of the processor to execute threads in limited quantities, especially the sequential algorithm which contains a nested loop. The number of the outer loop iterations is greater than the maximum number of threads that can be executed by a processor. The thread distribution technique that had been found previously only be applied by the high-level programmer. This paper generates a parallelization procedure for low-level programmer in dealing with 2-level nested loop problems with the maximum number of threads that can be executed by a processor is smaller than the number of the outer loop iterations. Data preprocessing which is related to the number of the outer loop and the inner loop iterations, the computational time required to execute each iteration and the maximum number of threads that can be executed by a processor are used as a strategy to determine which parallel region that will produce optimal speedup.

Multidisciplinary systems optimization by linear decomposition

NASA Technical Reports Server (NTRS)

Sobieski, J.

1984-01-01

In a typical design process major decisions are made sequentially. An illustrated example is given for an aircraft design in which the aerodynamic shape is usually decided first, then the airframe is sized for strength and so forth. An analogous sequence could be laid out for any other major industrial product, for instance, a ship. The loops in the discipline boxes symbolize iterative design improvements carried out within the confines of a single engineering discipline, or subsystem. The loops spanning several boxes depict multidisciplinary design improvement iterations. Omitted for graphical simplicity is parallelism of the disciplinary subtasks. The parallelism is important in order to develop a broad workfront necessary to shorten the design time. If all the intradisciplinary and interdisciplinary iterations were carried out to convergence, the process could yield a numerically optimal design. However, it usually stops short of that because of time and money limitations. This is especially true for the interdisciplinary iterations.

Towards the Experimental Assessment of the DQE in SPECT Scanners

NASA Astrophysics Data System (ADS)

Fountos, G. P.; Michail, C. M.

2017-11-01

The purpose of this work was to introduce the Detective Quantum Efficiency (DQE) in single photon emission computed tomography (SPECT) systems using a flood source. A Tc-99m-based flood source (Eγ = 140 keV) consisting of a radiopharmaceutical solution of dithiothreitol (DTT, 10-3 M)/Tc-99m(III)-DMSA, 40 mCi/40 ml bound to the grains of an Agfa MammoRay HDR Medical X-ray film) was prepared in laboratory. The source was placed between two PMMA blocks and images were obtained by using the brain tomographic acquisition protocol (DatScan-brain). The Modulation Transfer Function (MTF) was evaluated using the Iterative 2D algorithm. All imaging experiments were performed in a Siemens e-Cam gamma camera. The Normalized Noise Power spectra (NNPS) were obtained from the sagittal views of the source. The higher MTF values were obtained for the Flash Iterative 2D with 24 iterations and 20 subsets. The noise levels of the SPECT reconstructed images, in terms of the NNPS, were found to increase as the number of iterations increase. The behavior of the DQE was influenced by both MTF and NNPS. As the number of iterations was increased, higher MTF values were obtained, however with a parallel, increase of magnitude in image noise, as depicted from the NNPS results. DQE values, which were influenced by both MTF and NNPS, were found higher when the number of iterations results in resolution saturation. The method presented here is novel and easy to implement, requiring materials commonly found in clinical practice and can be useful in the quality control of SPECT scanners.

A third-generation density-functional-theory-based method for calculating canonical molecular orbitals of large molecules.

PubMed

Hirano, Toshiyuki; Sato, Fumitoshi

2014-07-28

We used grid-free modified Cholesky decomposition (CD) to develop a density-functional-theory (DFT)-based method for calculating the canonical molecular orbitals (CMOs) of large molecules. Our method can be used to calculate standard CMOs, analytically compute exchange-correlation terms, and maximise the capacity of next-generation supercomputers. Cholesky vectors were first analytically downscaled using low-rank pivoted CD and CD with adaptive metric (CDAM). The obtained Cholesky vectors were distributed and stored on each computer node in a parallel computer, and the Coulomb, Fock exchange, and pure exchange-correlation terms were calculated by multiplying the Cholesky vectors without evaluating molecular integrals in self-consistent field iterations. Our method enables DFT and massively distributed memory parallel computers to be used in order to very efficiently calculate the CMOs of large molecules.

Analysis and Design of ITER 1 MV Core Snubber

NASA Astrophysics Data System (ADS)

Wang, Haitian; Li, Ge

2012-11-01

The core snubber, as a passive protection device, can suppress arc current and absorb stored energy in stray capacitance during the electrical breakdown in accelerating electrodes of ITER NBI. In order to design the core snubber of ITER, the control parameters of the arc peak current have been firstly analyzed by the Fink-Baker-Owren (FBO) method, which are used for designing the DIIID 100 kV snubber. The B-H curve can be derived from the measured voltage and current waveforms, and the hysteresis loss of the core snubber can be derived using the revised parallelogram method. The core snubber can be a simplified representation as an equivalent parallel resistance and inductance, which has been neglected by the FBO method. A simulation code including the parallel equivalent resistance and inductance has been set up. The simulation and experiments result in dramatically large arc shorting currents due to the parallel inductance effect. The case shows that the core snubber utilizing the FBO method gives more compact design.

Towards a Better Distributed Framework for Learning Big Data

DTIC Science & Technology

2017-06-14

UNLIMITED: PB Public Release 13. SUPPLEMENTARY NOTES 14. ABSTRACT This work aimed at solving issues in distributed machine learning. The PI’s team proposed...communication load. Finally, the team proposed the parallel least-squares policy iteration (parallel LSPI) to parallelize a reinforcement policy learning. 15

Parallel/Vector Integration Methods for Dynamical Astronomy

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

1999-01-01

This paper reviews three recent works on the numerical methods to integrate ordinary differential equations (ODE), which are specially designed for parallel, vector, and/or multi-processor-unit(PU) computers. The first is the Picard-Chebyshev method (Fukushima, 1997a). It obtains a global solution of ODE in the form of Chebyshev polynomial of large (> 1000) degree by applying the Picard iteration repeatedly. The iteration converges for smooth problems and/or perturbed dynamics. The method runs around 100-1000 times faster in the vector mode than in the scalar mode of a certain computer with vector processors (Fukushima, 1997b). The second is a parallelization of a symplectic integrator (Saha et al., 1997). It regards the implicit midpoint rules covering thousands of timesteps as large-scale nonlinear equations and solves them by the fixed-point iteration. The method is applicable to Hamiltonian systems and is expected to lead an acceleration factor of around 50 in parallel computers with more than 1000 PUs. The last is a parallelization of the extrapolation method (Ito and Fukushima, 1997). It performs trial integrations in parallel. Also the trial integrations are further accelerated by balancing computational load among PUs by the technique of folding. The method is all-purpose and achieves an acceleration factor of around 3.5 by using several PUs. Finally, we give a perspective on the parallelization of some implicit integrators which require multiple corrections in solving implicit formulas like the implicit Hermitian integrators (Makino and Aarseth, 1992), (Hut et al., 1995) or the implicit symmetric multistep methods (Fukushima, 1998), (Fukushima, 1999).

A High Order, Locally-Adaptive Method for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Chan, Daniel

1998-11-01

I have extended the FOSLS method of Cai, Manteuffel and McCormick (1997) and implemented it within the framework of a spectral element formulation using the Legendre polynomial basis function. The FOSLS method solves the Navier-Stokes equations as a system of coupled first-order equations and provides the ellipticity that is needed for fast iterative matrix solvers like multigrid to operate efficiently. Each element is treated as an object and its properties are self-contained. Only C^0 continuity is imposed across element interfaces; this design allows local grid refinement and coarsening without the burden of having an elaborate data structure, since only information along element boundaries is needed. With the FORTRAN 90 programming environment, I can maintain a high computational efficiency by employing a hybrid parallel processing model. The OpenMP directives provides parallelism in the loop level which is executed in a shared-memory SMP and the MPI protocol allows the distribution of elements to a cluster of SMP's connected via a commodity network. This talk will provide timing results and a comparison with a second order finite difference method.

Construction, classification and parametrization of complex Hadamard matrices

NASA Astrophysics Data System (ADS)

Szöllősi, Ferenc

To improve the design of nuclear systems, high-fidelity neutron fluxes are required. Leadership-class machines provide platforms on which very large problems can be solved. Computing such fluxes efficiently requires numerical methods with good convergence properties and algorithms that can scale to hundreds of thousands of cores. Many 3-D deterministic transport codes are decomposable in space and angle only, limiting them to tens of thousands of cores. Most codes rely on methods such as Gauss Seidel for fixed source problems and power iteration for eigenvalue problems, which can be slow to converge for challenging problems like those with highly scattering materials or high dominance ratios. Three methods have been added to the 3-D SN transport code Denovo that are designed to improve convergence and enable the full use of cutting-edge computers. The first is a multigroup Krylov solver that converges more quickly than Gauss Seidel and parallelizes the code in energy such that Denovo can use hundreds of thousand of cores effectively. The second is Rayleigh quotient iteration (RQI), an old method applied in a new context. This eigenvalue solver finds the dominant eigenvalue in a mathematically optimal way and should converge in fewer iterations than power iteration. RQI creates energy-block-dense equations that the new Krylov solver treats efficiently. However, RQI can have convergence problems because it creates poorly conditioned systems. This can be overcome with preconditioning. The third method is a multigrid-in-energy preconditioner. The preconditioner takes advantage of the new energy decomposition because the grids are in energy rather than space or angle. The preconditioner greatly reduces iteration count for many problem types and scales well in energy. It also allows RQI to be successful for problems it could not solve otherwise. The methods added to Denovo accomplish the goals of this work. They converge in fewer iterations than traditional methods and enable the use of hundreds of thousands of cores. Each method can be used individually, with the multigroup Krylov solver and multigrid-in-energy preconditioner being particularly successful on their own. The largest benefit, though, comes from using these methods in concert.

A finite element solver for 3-D compressible viscous flows

NASA Technical Reports Server (NTRS)

Reddy, K. C.; Reddy, J. N.; Nayani, S.

1990-01-01

Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.

Block iterative restoration of astronomical images with the massively parallel processor

NASA Technical Reports Server (NTRS)

Heap, Sara R.; Lindler, Don J.

1987-01-01

A method is described for algebraic image restoration capable of treating astronomical images. For a typical 500 x 500 image, direct algebraic restoration would require the solution of a 250,000 x 250,000 linear system. The block iterative approach is used to reduce the problem to solving 4900 121 x 121 linear systems. The algorithm was implemented on the Goddard Massively Parallel Processor, which can solve a 121 x 121 system in approximately 0.06 seconds. Examples are shown of the results for various astronomical images.

Noniterative Multireference Coupled Cluster Methods on Heterogeneous CPU-GPU Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhaskaran-Nair, Kiran; Ma, Wenjing; Krishnamoorthy, Sriram

2013-04-09

A novel parallel algorithm for non-iterative multireference coupled cluster (MRCC) theories, which merges recently introduced reference-level parallelism (RLP) [K. Bhaskaran-Nair, J.Brabec, E. Aprà, H.J.J. van Dam, J. Pittner, K. Kowalski, J. Chem. Phys. 137, 094112 (2012)] with the possibility of accelerating numerical calculations using graphics processing unit (GPU) is presented. We discuss the performance of this algorithm on the example of the MRCCSD(T) method (iterative singles and doubles and perturbative triples), where the corrections due to triples are added to the diagonal elements of the MRCCSD (iterative singles and doubles) effective Hamiltonian matrix. The performance of the combined RLP/GPU algorithmmore » is illustrated on the example of the Brillouin-Wigner (BW) and Mukherjee (Mk) state-specific MRCCSD(T) formulations.« less

Hybrid cloud and cluster computing paradigms for life science applications

PubMed Central

2010-01-01

Background Clouds and MapReduce have shown themselves to be a broadly useful approach to scientific computing especially for parallel data intensive applications. However they have limited applicability to some areas such as data mining because MapReduce has poor performance on problems with an iterative structure present in the linear algebra that underlies much data analysis. Such problems can be run efficiently on clusters using MPI leading to a hybrid cloud and cluster environment. This motivates the design and implementation of an open source Iterative MapReduce system Twister. Results Comparisons of Amazon, Azure, and traditional Linux and Windows environments on common applications have shown encouraging performance and usability comparisons in several important non iterative cases. These are linked to MPI applications for final stages of the data analysis. Further we have released the open source Twister Iterative MapReduce and benchmarked it against basic MapReduce (Hadoop) and MPI in information retrieval and life sciences applications. Conclusions The hybrid cloud (MapReduce) and cluster (MPI) approach offers an attractive production environment while Twister promises a uniform programming environment for many Life Sciences applications. Methods We used commercial clouds Amazon and Azure and the NSF resource FutureGrid to perform detailed comparisons and evaluations of different approaches to data intensive computing. Several applications were developed in MPI, MapReduce and Twister in these different environments. PMID:21210982

Hybrid cloud and cluster computing paradigms for life science applications.

PubMed

Qiu, Judy; Ekanayake, Jaliya; Gunarathne, Thilina; Choi, Jong Youl; Bae, Seung-Hee; Li, Hui; Zhang, Bingjing; Wu, Tak-Lon; Ruan, Yang; Ekanayake, Saliya; Hughes, Adam; Fox, Geoffrey

2010-12-21

Clouds and MapReduce have shown themselves to be a broadly useful approach to scientific computing especially for parallel data intensive applications. However they have limited applicability to some areas such as data mining because MapReduce has poor performance on problems with an iterative structure present in the linear algebra that underlies much data analysis. Such problems can be run efficiently on clusters using MPI leading to a hybrid cloud and cluster environment. This motivates the design and implementation of an open source Iterative MapReduce system Twister. Comparisons of Amazon, Azure, and traditional Linux and Windows environments on common applications have shown encouraging performance and usability comparisons in several important non iterative cases. These are linked to MPI applications for final stages of the data analysis. Further we have released the open source Twister Iterative MapReduce and benchmarked it against basic MapReduce (Hadoop) and MPI in information retrieval and life sciences applications. The hybrid cloud (MapReduce) and cluster (MPI) approach offers an attractive production environment while Twister promises a uniform programming environment for many Life Sciences applications. We used commercial clouds Amazon and Azure and the NSF resource FutureGrid to perform detailed comparisons and evaluations of different approaches to data intensive computing. Several applications were developed in MPI, MapReduce and Twister in these different environments.

A Two Colorable Fourth Order Compact Difference Scheme and Parallel Iterative Solution of the 3D Convection Diffusion Equation

NASA Technical Reports Server (NTRS)

Zhang, Jun; Ge, Lixin; Kouatchou, Jules

2000-01-01

A new fourth order compact difference scheme for the three dimensional convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it Only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with the Gauss-Seidel type iterative method. This is compared with the known 19 point fourth order compact differenCe scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15 point and the 19 point fourth order compact schemes.

Xyce

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thomquist, Heidi K.; Fixel, Deborah A.; Fett, David Brian

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory

NASA Astrophysics Data System (ADS)

Jia, Weile; Lin, Lin

2017-10-01

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory.

PubMed

Jia, Weile; Lin, Lin

2017-10-14

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

A survey of packages for large linear systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Kesheng; Milne, Brent

2000-02-11

This paper evaluates portable software packages for the iterative solution of very large sparse linear systems on parallel architectures. While we cannot hope to tell individual users which package will best suit their needs, we do hope that our systematic evaluation provides essential unbiased information about the packages and the evaluation process may serve as an example on how to evaluate these packages. The information contained here include feature comparisons, usability evaluations and performance characterizations. This review is primarily focused on self-contained packages that can be easily integrated into an existing program and are capable of computing solutions to verymore » large sparse linear systems of equations. More specifically, it concentrates on portable parallel linear system solution packages that provide iterative solution schemes and related preconditioning schemes because iterative methods are more frequently used than competing schemes such as direct methods. The eight packages evaluated are: Aztec, BlockSolve,ISIS++, LINSOL, P-SPARSLIB, PARASOL, PETSc, and PINEAPL. Among the eight portable parallel iterative linear system solvers reviewed, we recommend PETSc and Aztec for most application programmers because they have well designed user interface, extensive documentation and very responsive user support. Both PETSc and Aztec are written in the C language and are callable from Fortran. For those users interested in using Fortran 90, PARASOL is a good alternative. ISIS++is a good alternative for those who prefer the C++ language. Both PARASOL and ISIS++ are relatively new and are continuously evolving. Thus their user interface may change. In general, those packages written in Fortran 77 are more cumbersome to use because the user may need to directly deal with a number of arrays of varying sizes. Languages like C++ and Fortran 90 offer more convenient data encapsulation mechanisms which make it easier to implement a clean and intuitive user interface. In addition to reviewing these portable parallel iterative solver packages, we also provide a more cursory assessment of a range of related packages, from specialized parallel preconditioners to direct methods for sparse linear systems.« less

Acceleration of the Particle Swarm Optimization for Peierls-Nabarro modeling of dislocations in conventional and high-entropy alloys

NASA Astrophysics Data System (ADS)

Pei, Zongrui; Eisenbach, Markus

2017-06-01

Dislocations are among the most important defects in determining the mechanical properties of both conventional alloys and high-entropy alloys. The Peierls-Nabarro model supplies an efficient pathway to their geometries and mobility. The difficulty in solving the integro-differential Peierls-Nabarro equation is how to effectively avoid the local minima in the energy landscape of a dislocation core. Among the other methods to optimize the dislocation core structures, we choose the algorithm of Particle Swarm Optimization, an algorithm that simulates the social behaviors of organisms. By employing more particles (bigger swarm) and more iterative steps (allowing them to explore for longer time), the local minima can be effectively avoided. But this would require more computational cost. The advantage of this algorithm is that it is readily parallelized in modern high computing architecture. We demonstrate the performance of our parallelized algorithm scales linearly with the number of employed cores.

Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.; Ovall, J.; Holst, M.

2014-12-01

We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented adaptive refinement code named MARE2DEM. We demonstrate the performance and parallel scaling of this algorithm on a medium-scale computing cluster with a marine controlled-source EM example that includes a 3D array of receivers located over a 3D model that includes significant seafloor bathymetry variations and a heterogeneous subsurface.

Efficient generation of discontinuity-preserving adaptive triangulations from range images.

PubMed

Garcia, Miguel Angel; Sappa, Angel Domingo

2004-10-01

This paper presents an efficient technique for generating adaptive triangular meshes from range images. The algorithm consists of two stages. First, a user-defined number of points is adaptively sampled from the given range image. Those points are chosen by taking into account the surface shapes represented in the range image in such a way that points tend to group in areas of high curvature and to disperse in low-variation regions. This selection process is done through a noniterative, inherently parallel algorithm in order to gain efficiency. Once the image has been subsampled, the second stage applies a two and one half-dimensional Delaunay triangulation to obtain an initial triangular mesh. To favor the preservation of surface and orientation discontinuities (jump and crease edges) present in the original range image, the aforementioned triangular mesh is iteratively modified by applying an efficient edge flipping technique. Results with real range images show accurate triangular approximations of the given range images with low processing times.

SQDFT: Spectral Quadrature method for large-scale parallel O(N) Kohn-Sham calculations at high temperature

NASA Astrophysics Data System (ADS)

Suryanarayana, Phanish; Pratapa, Phanisri P.; Sharma, Abhiraj; Pask, John E.

2018-03-01

We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method for O(N) Kohn-Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw-Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw-Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. We further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect O(N) scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.

On the Development of an Efficient Parallel Hybrid Solver with Application to Acoustically Treated Aero-Engine Nacelles

NASA Technical Reports Server (NTRS)

Watson, Willie R.; Nark, Douglas M.; Nguyen, Duc T.; Tungkahotara, Siroj

2006-01-01

A finite element solution to the convected Helmholtz equation in a nonuniform flow is used to model the noise field within 3-D acoustically treated aero-engine nacelles. Options to select linear or cubic Hermite polynomial basis functions and isoparametric elements are included. However, the key feature of the method is a domain decomposition procedure that is based upon the inter-mixing of an iterative and a direct solve strategy for solving the discrete finite element equations. This procedure is optimized to take full advantage of sparsity and exploit the increased memory and parallel processing capability of modern computer architectures. Example computations are presented for the Langley Flow Impedance Test facility and a rectangular mapping of a full scale, generic aero-engine nacelle. The accuracy and parallel performance of this new solver are tested on both model problems using a supercomputer that contains hundreds of central processing units. Results show that the method gives extremely accurate attenuation predictions, achieves super-linear speedup over hundreds of CPUs, and solves upward of 25 million complex equations in a quarter of an hour.

NDetermin: Inferring Nondeterministic Sequential Specifications for Parallelism Correctness

DTIC Science & Technology

2011-12-16

other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a...Lab affiliates National Instruments, NEC, Nokia , NVIDIA, and Samsung. NDetermin: Inferring Nondeterministic Sequential Specifications for Parallelism...concurrently update x, some of these CAS’s will fail and those parallel loop iterations will recompute their updates to x and try again. Consider the parallel

Learning control system design based on 2-D theory - An application to parallel link manipulator

NASA Technical Reports Server (NTRS)

Geng, Z.; Carroll, R. L.; Lee, J. D.; Haynes, L. H.

1990-01-01

An approach to iterative learning control system design based on two-dimensional system theory is presented. A two-dimensional model for the iterative learning control system which reveals the connections between learning control systems and two-dimensional system theory is established. A learning control algorithm is proposed, and the convergence of learning using this algorithm is guaranteed by two-dimensional stability. The learning algorithm is applied successfully to the trajectory tracking control problem for a parallel link robot manipulator. The excellent performance of this learning algorithm is demonstrated by the computer simulation results.

Adaptive implicit-explicit and parallel element-by-element iteration schemes

NASA Technical Reports Server (NTRS)

Tezduyar, T. E.; Liou, J.; Nguyen, T.; Poole, S.

1989-01-01

Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.

2D Seismic Imaging of Elastic Parameters by Frequency Domain Full Waveform Inversion

NASA Astrophysics Data System (ADS)

Brossier, R.; Virieux, J.; Operto, S.

2008-12-01

Thanks to recent advances in parallel computing, full waveform inversion is today a tractable seismic imaging method to reconstruct physical parameters of the earth interior at different scales ranging from the near- surface to the deep crust. We present a massively parallel 2D frequency-domain full-waveform algorithm for imaging visco-elastic media from multi-component seismic data. The forward problem (i.e. the resolution of the frequency-domain 2D PSV elastodynamics equations) is based on low-order Discontinuous Galerkin (DG) method (P0 and/or P1 interpolations). Thanks to triangular unstructured meshes, the DG method allows accurate modeling of both body waves and surface waves in case of complex topography for a discretization of 10 to 15 cells per shear wavelength. The frequency-domain DG system is solved efficiently for multiple sources with the parallel direct solver MUMPS. The local inversion procedure (i.e. minimization of residuals between observed and computed data) is based on the adjoint-state method which allows to efficiently compute the gradient of the objective function. Applying the inversion hierarchically from the low frequencies to the higher ones defines a multiresolution imaging strategy which helps convergence towards the global minimum. In place of expensive Newton algorithm, the combined use of the diagonal terms of the approximate Hessian matrix and optimization algorithms based on quasi-Newton methods (Conjugate Gradient, LBFGS, ...) allows to improve the convergence of the iterative inversion. The distribution of forward problem solutions over processors driven by a mesh partitioning performed by METIS allows to apply most of the inversion in parallel. We shall present the main features of the parallel modeling/inversion algorithm, assess its scalability and illustrate its performances with realistic synthetic case studies.

Soft-output decoding algorithms in iterative decoding of turbo codes

NASA Technical Reports Server (NTRS)

Benedetto, S.; Montorsi, G.; Divsalar, D.; Pollara, F.

1996-01-01

In this article, we present two versions of a simplified maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring code trellis termination. A heuristic explanation is also given of how to embed the maximum a posteriori algorithms into the iterative decoding of parallel concatenated codes (turbo codes). The performances of the two algorithms are compared on the basis of a powerful rate 1/3 parallel concatenated code. Basic circuits to implement the simplified a posteriori decoding algorithm using lookup tables, and two further approximations (linear and threshold), with a very small penalty, to eliminate the need for lookup tables are proposed.

Limits on the Efficiency of Event-Based Algorithms for Monte Carlo Neutron Transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romano, Paul K.; Siegel, Andrew R.

The traditional form of parallelism in Monte Carlo particle transport simulations, wherein each individual particle history is considered a unit of work, does not lend itself well to data-level parallelism. Event-based algorithms, which were originally used for simulations on vector processors, may offer a path toward better utilizing data-level parallelism in modern computer architectures. In this study, a simple model is developed for estimating the efficiency of the event-based particle transport algorithm under two sets of assumptions. Data collected from simulations of four reactor problems using OpenMC was then used in conjunction with the models to calculate the speedup duemore » to vectorization as a function of two parameters: the size of the particle bank and the vector width. When each event type is assumed to have constant execution time, the achievable speedup is directly related to the particle bank size. We observed that the bank size generally needs to be at least 20 times greater than vector size in order to achieve vector efficiency greater than 90%. When the execution times for events are allowed to vary, however, the vector speedup is also limited by differences in execution time for events being carried out in a single event-iteration. For some problems, this implies that vector effciencies over 50% may not be attainable. While there are many factors impacting performance of an event-based algorithm that are not captured by our model, it nevertheless provides insights into factors that may be limiting in a real implementation.« less

Algebraic multigrid preconditioning within parallel finite-element solvers for 3-D electromagnetic modelling problems in geophysics

NASA Astrophysics Data System (ADS)

Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María

2014-06-01

We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the parallel context.

Comparison of multihardware parallel implementations for a phase unwrapping algorithm

NASA Astrophysics Data System (ADS)

Hernandez-Lopez, Francisco Javier; Rivera, Mariano; Salazar-Garibay, Adan; Legarda-Sáenz, Ricardo

2018-04-01

Phase unwrapping is an important problem in the areas of optical metrology, synthetic aperture radar (SAR) image analysis, and magnetic resonance imaging (MRI) analysis. These images are becoming larger in size and, particularly, the availability and need for processing of SAR and MRI data have increased significantly with the acquisition of remote sensing data and the popularization of magnetic resonators in clinical diagnosis. Therefore, it is important to develop faster and accurate phase unwrapping algorithms. We propose a parallel multigrid algorithm of a phase unwrapping method named accumulation of residual maps, which builds on a serial algorithm that consists of the minimization of a cost function; minimization achieved by means of a serial Gauss-Seidel kind algorithm. Our algorithm also optimizes the original cost function, but unlike the original work, our algorithm is a parallel Jacobi class with alternated minimizations. This strategy is known as the chessboard type, where red pixels can be updated in parallel at same iteration since they are independent. Similarly, black pixels can be updated in parallel in an alternating iteration. We present parallel implementations of our algorithm for different parallel multicore architecture such as CPU-multicore, Xeon Phi coprocessor, and Nvidia graphics processing unit. In all the cases, we obtain a superior performance of our parallel algorithm when compared with the original serial version. In addition, we present a detailed comparative performance of the developed parallel versions.

Hierarchical Image Segmentation of Remotely Sensed Data using Massively Parallel GNU-LINUX Software

NASA Technical Reports Server (NTRS)

Tilton, James C.

2003-01-01

A hierarchical set of image segmentations is a set of several image segmentations of the same image at different levels of detail in which the segmentations at coarser levels of detail can be produced from simple merges of regions at finer levels of detail. In [1], Tilton, et a1 describes an approach for producing hierarchical segmentations (called HSEG) and gave a progress report on exploiting these hierarchical segmentations for image information mining. The HSEG algorithm is a hybrid of region growing and constrained spectral clustering that produces a hierarchical set of image segmentations based on detected convergence points. In the main, HSEG employs the hierarchical stepwise optimization (HSWO) approach to region growing, which was described as early as 1989 by Beaulieu and Goldberg. The HSWO approach seeks to produce segmentations that are more optimized than those produced by more classic approaches to region growing (e.g. Horowitz and T. Pavlidis, [3]). In addition, HSEG optionally interjects between HSWO region growing iterations, merges between spatially non-adjacent regions (i.e., spectrally based merging or clustering) constrained by a threshold derived from the previous HSWO region growing iteration. While the addition of constrained spectral clustering improves the utility of the segmentation results, especially for larger images, it also significantly increases HSEG s computational requirements. To counteract this, a computationally efficient recursive, divide-and-conquer, implementation of HSEG (RHSEG) was devised, which includes special code to avoid processing artifacts caused by RHSEG s recursive subdivision of the image data. The recursive nature of RHSEG makes for a straightforward parallel implementation. This paper describes the HSEG algorithm, its recursive formulation (referred to as RHSEG), and the implementation of RHSEG using massively parallel GNU-LINUX software. Results with Landsat TM data are included comparing RHSEG with classic region growing.

FaCSI: A block parallel preconditioner for fluid-structure interaction in hemodynamics

NASA Astrophysics Data System (ADS)

Deparis, Simone; Forti, Davide; Grandperrin, Gwenol; Quarteroni, Alfio

2016-12-01

Modeling Fluid-Structure Interaction (FSI) in the vascular system is mandatory to reliably compute mechanical indicators in vessels undergoing large deformations. In order to cope with the computational complexity of the coupled 3D FSI problem after discretizations in space and time, a parallel solution is often mandatory. In this paper we propose a new block parallel preconditioner for the coupled linearized FSI system obtained after space and time discretization. We name it FaCSI to indicate that it exploits the Factorized form of the linearized FSI matrix, the use of static Condensation to formally eliminate the interface degrees of freedom of the fluid equations, and the use of a SIMPLE preconditioner for saddle-point problems. FaCSI is built upon a block Gauss-Seidel factorization of the FSI Jacobian matrix and it uses ad-hoc preconditioners for each physical component of the coupled problem, namely the fluid, the structure and the geometry. In the fluid subproblem, after operating static condensation of the interface fluid variables, we use a SIMPLE preconditioner on the reduced fluid matrix. Moreover, to efficiently deal with a large number of processes, FaCSI exploits efficient single field preconditioners, e.g., based on domain decomposition or the multigrid method. We measure the parallel performances of FaCSI on a benchmark cylindrical geometry and on a problem of physiological interest, namely the blood flow through a patient-specific femoropopliteal bypass. We analyze the dependence of the number of linear solver iterations on the cores count (scalability of the preconditioner) and on the mesh size (optimality).

Efficient Parallel Formulations of Hierarchical Methods and Their Applications

NASA Astrophysics Data System (ADS)

Grama, Ananth Y.

1996-01-01

Hierarchical methods such as the Fast Multipole Method (FMM) and Barnes-Hut (BH) are used for rapid evaluation of potential (gravitational, electrostatic) fields in particle systems. They are also used for solving integral equations using boundary element methods. The linear systems arising from these methods are dense and are solved iteratively. Hierarchical methods reduce the complexity of the core matrix-vector product from O(n^2) to O(n log n) and the memory requirement from O(n^2) to O(n). We have developed highly scalable parallel formulations of a hybrid FMM/BH method that are capable of handling arbitrarily irregular distributions. We apply these formulations to astrophysical simulations of Plummer and Gaussian galaxies. We have used our parallel formulations to solve the integral form of the Laplace equation. We show that our parallel hierarchical mat-vecs yield high efficiency and overall performance even on relatively small problems. A problem containing approximately 200K nodes takes under a second to compute on 256 processors and yet yields over 85% efficiency. The efficiency and raw performance is expected to increase for bigger problems. For the 200K node problem, our code delivers about 5 GFLOPS of performance on a 256 processor T3D. This is impressive considering the fact that the problem has floating point divides and roots, and very little locality resulting in poor cache performance. A dense matrix-vector product of the same dimensions would require about 0.5 TeraBytes of memory and about 770 TeraFLOPS of computing speed. Clearly, if the loss in accuracy resulting from the use of hierarchical methods is acceptable, our code yields significant savings in time and memory. We also study the convergence of a GMRES solver built around this mat-vec. We accelerate the convergence of the solver using three preconditioning techniques: diagonal scaling, block-diagonal preconditioning, and inner-outer preconditioning. We study the performance and parallel efficiency of these preconditioned solvers. Using this solver, we solve dense linear systems with hundreds of thousands of unknowns. Solving a 105K unknown problem takes about 10 minutes on a 64 processor T3D. Until very recently, boundary element problems of this magnitude could not even be generated, let alone solved.

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

NASA Astrophysics Data System (ADS)

Shao, Meiyue; Aktulga, H. Metin; Yang, Chao; Ng, Esmond G.; Maris, Pieter; Vary, James P.

2018-01-01

We describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. The use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. We also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.

Complex wet-environments in electronic-structure calculations

NASA Astrophysics Data System (ADS)

Fisicaro, Giuseppe; Genovese, Luigi; Andreussi, Oliviero; Marzari, Nicola; Goedecker, Stefan

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of an applied electrochemical potentials, including complex electrostatic screening coming from the solvent. In the present work we present a solver to handle both the Generalized Poisson and the Poisson-Boltzmann equation. A preconditioned conjugate gradient (PCG) method has been implemented for the Generalized Poisson and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations. On the other hand, a self-consistent procedure enables us to solve the Poisson-Boltzmann problem. The algorithms take advantage of a preconditioning procedure based on the BigDFT Poisson solver for the standard Poisson equation. They exhibit very high accuracy and parallel efficiency, and allow different boundary conditions, including surfaces. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and it will be released as a independent program, suitable for integration in other codes. We present test calculations for large proteins to demonstrate efficiency and performances. This work was done within the PASC and NCCR MARVEL projects. Computer resources were provided by the Swiss National Supercomputing Centre (CSCS) under Project ID s499. LG acknowledges also support from the EXTMOS EU project.

Solution of a tridiagonal system of equations on the finite element machine

NASA Technical Reports Server (NTRS)

Bostic, S. W.

1984-01-01

Two parallel algorithms for the solution of tridiagonal systems of equations were implemented on the Finite Element Machine. The Accelerated Parallel Gauss method, an iterative method, and the Buneman algorithm, a direct method, are discussed and execution statistics are presented.

Fast Time and Space Parallel Algorithms for Solution of Parabolic Partial Differential Equations

NASA Technical Reports Server (NTRS)

Fijany, Amir

1993-01-01

In this paper, fast time- and Space -Parallel agorithms for solution of linear parabolic PDEs are developed. It is shown that the seemingly strictly serial iterations of the time-stepping procedure for solution of the problem can be completed decoupled.

Hybrid parallelization of the XTOR-2F code for the simulation of two-fluid MHD instabilities in tokamaks

NASA Astrophysics Data System (ADS)

Marx, Alain; Lütjens, Hinrich

2017-03-01

A hybrid MPI/OpenMP parallel version of the XTOR-2F code [Lütjens and Luciani, J. Comput. Phys. 229 (2010) 8130] solving the two-fluid MHD equations in full tokamak geometry by means of an iterative Newton-Krylov matrix-free method has been developed. The present work shows that the code has been parallelized significantly despite the numerical profile of the problem solved by XTOR-2F, i.e. a discretization with pseudo-spectral representations in all angular directions, the stiffness of the two-fluid stability problem in tokamaks, and the use of a direct LU decomposition to invert the physical pre-conditioner at every Krylov iteration of the solver. The execution time of the parallelized version is an order of magnitude smaller than the sequential one for low resolution cases, with an increasing speedup when the discretization mesh is refined. Moreover, it allows to perform simulations with higher resolutions, previously forbidden because of memory limitations.

Parallel fast multipole boundary element method applied to computational homogenization

NASA Astrophysics Data System (ADS)

Ptaszny, Jacek

2018-01-01

In the present work, a fast multipole boundary element method (FMBEM) and a parallel computer code for 3D elasticity problem is developed and applied to the computational homogenization of a solid containing spherical voids. The system of equation is solved by using the GMRES iterative solver. The boundary of the body is dicretized by using the quadrilateral serendipity elements with an adaptive numerical integration. Operations related to a single GMRES iteration, performed by traversing the corresponding tree structure upwards and downwards, are parallelized by using the OpenMP standard. The assignment of tasks to threads is based on the assumption that the tree nodes at which the moment transformations are initialized can be partitioned into disjoint sets of equal or approximately equal size and assigned to the threads. The achieved speedup as a function of number of threads is examined.

The Battlefield Environment Division Modeling Framework (BMF). Part 1: Optimizing the Atmospheric Boundary Layer Environment Model for Cluster Computing

DTIC Science & Technology

2014-02-01

idle waiting for the wavefront to reach it. To overcome this, Reeve et al. (2001) 3 developed a scheme in analogy to the red-black Gauss - Seidel iterative ...understandable procedure calls. Parallelization of the SIMPLE iterative scheme with SIP used a red-black scheme similar to the red-black Gauss - Seidel ...scheme, the SIMPLE method, for pressure-velocity coupling. The result is a slowing convergence of the outer iterations . The red-black scheme excites a 2

Development of parallel algorithms for electrical power management in space applications

NASA Technical Reports Server (NTRS)

Berry, Frederick C.

1989-01-01

The application of parallel techniques for electrical power system analysis is discussed. The Newton-Raphson method of load flow analysis was used along with the decomposition-coordination technique to perform load flow analysis. The decomposition-coordination technique enables tasks to be performed in parallel by partitioning the electrical power system into independent local problems. Each independent local problem represents a portion of the total electrical power system on which a loan flow analysis can be performed. The load flow analysis is performed on these partitioned elements by using the Newton-Raphson load flow method. These independent local problems will produce results for voltage and power which can then be passed to the coordinator portion of the solution procedure. The coordinator problem uses the results of the local problems to determine if any correction is needed on the local problems. The coordinator problem is also solved by an iterative method much like the local problem. The iterative method for the coordination problem will also be the Newton-Raphson method. Therefore, each iteration at the coordination level will result in new values for the local problems. The local problems will have to be solved again along with the coordinator problem until some convergence conditions are met.

Research in computer science

NASA Technical Reports Server (NTRS)

Ortega, J. M.

1986-01-01

Various graduate research activities in the field of computer science are reported. Among the topics discussed are: (1) failure probabilities in multi-version software; (2) Gaussian Elimination on parallel computers; (3) three dimensional Poisson solvers on parallel/vector computers; (4) automated task decomposition for multiple robot arms; (5) multi-color incomplete cholesky conjugate gradient methods on the Cyber 205; and (6) parallel implementation of iterative methods for solving linear equations.

Parallel implementation of the particle simulation method with dynamic load balancing: Toward realistic geodynamical simulation

NASA Astrophysics Data System (ADS)

Furuichi, M.; Nishiura, D.

2015-12-01

Fully Lagrangian methods such as Smoothed Particle Hydrodynamics (SPH) and Discrete Element Method (DEM) have been widely used to solve the continuum and particles motions in the computational geodynamics field. These mesh-free methods are suitable for the problems with the complex geometry and boundary. In addition, their Lagrangian nature allows non-diffusive advection useful for tracking history dependent properties (e.g. rheology) of the material. These potential advantages over the mesh-based methods offer effective numerical applications to the geophysical flow and tectonic processes, which are for example, tsunami with free surface and floating body, magma intrusion with fracture of rock, and shear zone pattern generation of granular deformation. In order to investigate such geodynamical problems with the particle based methods, over millions to billion particles are required for the realistic simulation. Parallel computing is therefore important for handling such huge computational cost. An efficient parallel implementation of SPH and DEM methods is however known to be difficult especially for the distributed-memory architecture. Lagrangian methods inherently show workload imbalance problem for parallelization with the fixed domain in space, because particles move around and workloads change during the simulation. Therefore dynamic load balance is key technique to perform the large scale SPH and DEM simulation. In this work, we present the parallel implementation technique of SPH and DEM method utilizing dynamic load balancing algorithms toward the high resolution simulation over large domain using the massively parallel super computer system. Our method utilizes the imbalances of the executed time of each MPI process as the nonlinear term of parallel domain decomposition and minimizes them with the Newton like iteration method. In order to perform flexible domain decomposition in space, the slice-grid algorithm is used. Numerical tests show that our approach is suitable for solving the particles with different calculation costs (e.g. boundary particles) as well as the heterogeneous computer architecture. We analyze the parallel efficiency and scalability on the super computer systems (K-computer, Earth simulator 3, etc.).

Efficient parallel reconstruction for high resolution multishot spiral diffusion data with low rank constraint.

PubMed

Liao, Congyu; Chen, Ying; Cao, Xiaozhi; Chen, Song; He, Hongjian; Mani, Merry; Jacob, Mathews; Magnotta, Vincent; Zhong, Jianhui

2017-03-01

To propose a novel reconstruction method using parallel imaging with low rank constraint to accelerate high resolution multishot spiral diffusion imaging. The undersampled high resolution diffusion data were reconstructed based on a low rank (LR) constraint using similarities between the data of different interleaves from a multishot spiral acquisition. The self-navigated phase compensation using the low resolution phase data in the center of k-space was applied to correct shot-to-shot phase variations induced by motion artifacts. The low rank reconstruction was combined with sensitivity encoding (SENSE) for further acceleration. The efficiency of the proposed joint reconstruction framework, dubbed LR-SENSE, was evaluated through error quantifications and compared with ℓ1 regularized compressed sensing method and conventional iterative SENSE method using the same datasets. It was shown that with a same acceleration factor, the proposed LR-SENSE method had the smallest normalized sum-of-squares errors among all the compared methods in all diffusion weighted images and DTI-derived index maps, when evaluated with different acceleration factors (R = 2, 3, 4) and for all the acquired diffusion directions. Robust high resolution diffusion weighted image can be efficiently reconstructed from highly undersampled multishot spiral data with the proposed LR-SENSE method. Magn Reson Med 77:1359-1366, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

GPU-Accelerated Forward and Back-Projections with Spatially Varying Kernels for 3D DIRECT TOF PET Reconstruction.

PubMed

Ha, S; Matej, S; Ispiryan, M; Mueller, K

2013-02-01

We describe a GPU-accelerated framework that efficiently models spatially (shift) variant system response kernels and performs forward- and back-projection operations with these kernels for the DIRECT (Direct Image Reconstruction for TOF) iterative reconstruction approach. Inherent challenges arise from the poor memory cache performance at non-axis aligned TOF directions. Focusing on the GPU memory access patterns, we utilize different kinds of GPU memory according to these patterns in order to maximize the memory cache performance. We also exploit the GPU instruction-level parallelism to efficiently hide long latencies from the memory operations. Our experiments indicate that our GPU implementation of the projection operators has slightly faster or approximately comparable time performance than FFT-based approaches using state-of-the-art FFTW routines. However, most importantly, our GPU framework can also efficiently handle any generic system response kernels, such as spatially symmetric and shift-variant as well as spatially asymmetric and shift-variant, both of which an FFT-based approach cannot cope with.

GPU-Accelerated Forward and Back-Projections With Spatially Varying Kernels for 3D DIRECT TOF PET Reconstruction

NASA Astrophysics Data System (ADS)

Ha, S.; Matej, S.; Ispiryan, M.; Mueller, K.

2013-02-01

We describe a GPU-accelerated framework that efficiently models spatially (shift) variant system response kernels and performs forward- and back-projection operations with these kernels for the DIRECT (Direct Image Reconstruction for TOF) iterative reconstruction approach. Inherent challenges arise from the poor memory cache performance at non-axis aligned TOF directions. Focusing on the GPU memory access patterns, we utilize different kinds of GPU memory according to these patterns in order to maximize the memory cache performance. We also exploit the GPU instruction-level parallelism to efficiently hide long latencies from the memory operations. Our experiments indicate that our GPU implementation of the projection operators has slightly faster or approximately comparable time performance than FFT-based approaches using state-of-the-art FFTW routines. However, most importantly, our GPU framework can also efficiently handle any generic system response kernels, such as spatially symmetric and shift-variant as well as spatially asymmetric and shift-variant, both of which an FFT-based approach cannot cope with.

Adapting high-level language programs for parallel processing using data flow

NASA Technical Reports Server (NTRS)

Standley, Hilda M.

1988-01-01

EASY-FLOW, a very high-level data flow language, is introduced for the purpose of adapting programs written in a conventional high-level language to a parallel environment. The level of parallelism provided is of the large-grained variety in which parallel activities take place between subprograms or processes. A program written in EASY-FLOW is a set of subprogram calls as units, structured by iteration, branching, and distribution constructs. A data flow graph may be deduced from an EASY-FLOW program.

Current status and recent research achievements in ferritic/martensitic steels

NASA Astrophysics Data System (ADS)

Tavassoli, A.-A. F.; Diegele, E.; Lindau, R.; Luzginova, N.; Tanigawa, H.

2014-12-01

When the austenitic stainless steel 316L(N) was selected for ITER, it was well known that it would not be suitable for DEMO and fusion reactors due to its irradiation swelling at high doses. A parallel programme to ITER collaboration already had been put in place, under an IEA fusion materials implementing agreement for the development of a low activation ferritic/martensitic steel, known for their excellent high dose irradiation swelling resistance. After extensive screening tests on different compositions of Fe-Cr alloys, the chromium range was narrowed to 7-9% and the first RAFM was industrially produced in Japan (F82H: Fe-8%Cr-2%W-TaV). All IEA partners tested this steel and contributed to its maturity. In parallel several other RAFM steels were produced in other countries. From those experiences and also for improving neutron efficiency and corrosion resistance, European Union opted for a higher chromium lower tungsten grade, Fe-9%Cr-1%W-TaV steel (Eurofer), and in 1997 ordered the first industrial heats. Other industrial heats have been produced since and characterised in different states, including irradiated up to 80 dpa. China, India, Russia, Korea and US have also produced their grades of RAFM steels, contributing to overall maturity of these steels. This paper reviews the work done on RAFM steels by the fusion materials community over the past 30 years, in particular on the Eurofer steel and its design code qualification for RCC-MRx.

Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

DOE PAGES

Zhang, Bo; Lu, Benzhuo; Cheng, Xiaolin; ...

2013-01-01

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numericalmore » results.« less

Acceleration of the Particle Swarm Optimization for Peierls–Nabarro modeling of dislocations in conventional and high-entropy alloys

DOE PAGES

Pei, Zongrui; Max-Planck-Inst. fur Eisenforschung, Duseldorf; Eisenbach, Markus

2017-02-06

Dislocations are among the most important defects in determining the mechanical properties of both conventional alloys and high-entropy alloys. The Peierls-Nabarro model supplies an efficient pathway to their geometries and mobility. The difficulty in solving the integro-differential Peierls-Nabarro equation is how to effectively avoid the local minima in the energy landscape of a dislocation core. Among the other methods to optimize the dislocation core structures, we choose the algorithm of Particle Swarm Optimization, an algorithm that simulates the social behaviors of organisms. By employing more particles (bigger swarm) and more iterative steps (allowing them to explore for longer time), themore » local minima can be effectively avoided. But this would require more computational cost. The advantage of this algorithm is that it is readily parallelized in modern high computing architecture. We demonstrate the performance of our parallelized algorithm scales linearly with the number of employed cores.« less

Parallel processing of real-time dynamic systems simulation on OSCAR (Optimally SCheduled Advanced multiprocessoR)

NASA Technical Reports Server (NTRS)

Kasahara, Hironori; Honda, Hiroki; Narita, Seinosuke

1989-01-01

Parallel processing of real-time dynamic systems simulation on a multiprocessor system named OSCAR is presented. In the simulation of dynamic systems, generally, the same calculation are repeated every time step. However, we cannot apply to Do-all or the Do-across techniques for parallel processing of the simulation since there exist data dependencies from the end of an iteration to the beginning of the next iteration and furthermore data-input and data-output are required every sampling time period. Therefore, parallelism inside the calculation required for a single time step, or a large basic block which consists of arithmetic assignment statements, must be used. In the proposed method, near fine grain tasks, each of which consists of one or more floating point operations, are generated to extract the parallelism from the calculation and assigned to processors by using optimal static scheduling at compile time in order to reduce large run time overhead caused by the use of near fine grain tasks. The practicality of the scheme is demonstrated on OSCAR (Optimally SCheduled Advanced multiprocessoR) which has been developed to extract advantageous features of static scheduling algorithms to the maximum extent.

SQDFT: Spectral Quadrature method for large-scale parallel O ( N ) Kohn–Sham calculations at high temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suryanarayana, Phanish; Pratapa, Phanisri P.; Sharma, Abhiraj

We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method formore » $$\\mathscr{O}(N)$$ Kohn–Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw–Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw–Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. Here, we further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect $$\\mathscr{O}(N)$$ scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.« less

SQDFT: Spectral Quadrature method for large-scale parallel O ( N ) Kohn–Sham calculations at high temperature

DOE PAGES

Suryanarayana, Phanish; Pratapa, Phanisri P.; Sharma, Abhiraj; ...

2017-12-07

We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method formore » $$\\mathscr{O}(N)$$ Kohn–Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw–Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw–Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. Here, we further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect $$\\mathscr{O}(N)$$ scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.« less

Face classification using electronic synapses

NASA Astrophysics Data System (ADS)

Yao, Peng; Wu, Huaqiang; Gao, Bin; Eryilmaz, Sukru Burc; Huang, Xueyao; Zhang, Wenqiang; Zhang, Qingtian; Deng, Ning; Shi, Luping; Wong, H.-S. Philip; Qian, He

2017-05-01

Conventional hardware platforms consume huge amount of energy for cognitive learning due to the data movement between the processor and the off-chip memory. Brain-inspired device technologies using analogue weight storage allow to complete cognitive tasks more efficiently. Here we present an analogue non-volatile resistive memory (an electronic synapse) with foundry friendly materials. The device shows bidirectional continuous weight modulation behaviour. Grey-scale face classification is experimentally demonstrated using an integrated 1024-cell array with parallel online training. The energy consumption within the analogue synapses for each iteration is 1,000 × (20 ×) lower compared to an implementation using Intel Xeon Phi processor with off-chip memory (with hypothetical on-chip digital resistive random access memory). The accuracy on test sets is close to the result using a central processing unit. These experimental results consolidate the feasibility of analogue synaptic array and pave the way toward building an energy efficient and large-scale neuromorphic system.

Face classification using electronic synapses.

PubMed

Yao, Peng; Wu, Huaqiang; Gao, Bin; Eryilmaz, Sukru Burc; Huang, Xueyao; Zhang, Wenqiang; Zhang, Qingtian; Deng, Ning; Shi, Luping; Wong, H-S Philip; Qian, He

2017-05-12

Conventional hardware platforms consume huge amount of energy for cognitive learning due to the data movement between the processor and the off-chip memory. Brain-inspired device technologies using analogue weight storage allow to complete cognitive tasks more efficiently. Here we present an analogue non-volatile resistive memory (an electronic synapse) with foundry friendly materials. The device shows bidirectional continuous weight modulation behaviour. Grey-scale face classification is experimentally demonstrated using an integrated 1024-cell array with parallel online training. The energy consumption within the analogue synapses for each iteration is 1,000 × (20 ×) lower compared to an implementation using Intel Xeon Phi processor with off-chip memory (with hypothetical on-chip digital resistive random access memory). The accuracy on test sets is close to the result using a central processing unit. These experimental results consolidate the feasibility of analogue synaptic array and pave the way toward building an energy efficient and large-scale neuromorphic system.

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

DOE PAGES

Shao, Meiyue; Aktulga, H.  Metin; Yang, Chao; ...

2017-09-14

In this paper, we describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. Themore » use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. Finally, we also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.« less

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shao, Meiyue; Aktulga, H.  Metin; Yang, Chao

In this paper, we describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. Themore » use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. Finally, we also discuss the implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.« less

Performance Analysis of Iterative Channel Estimation and Multiuser Detection in Multipath DS-CDMA Channels

NASA Astrophysics Data System (ADS)

Li, Husheng; Betz, Sharon M.; Poor, H. Vincent

2007-05-01

This paper examines the performance of decision feedback based iterative channel estimation and multiuser detection in channel coded aperiodic DS-CDMA systems operating over multipath fading channels. First, explicit expressions describing the performance of channel estimation and parallel interference cancellation based multiuser detection are developed. These results are then combined to characterize the evolution of the performance of a system that iterates among channel estimation, multiuser detection and channel decoding. Sufficient conditions for convergence of this system to a unique fixed point are developed.

Local sharpening and subspace wavefront correction with predictive dynamic digital holography

NASA Astrophysics Data System (ADS)

Sulaiman, Sennan; Gibson, Steve

2017-09-01

Digital holography holds several advantages over conventional imaging and wavefront sensing, chief among these being significantly fewer and simpler optical components and the retrieval of complex field. Consequently, many imaging and sensing applications including microscopy and optical tweezing have turned to using digital holography. A significant obstacle for digital holography in real-time applications, such as wavefront sensing for high energy laser systems and high speed imaging for target racking, is the fact that digital holography is computationally intensive; it requires iterative virtual wavefront propagation and hill-climbing to optimize some sharpness criteria. It has been shown recently that minimum-variance wavefront prediction can be integrated with digital holography and image sharpening to reduce significantly large number of costly sharpening iterations required to achieve near-optimal wavefront correction. This paper demonstrates further gains in computational efficiency with localized sharpening in conjunction with predictive dynamic digital holography for real-time applications. The method optimizes sharpness of local regions in a detector plane by parallel independent wavefront correction on reduced-dimension subspaces of the complex field in a spectral plane.

FoSSI: the family of simplified solver interfaces for the rapid development of parallel numerical atmosphere and ocean models

NASA Astrophysics Data System (ADS)

Frickenhaus, Stephan; Hiller, Wolfgang; Best, Meike

The portable software FoSSI is introduced that—in combination with additional free solver software packages—allows for an efficient and scalable parallel solution of large sparse linear equations systems arising in finite element model codes. FoSSI is intended to support rapid model code development, completely hiding the complexity of the underlying solver packages. In particular, the model developer need not be an expert in parallelization and is yet free to switch between different solver packages by simple modifications of the interface call. FoSSI offers an efficient and easy, yet flexible interface to several parallel solvers, most of them available on the web, such as PETSC, AZTEC, MUMPS, PILUT and HYPRE. FoSSI makes use of the concept of handles for vectors, matrices, preconditioners and solvers, that is frequently used in solver libraries. Hence, FoSSI allows for a flexible treatment of several linear equations systems and associated preconditioners at the same time, even in parallel on separate MPI-communicators. The second special feature in FoSSI is the task specifier, being a combination of keywords, each configuring a certain phase in the solver setup. This enables the user to control a solver over one unique subroutine. Furthermore, FoSSI has rather similar features for all solvers, making a fast solver intercomparison or exchange an easy task. FoSSI is a community software, proven in an adaptive 2D-atmosphere model and a 3D-primitive equation ocean model, both formulated in finite elements. The present paper discusses perspectives of an OpenMP-implementation of parallel iterative solvers based on domain decomposition methods. This approach to OpenMP solvers is rather attractive, as the code for domain-local operations of factorization, preconditioning and matrix-vector product can be readily taken from a sequential implementation that is also suitable to be used in an MPI-variant. Code development in this direction is in an advanced state under the name ScOPES: the Scalable Open Parallel sparse linear Equations Solver.

Performance and capacity analysis of Poisson photon-counting based Iter-PIC OCDMA systems.

PubMed

Li, Lingbin; Zhou, Xiaolin; Zhang, Rong; Zhang, Dingchen; Hanzo, Lajos

2013-11-04

In this paper, an iterative parallel interference cancellation (Iter-PIC) technique is developed for optical code-division multiple-access (OCDMA) systems relying on shot-noise limited Poisson photon-counting reception. The novel semi-analytical tool of extrinsic information transfer (EXIT) charts is used for analysing both the bit error rate (BER) performance as well as the channel capacity of these systems and the results are verified by Monte Carlo simulations. The proposed Iter-PIC OCDMA system is capable of achieving two orders of magnitude BER improvements and a 0.1 nats of capacity improvement over the conventional chip-level OCDMA systems at a coding rate of 1/10.

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

DOE PAGES

Benzi, Michele; Evans, Thomas M.; Hamilton, Steven P.; ...

2017-03-05

Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

An efficient decoding for low density parity check codes

NASA Astrophysics Data System (ADS)

Zhao, Ling; Zhang, Xiaolin; Zhu, Manjie

2009-12-01

Low density parity check (LDPC) codes are a class of forward-error-correction codes. They are among the best-known codes capable of achieving low bit error rates (BER) approaching Shannon's capacity limit. Recently, LDPC codes have been adopted by the European Digital Video Broadcasting (DVB-S2) standard, and have also been proposed for the emerging IEEE 802.16 fixed and mobile broadband wireless-access standard. The consultative committee for space data system (CCSDS) has also recommended using LDPC codes in the deep space communications and near-earth communications. It is obvious that LDPC codes will be widely used in wired and wireless communication, magnetic recording, optical networking, DVB, and other fields in the near future. Efficient hardware implementation of LDPC codes is of great interest since LDPC codes are being considered for a wide range of applications. This paper presents an efficient partially parallel decoder architecture suited for quasi-cyclic (QC) LDPC codes using Belief propagation algorithm for decoding. Algorithmic transformation and architectural level optimization are incorporated to reduce the critical path. First, analyze the check matrix of LDPC code, to find out the relationship between the row weight and the column weight. And then, the sharing level of the check node updating units (CNU) and the variable node updating units (VNU) are determined according to the relationship. After that, rearrange the CNU and the VNU, and divide them into several smaller parts, with the help of some assistant logic circuit, these smaller parts can be grouped into CNU during the check node update processing and grouped into VNU during the variable node update processing. These smaller parts are called node update kernel units (NKU) and the assistant logic circuit are called node update auxiliary unit (NAU). With NAUs' help, the two steps of iteration operation are completed by NKUs, which brings in great hardware resource reduction. Meanwhile, efficient techniques have been developed to reduce the computation delay of the node processing units and to minimize hardware overhead for parallel processing. This method may be applied not only to regular LDPC codes, but also to the irregular ones. Based on the proposed architectures, a (7493, 6096) irregular QC-LDPC code decoder is described using verilog hardware design language and implemented on Altera field programmable gate array (FPGA) StratixII EP2S130. The implementation results show that over 20% of logic core size can be saved than conventional partially parallel decoder architectures without any performance degradation. If the decoding clock is 100MHz, the proposed decoder can achieve a maximum (source data) decoding throughput of 133 Mb/s at 18 iterations.

Glenn-ht/bem Conjugate Heat Transfer Solver for Large-scale Turbomachinery Models

NASA Technical Reports Server (NTRS)

Divo, E.; Steinthorsson, E.; Rodriquez, F.; Kassab, A. J.; Kapat, J. S.; Heidmann, James D. (Technical Monitor)

2003-01-01

A coupled Boundary Element/Finite Volume Method temperature-forward/flux-hack algorithm is developed for conjugate heat transfer (CHT) applications. A loosely coupled strategy is adopted with each field solution providing boundary conditions for the other in an iteration seeking continuity of temperature and heat flux at the fluid-solid interface. The NASA Glenn Navier-Stokes code Glenn-HT is coupled to a 3-D BEM steady state heat conduction code developed at the University of Central Florida. Results from CHT simulation of a 3-D film-cooled blade section are presented and compared with those computed by a two-temperature approach. Also presented are current developments of an iterative domain decomposition strategy accommodating large numbers of unknowns in the BEM. The blade is artificially sub-sectioned in the span-wise direction, 3-D BEM solutions are obtained in the subdomains, and interface temperatures are averaged symmetrically when the flux is updated while the fluxes are averaged anti-symmetrically to maintain continuity of heat flux when the temperatures are updated. An initial guess for interface temperatures uses a physically-based 1-D conduction argument to provide an effective starting point and significantly reduce iteration. 2-D and 3-D results show the process converges efficiently and offers substantial computational and storage savings. Future developments include a parallel multi-grid implementation of the approach under MPI for computation on PC clusters.

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Qiaofeng; Sawatzky, Alex; Anastasio, Mark A., E-mail: anastasio@wustl.edu

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that ismore » solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.« less

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction.

PubMed

Xu, Qiaofeng; Yang, Deshan; Tan, Jun; Sawatzky, Alex; Anastasio, Mark A

2016-04-01

The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

PubMed Central

Xu, Qiaofeng; Yang, Deshan; Tan, Jun; Sawatzky, Alex; Anastasio, Mark A.

2016-01-01

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets. PMID:27036582

Domain decomposition preconditioners for the spectral collocation method

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio; Sacchilandriani, Giovanni

1988-01-01

Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.

Parallel programming of gradient-based iterative image reconstruction schemes for optical tomography.

PubMed

Hielscher, Andreas H; Bartel, Sebastian

2004-02-01

Optical tomography (OT) is a fast developing novel imaging modality that uses near-infrared (NIR) light to obtain cross-sectional views of optical properties inside the human body. A major challenge remains the time-consuming, computational-intensive image reconstruction problem that converts NIR transmission measurements into cross-sectional images. To increase the speed of iterative image reconstruction schemes that are commonly applied for OT, we have developed and implemented several parallel algorithms on a cluster of workstations. Static process distribution as well as dynamic load balancing schemes suitable for heterogeneous clusters and varying machine performances are introduced and tested. The resulting algorithms are shown to accelerate the reconstruction process to various degrees, substantially reducing the computation times for clinically relevant problems.

Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

DOE PAGES

Abhyankar, Shrirang; Constantinescu, Emil M.; Smith, Barry F.; ...

2016-11-07

Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including amore » real utility network, show good scalability on different computing architectures.« less

Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abhyankar, Shrirang; Constantinescu, Emil M.; Smith, Barry F.

Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including amore » real utility network, show good scalability on different computing architectures.« less

Dissipation, Voltage Profile and Levy Dragon in a Special Ladder Network

ERIC Educational Resources Information Center

Ucak, C.

2009-01-01

A ladder network constructed by an elementary two-terminal network consisting of a parallel resistor-inductor block in series with a parallel resistor-capacitor block sometimes is said to have a non-dispersive dissipative response. This special ladder network is created iteratively by replacing the elementary two-terminal network in place of the…

Tuning iteration space slicing based tiled multi-core code implementing Nussinov's RNA folding.

PubMed

Palkowski, Marek; Bielecki, Wlodzimierz

2018-01-15

RNA folding is an ongoing compute-intensive task of bioinformatics. Parallelization and improving code locality for this kind of algorithms is one of the most relevant areas in computational biology. Fortunately, RNA secondary structure approaches, such as Nussinov's recurrence, involve mathematical operations over affine control loops whose iteration space can be represented by the polyhedral model. This allows us to apply powerful polyhedral compilation techniques based on the transitive closure of dependence graphs to generate parallel tiled code implementing Nussinov's RNA folding. Such techniques are within the iteration space slicing framework - the transitive dependences are applied to the statement instances of interest to produce valid tiles. The main problem at generating parallel tiled code is defining a proper tile size and tile dimension which impact parallelism degree and code locality. To choose the best tile size and tile dimension, we first construct parallel parametric tiled code (parameters are variables defining tile size). With this purpose, we first generate two nonparametric tiled codes with different fixed tile sizes but with the same code structure and then derive a general affine model, which describes all integer factors available in expressions of those codes. Using this model and known integer factors present in the mentioned expressions (they define the left-hand side of the model), we find unknown integers in this model for each integer factor available in the same fixed tiled code position and replace in this code expressions, including integer factors, with those including parameters. Then we use this parallel parametric tiled code to implement the well-known tile size selection (TSS) technique, which allows us to discover in a given search space the best tile size and tile dimension maximizing target code performance. For a given search space, the presented approach allows us to choose the best tile size and tile dimension in parallel tiled code implementing Nussinov's RNA folding. Experimental results, received on modern Intel multi-core processors, demonstrate that this code outperforms known closely related implementations when the length of RNA strands is bigger than 2500.

Myria: Scalable Analytics as a Service

NASA Astrophysics Data System (ADS)

Howe, B.; Halperin, D.; Whitaker, A.

2014-12-01

At the UW eScience Institute, we're working to empower non-experts, especially in the sciences, to write and use data-parallel algorithms. To this end, we are building Myria, a web-based platform for scalable analytics and data-parallel programming. Myria's internal model of computation is the relational algebra extended with iteration, such that every program is inherently data-parallel, just as every query in a database is inherently data-parallel. But unlike databases, iteration is a first class concept, allowing us to express machine learning tasks, graph traversal tasks, and more. Programs can be expressed in a number of languages and can be executed on a number of execution environments, but we emphasize a particular language called MyriaL that supports both imperative and declarative styles and a particular execution engine called MyriaX that uses an in-memory column-oriented representation and asynchronous iteration. We deliver Myria over the web as a service, providing an editor, performance analysis tools, and catalog browsing features in a single environment. We find that this web-based "delivery vector" is critical in reaching non-experts: they are insulated from irrelevant effort technical work associated with installation, configuration, and resource management. The MyriaX backend, one of several execution runtimes we support, is a main-memory, column-oriented, RDBMS-on-the-worker system that supports cyclic data flows as a first-class citizen and has been shown to outperform competitive systems on 100-machine cluster sizes. I will describe the Myria system, give a demo, and present some new results in large-scale oceanographic microbiology.

Incoherent beam combining based on the momentum SPGD algorithm

NASA Astrophysics Data System (ADS)

Yang, Guoqing; Liu, Lisheng; Jiang, Zhenhua; Guo, Jin; Wang, Tingfeng

2018-05-01

Incoherent beam combining (ICBC) technology is one of the most promising ways to achieve high-energy, near-diffraction laser output. In this paper, the momentum method is proposed as a modification of the stochastic parallel gradient descent (SPGD) algorithm. The momentum method can improve the speed of convergence of the combining system efficiently. The analytical method is employed to interpret the principle of the momentum method. Furthermore, the proposed algorithm is testified through simulations as well as experiments. The results of the simulations and the experiments show that the proposed algorithm not only accelerates the speed of the iteration, but also keeps the stability of the combining process. Therefore the feasibility of the proposed algorithm in the beam combining system is testified.

MUTILS - a set of efficient modeling tools for multi-core CPUs implemented in MEX

NASA Astrophysics Data System (ADS)

Krotkiewski, Marcin; Dabrowski, Marcin

2013-04-01

The need for computational performance is common in scientific applications, and in particular in numerical simulations, where high resolution models require efficient processing of large amounts of data. Especially in the context of geological problems the need to increase the model resolution to resolve physical and geometrical complexities seems to have no limits. Alas, the performance of new generations of CPUs does not improve any longer by simply increasing clock speeds. Current industrial trends are to increase the number of computational cores. As a result, parallel implementations are required in order to fully utilize the potential of new processors, and to study more complex models. We target simulations on small to medium scale shared memory computers: laptops and desktop PCs with ~8 CPU cores and up to tens of GB of memory to high-end servers with ~50 CPU cores and hundereds of GB of memory. In this setting MATLAB is often the environment of choice for scientists that want to implement their own models with little effort. It is a useful general purpose mathematical software package, but due to its versatility some of its functionality is not as efficient as it could be. In particular, the challanges of modern multi-core architectures are not fully addressed. We have developed MILAMIN 2 - an efficient FEM modeling environment written in native MATLAB. Amongst others, MILAMIN provides functions to define model geometry, generate and convert structured and unstructured meshes (also through interfaces to external mesh generators), compute element and system matrices, apply boundary conditions, solve the system of linear equations, address non-linear and transient problems, and perform post-processing. MILAMIN strives to combine the ease of code development and the computational efficiency. Where possible, the code is optimized and/or parallelized within the MATLAB framework. Native MATLAB is augmented with the MUTILS library - a set of MEX functions that implement the computationally intensive, performance critical parts of the code, which we have identified to be bottlenecks. Here, we discuss the functionality and performance of the MUTILS library. Currently, it includes: 1. time and memory efficient assembly of sparse matrices for FEM simulations 2. parallel sparse matrix - vector product with optimizations speficic to symmetric matrices and multiple degrees of freedom per node 3. parallel point in triangle location and point in tetrahedron location for unstructured, adaptive 2D and 3D meshes (useful for 'marker in cell' type of methods) 4. parallel FEM interpolation for 2D and 3D meshes of elements of different types and orders, and for different number of degrees of freedom per node 5. a stand-alone, MEX implementation of the Conjugate Gradients iterative solver 6. interface to METIS graph partitioning and a fast implementation of RCM reordering

An accurate, fast, and scalable solver for high-frequency wave propagation

NASA Astrophysics Data System (ADS)

Zepeda-Núñez, L.; Taus, M.; Hewett, R.; Demanet, L.

2017-12-01

In many science and engineering applications, solving time-harmonic high-frequency wave propagation problems quickly and accurately is of paramount importance. For example, in geophysics, particularly in oil exploration, such problems can be the forward problem in an iterative process for solving the inverse problem of subsurface inversion. It is important to solve these wave propagation problems accurately in order to efficiently obtain meaningful solutions of the inverse problems: low order forward modeling can hinder convergence. Additionally, due to the volume of data and the iterative nature of most optimization algorithms, the forward problem must be solved many times. Therefore, a fast solver is necessary to make solving the inverse problem feasible. For time-harmonic high-frequency wave propagation, obtaining both speed and accuracy is historically challenging. Recently, there have been many advances in the development of fast solvers for such problems, including methods which have linear complexity with respect to the number of degrees of freedom. While most methods scale optimally only in the context of low-order discretizations and smooth wave speed distributions, the method of polarized traces has been shown to retain optimal scaling for high-order discretizations, such as hybridizable discontinuous Galerkin methods and for highly heterogeneous (and even discontinuous) wave speeds. The resulting fast and accurate solver is consequently highly attractive for geophysical applications. To date, this method relies on a layered domain decomposition together with a preconditioner applied in a sweeping fashion, which has limited straight-forward parallelization. In this work, we introduce a new version of the method of polarized traces which reveals more parallel structure than previous versions while preserving all of its other advantages. We achieve this by further decomposing each layer and applying the preconditioner to these new components separately and in parallel. We demonstrate that this produces an even more effective and parallelizable preconditioner for a single right-hand side. As before, additional speed can be gained by pipelining several right-hand-sides.

Tinker-HP: a massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields.

PubMed

Lagardère, Louis; Jolly, Luc-Henri; Lipparini, Filippo; Aviat, Félix; Stamm, Benjamin; Jing, Zhifeng F; Harger, Matthew; Torabifard, Hedieh; Cisneros, G Andrés; Schnieders, Michael J; Gresh, Nohad; Maday, Yvon; Ren, Pengyu Y; Ponder, Jay W; Piquemal, Jean-Philip

2018-01-28

We present Tinker-HP, a massively MPI parallel package dedicated to classical molecular dynamics (MD) and to multiscale simulations, using advanced polarizable force fields (PFF) encompassing distributed multipoles electrostatics. Tinker-HP is an evolution of the popular Tinker package code that conserves its simplicity of use and its reference double precision implementation for CPUs. Grounded on interdisciplinary efforts with applied mathematics, Tinker-HP allows for long polarizable MD simulations on large systems up to millions of atoms. We detail in the paper the newly developed extension of massively parallel 3D spatial decomposition to point dipole polarizable models as well as their coupling to efficient Krylov iterative and non-iterative polarization solvers. The design of the code allows the use of various computer systems ranging from laboratory workstations to modern petascale supercomputers with thousands of cores. Tinker-HP proposes therefore the first high-performance scalable CPU computing environment for the development of next generation point dipole PFFs and for production simulations. Strategies linking Tinker-HP to Quantum Mechanics (QM) in the framework of multiscale polarizable self-consistent QM/MD simulations are also provided. The possibilities, performances and scalability of the software are demonstrated via benchmarks calculations using the polarizable AMOEBA force field on systems ranging from large water boxes of increasing size and ionic liquids to (very) large biosystems encompassing several proteins as well as the complete satellite tobacco mosaic virus and ribosome structures. For small systems, Tinker-HP appears to be competitive with the Tinker-OpenMM GPU implementation of Tinker. As the system size grows, Tinker-HP remains operational thanks to its access to distributed memory and takes advantage of its new algorithmic enabling for stable long timescale polarizable simulations. Overall, a several thousand-fold acceleration over a single-core computation is observed for the largest systems. The extension of the present CPU implementation of Tinker-HP to other computational platforms is discussed.

Performance Implications of Synchronization Support for Parallel FORTRAN Programs

DTIC Science & Technology

1991-06-17

applications we used in this study are BDNA and FLO52. BDNA is a molecular dy- I namics simulator for biomolecules in water and it uses ordinary...parallelism structures and loop granularity. In the BDNA program, most of the parallel loops are not nested and the iterations are 200-1000 instructions long...are of concern. The BDNA curve in Figure 21 shows that for this program only 17% of all 32 I I 100 BDNA -4 FLO52 -I 80 3 CumuilatQe percentage of3

A highly parallel multigrid-like method for the solution of the Euler equations

NASA Technical Reports Server (NTRS)

Tuminaro, Ray S.

1989-01-01

We consider a highly parallel multigrid-like method for the solution of the two dimensional steady Euler equations. The new method, introduced as filtering multigrid, is similar to a standard multigrid scheme in that convergence on the finest grid is accelerated by iterations on coarser grids. In the filtering method, however, additional fine grid subproblems are processed concurrently with coarse grid computations to further accelerate convergence. These additional problems are obtained by splitting the residual into a smooth and an oscillatory component. The smooth component is then used to form a coarse grid problem (similar to standard multigrid) while the oscillatory component is used for a fine grid subproblem. The primary advantage in the filtering approach is that fewer iterations are required and that most of the additional work per iteration can be performed in parallel with the standard coarse grid computations. We generalize the filtering algorithm to a version suitable for nonlinear problems. We emphasize that this generalization is conceptually straight-forward and relatively easy to implement. In particular, no explicit linearization (e.g., formation of Jacobians) needs to be performed (similar to the FAS multigrid approach). We illustrate the nonlinear version by applying it to the Euler equations, and presenting numerical results. Finally, a performance evaluation is made based on execution time models and convergence information obtained from numerical experiments.

Scalable and balanced dynamic hybrid data assimilation

NASA Astrophysics Data System (ADS)

Kauranne, Tuomo; Amour, Idrissa; Gunia, Martin; Kallio, Kari; Lepistö, Ahti; Koponen, Sampsa

2017-04-01

Scalability of complex weather forecasting suites is dependent on the technical tools available for implementing highly parallel computational kernels, but to an equally large extent also on the dependence patterns between various components of the suite, such as observation processing, data assimilation and the forecast model. Scalability is a particular challenge for 4D variational assimilation methods that necessarily couple the forecast model into the assimilation process and subject this combination to an inherently serial quasi-Newton minimization process. Ensemble based assimilation methods are naturally more parallel, but large models force ensemble sizes to be small and that results in poor assimilation accuracy, somewhat akin to shooting with a shotgun in a million-dimensional space. The Variational Ensemble Kalman Filter (VEnKF) is an ensemble method that can attain the accuracy of 4D variational data assimilation with a small ensemble size. It achieves this by processing a Gaussian approximation of the current error covariance distribution, instead of a set of ensemble members, analogously to the Extended Kalman Filter EKF. Ensemble members are re-sampled every time a new set of observations is processed from a new approximation of that Gaussian distribution which makes VEnKF a dynamic assimilation method. After this a smoothing step is applied that turns VEnKF into a dynamic Variational Ensemble Kalman Smoother VEnKS. In this smoothing step, the same process is iterated with frequent re-sampling of the ensemble but now using past iterations as surrogate observations until the end result is a smooth and balanced model trajectory. In principle, VEnKF could suffer from similar scalability issues as 4D-Var. However, this can be avoided by isolating the forecast model completely from the minimization process by implementing the latter as a wrapper code whose only link to the model is calling for many parallel and totally independent model runs, all of them implemented as parallel model runs themselves. The only bottleneck in the process is the gathering and scattering of initial and final model state snapshots before and after the parallel runs which requires a very efficient and low-latency communication network. However, the volume of data communicated is small and the intervening minimization steps are only 3D-Var, which means their computational load is negligible compared with the fully parallel model runs. We present example results of scalable VEnKF with the 4D lake and shallow sea model COHERENS, assimilating simultaneously continuous in situ measurements in a single point and infrequent satellite images that cover a whole lake, with the fully scalable VEnKF.

GPU-accelerated iterative reconstruction from Compton scattered data using a matched pair of conic projector and backprojector.

PubMed

Nguyen, Van-Giang; Lee, Soo-Jin

2016-07-01

Iterative reconstruction from Compton scattered data is known to be computationally more challenging than that from conventional line-projection based emission data in that the gamma rays that undergo Compton scattering are modeled as conic projections rather than line projections. In conventional tomographic reconstruction, to parallelize the projection and backprojection operations using the graphics processing unit (GPU), approximated methods that use an unmatched pair of ray-tracing forward projector and voxel-driven backprojector have been widely used. In this work, we propose a new GPU-accelerated method for Compton camera reconstruction which is more accurate by using exactly matched pair of projector and backprojector. To calculate conic forward projection, we first sample the cone surface into conic rays and accumulate the intersecting chord lengths of the conic rays passing through voxels using a fast ray-tracing method (RTM). For conic backprojection, to obtain the true adjoint of the conic forward projection, while retaining the computational efficiency of the GPU, we use a voxel-driven RTM which is essentially the same as the standard RTM used for the conic forward projector. Our simulation results show that, while the new method is about 3 times slower than the approximated method, it is still about 16 times faster than the CPU-based method without any loss of accuracy. The net conclusion is that our proposed method is guaranteed to retain the reconstruction accuracy regardless of the number of iterations by providing a perfectly matched projector-backprojector pair, which makes iterative reconstruction methods for Compton imaging faster and more accurate. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations

DOE PAGES

Banerjee, Amartya S.; Suryanarayana, Phanish; Pask, John E.

2016-01-21

Pulay's Direct Inversion in the Iterative Subspace (DIIS) method is one of the most widely used mixing schemes for accelerating the self-consistent solution of electronic structure problems. In this work, we propose a simple generalization of DIIS in which Pulay extrapolation is performed at periodic intervals rather than on every self-consistent field iteration, and linear mixing is performed on all other iterations. Lastly, we demonstrate through numerical tests on a wide variety of materials systems in the framework of density functional theory that the proposed generalization of Pulay's method significantly improves its robustness and efficiency.

The fusion code XGC: Enabling kinetic study of multi-scale edge turbulent transport in ITER [Book Chapter

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Azevedo, Eduardo; Abbott, Stephen; Koskela, Tuomas

The XGC fusion gyrokinetic code combines state-of-the-art, portable computational and algorithmic technologies to enable complicated multiscale simulations of turbulence and transport dynamics in ITER edge plasma on the largest US open-science computer, the CRAY XK7 Titan, at its maximal heterogeneous capability, which have not been possible before due to a factor of over 10 shortage in the time-to-solution for less than 5 days of wall-clock time for one physics case. Frontier techniques such as nested OpenMP parallelism, adaptive parallel I/O, staging I/O and data reduction using dynamic and asynchronous applications interactions, dynamic repartitioning for balancing computational work in pushing particlesmore » and in grid related work, scalable and accurate discretization algorithms for non-linear Coulomb collisions, and communication-avoiding subcycling technology for pushing particles on both CPUs and GPUs are also utilized to dramatically improve the scalability and time-to-solution, hence enabling the difficult kinetic ITER edge simulation on a present-day leadership class computer.« less

Interpretation of deep directional resistivity measurements acquired in high-angle and horizontal wells using 3-D inversion

NASA Astrophysics Data System (ADS)

Puzyrev, Vladimir; Torres-Verdín, Carlos; Calo, Victor

2018-05-01

The interpretation of resistivity measurements acquired in high-angle and horizontal wells is a critical technical problem in formation evaluation. We develop an efficient parallel 3-D inversion method to estimate the spatial distribution of electrical resistivity in the neighbourhood of a well from deep directional electromagnetic induction measurements. The methodology places no restriction on the spatial distribution of the electrical resistivity around arbitrary well trajectories. The fast forward modelling of triaxial induction measurements performed with multiple transmitter-receiver configurations employs a parallel direct solver. The inversion uses a pre-conditioned gradient-based method whose accuracy is improved using the Wolfe conditions to estimate optimal step lengths at each iteration. The large transmitter-receiver offsets, used in the latest generation of commercial directional resistivity tools, improve the depth of investigation to over 30 m from the wellbore. Several challenging synthetic examples confirm the feasibility of the full 3-D inversion-based interpretations for these distances, hence enabling the integration of resistivity measurements with seismic amplitude data to improve the forecast of the petrophysical and fluid properties. Employing parallel direct solvers for the triaxial induction problems allows for large reductions in computational effort, thereby opening the possibility to invert multiposition 3-D data in practical CPU times.

Multiple grid problems on concurrent-processing computers

NASA Technical Reports Server (NTRS)

Eberhardt, D. S.; Baganoff, D.

1986-01-01

Three computer codes were studied which make use of concurrent processing computer architectures in computational fluid dynamics (CFD). The three parallel codes were tested on a two processor multiple-instruction/multiple-data (MIMD) facility at NASA Ames Research Center, and are suggested for efficient parallel computations. The first code is a well-known program which makes use of the Beam and Warming, implicit, approximate factored algorithm. This study demonstrates the parallelism found in a well-known scheme and it achieved speedups exceeding 1.9 on the two processor MIMD test facility. The second code studied made use of an embedded grid scheme which is used to solve problems having complex geometries. The particular application for this study considered an airfoil/flap geometry in an incompressible flow. The scheme eliminates some of the inherent difficulties found in adapting approximate factorization techniques onto MIMD machines and allows the use of chaotic relaxation and asynchronous iteration techniques. The third code studied is an application of overset grids to a supersonic blunt body problem. The code addresses the difficulties encountered when using embedded grids on a compressible, and therefore nonlinear, problem. The complex numerical boundary system associated with overset grids is discussed and several boundary schemes are suggested. A boundary scheme based on the method of characteristics achieved the best results.

Efficiency trade-offs of steady-state methods using FEM and FDM. [iterative solutions for nonlinear flow equations

NASA Technical Reports Server (NTRS)

Gartling, D. K.; Roache, P. J.

1978-01-01

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

Modeling cardiovascular hemodynamics using the lattice Boltzmann method on massively parallel supercomputers

NASA Astrophysics Data System (ADS)

Randles, Amanda Elizabeth

Accurate and reliable modeling of cardiovascular hemodynamics has the potential to improve understanding of the localization and progression of heart diseases, which are currently the most common cause of death in Western countries. However, building a detailed, realistic model of human blood flow is a formidable mathematical and computational challenge. The simulation must combine the motion of the fluid, the intricate geometry of the blood vessels, continual changes in flow and pressure driven by the heartbeat, and the behavior of suspended bodies such as red blood cells. Such simulations can provide insight into factors like endothelial shear stress that act as triggers for the complex biomechanical events that can lead to atherosclerotic pathologies. Currently, it is not possible to measure endothelial shear stress in vivo, making these simulations a crucial component to understanding and potentially predicting the progression of cardiovascular disease. In this thesis, an approach for efficiently modeling the fluid movement coupled to the cell dynamics in real-patient geometries while accounting for the additional force from the expansion and contraction of the heart will be presented and examined. First, a novel method to couple a mesoscopic lattice Boltzmann fluid model to the microscopic molecular dynamics model of cell movement is elucidated. A treatment of red blood cells as extended structures, a method to handle highly irregular geometries through topology driven graph partitioning, and an efficient molecular dynamics load balancing scheme are introduced. These result in a large-scale simulation of the cardiovascular system, with a realistic description of the complex human arterial geometry, from centimeters down to the spatial resolution of red-blood cells. The computational methods developed to enable scaling of the application to 294,912 processors are discussed, thus empowering the simulation of a full heartbeat. Second, further extensions to enable the modeling of fluids in vessels with smaller diameters and a method for introducing the deformational forces exerted on the arterial flows from the movement of the heart by borrowing concepts from cosmodynamics are presented. These additional forces have a great impact on the endothelial shear stress. Third, the fluid model is extended to not only recover Navier-Stokes hydrodynamics, but also a wider range of Knudsen numbers, which is especially important in micro- and nano-scale flows. The tradeoffs of many optimizations methods such as the use of deep halo level ghost cells that, alongside hybrid programming models, reduce the impact of such higher-order models and enable efficient modeling of extreme regimes of computational fluid dynamics are discussed. Fourth, the extension of these models to other research questions like clogging in microfluidic devices and determining the severity of co-arctation of the aorta is presented. Through this work, a validation of these methods by taking real patient data and the measured pressure value before the narrowing of the aorta and predicting the pressure drop across the co-arctation is shown. Comparison with the measured pressure drop in vivo highlights the accuracy and potential impact of such patient specific simulations. Finally, a method to enable the simulation of longer trajectories in time by discretizing both spatially and temporally is presented. In this method, a serial coarse iterator is used to initialize data at discrete time steps for a fine model that runs in parallel. This coarse solver is based on a larger time step and typically a coarser discretization in space. Iterative refinement enables the compute-intensive fine iterator to be modeled with temporal parallelization. The algorithm consists of a series of prediction-corrector iterations completing when the results have converged within a certain tolerance. Combined, these developments allow large fluid models to be simulated for longer time durations than previously possible.

A high-performance spatial database based approach for pathology imaging algorithm evaluation

PubMed Central

Wang, Fusheng; Kong, Jun; Gao, Jingjing; Cooper, Lee A.D.; Kurc, Tahsin; Zhou, Zhengwen; Adler, David; Vergara-Niedermayr, Cristobal; Katigbak, Bryan; Brat, Daniel J.; Saltz, Joel H.

2013-01-01

Background: Algorithm evaluation provides a means to characterize variability across image analysis algorithms, validate algorithms by comparison with human annotations, combine results from multiple algorithms for performance improvement, and facilitate algorithm sensitivity studies. The sizes of images and image analysis results in pathology image analysis pose significant challenges in algorithm evaluation. We present an efficient parallel spatial database approach to model, normalize, manage, and query large volumes of analytical image result data. This provides an efficient platform for algorithm evaluation. Our experiments with a set of brain tumor images demonstrate the application, scalability, and effectiveness of the platform. Context: The paper describes an approach and platform for evaluation of pathology image analysis algorithms. The platform facilitates algorithm evaluation through a high-performance database built on the Pathology Analytic Imaging Standards (PAIS) data model. Aims: (1) Develop a framework to support algorithm evaluation by modeling and managing analytical results and human annotations from pathology images; (2) Create a robust data normalization tool for converting, validating, and fixing spatial data from algorithm or human annotations; (3) Develop a set of queries to support data sampling and result comparisons; (4) Achieve high performance computation capacity via a parallel data management infrastructure, parallel data loading and spatial indexing optimizations in this infrastructure. Materials and Methods: We have considered two scenarios for algorithm evaluation: (1) algorithm comparison where multiple result sets from different methods are compared and consolidated; and (2) algorithm validation where algorithm results are compared with human annotations. We have developed a spatial normalization toolkit to validate and normalize spatial boundaries produced by image analysis algorithms or human annotations. The validated data were formatted based on the PAIS data model and loaded into a spatial database. To support efficient data loading, we have implemented a parallel data loading tool that takes advantage of multi-core CPUs to accelerate data injection. The spatial database manages both geometric shapes and image features or classifications, and enables spatial sampling, result comparison, and result aggregation through expressive structured query language (SQL) queries with spatial extensions. To provide scalable and efficient query support, we have employed a shared nothing parallel database architecture, which distributes data homogenously across multiple database partitions to take advantage of parallel computation power and implements spatial indexing to achieve high I/O throughput. Results: Our work proposes a high performance, parallel spatial database platform for algorithm validation and comparison. This platform was evaluated by storing, managing, and comparing analysis results from a set of brain tumor whole slide images. The tools we develop are open source and available to download. Conclusions: Pathology image algorithm validation and comparison are essential to iterative algorithm development and refinement. One critical component is the support for queries involving spatial predicates and comparisons. In our work, we develop an efficient data model and parallel database approach to model, normalize, manage and query large volumes of analytical image result data. Our experiments demonstrate that the data partitioning strategy and the grid-based indexing result in good data distribution across database nodes and reduce I/O overhead in spatial join queries through parallel retrieval of relevant data and quick subsetting of datasets. The set of tools in the framework provide a full pipeline to normalize, load, manage and query analytical results for algorithm evaluation. PMID:23599905

Nonlinear and parallel algorithms for finite element discretizations of the incompressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Arteaga, Santiago Egido

1998-12-01

The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the linearization strategies considered and whose computational cost is negligible. The algebraic properties of these systems depend on both the discretization and nonlinear method used. We study in detail the positive definiteness and skewsymmetry of the advection submatrices (essentially, convection-diffusion problems). We propose a discretization based on a new trilinear form for Newton's method. We solve the linear systems using three Krylov subspace methods, GMRES, QMR and TFQMR, and compare the advantages of each. Our emphasis is on parallel algorithms, and so we consider preconditioners suitable for parallel computers such as line variants of the Jacobi and Gauss- Seidel methods, alternating direction implicit methods, and Chebyshev and least squares polynomial preconditioners. These work well for moderate viscosities (moderate Reynolds number). For small viscosities we show that effective parallel solution of the advection subproblem is a critical factor to improve performance. Implementation details on a CM-5 are presented.

Effects of Ordering Strategies and Programming Paradigms on Sparse Matrix Computations

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Li, Xiaoye; Husbands, Parry; Biswas, Rupak; Biegel, Bryan (Technical Monitor)

2002-01-01

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. For systems that are ill-conditioned, it is often necessary to use a preconditioning technique. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and ILU(O) preconditioned CG (PCG) using different programming paradigms and architectures. Results show that for this class of applications: ordering significantly improves overall performance on both distributed and distributed shared-memory systems, that cache reuse may be more important than reducing communication, that it is possible to achieve message-passing performance using shared-memory constructs through careful data ordering and distribution, and that a hybrid MPI+OpenMP paradigm increases programming complexity with little performance gains. A implementation of CG on the Cray MTA does not require special ordering or partitioning to obtain high efficiency and scalability, giving it a distinct advantage for adaptive applications; however, it shows limited scalability for PCG due to a lack of thread level parallelism.

Effect of Topology Structure on the Output Performance of an Automobile Exhaust Thermoelectric Generator

NASA Astrophysics Data System (ADS)

Fang, W.; Quan, S. H.; Xie, C. J.; Ran, B.; Li, X. L.; Wang, L.; Jiao, Y. T.; Xu, T. W.

2017-05-01

The majority of the thermal energy released in an automotive internal combustion cycle is exhausted as waste heat through the tail pipe. This paper describes an automobile exhaust thermoelectric generator (AETEG), designed to recycle automobile waste heat. A model of the output characteristics of each thermoelectric device was established by testing their open circuit voltage and internal resistance, and combining the output characteristics. To better describe the relationship, the physical model was transformed into a topological model. The connection matrix was used to describe the relationship between any two thermoelectric devices in the topological structure. Different topological structures produced different power outputs; their output power was maximised by using an iterative algorithm to optimize the series-parallel electrical topology structure. The experimental results have shown that the output power of the optimal topology structure increases by 18.18% and 29.35% versus that of a pure in-series or parallel topology, respectively, and by 10.08% versus a manually defined structure (based on user experience). The thermoelectric conversion device increased energy efficiency by 40% when compared with a traditional car.

High-speed technique based on a parallel projection correlation procedure for digital image correlation

NASA Astrophysics Data System (ADS)

Zaripov, D. I.; Renfu, Li

2018-05-01

The implementation of high-efficiency digital image correlation methods based on a zero-normalized cross-correlation (ZNCC) procedure for high-speed, time-resolved measurements using a high-resolution digital camera is associated with big data processing and is often time consuming. In order to speed-up ZNCC computation, a high-speed technique based on a parallel projection correlation procedure is proposed. The proposed technique involves the use of interrogation window projections instead of its two-dimensional field of luminous intensity. This simplification allows acceleration of ZNCC computation up to 28.8 times compared to ZNCC calculated directly, depending on the size of interrogation window and region of interest. The results of three synthetic test cases, such as a one-dimensional uniform flow, a linear shear flow and a turbulent boundary-layer flow, are discussed in terms of accuracy. In the latter case, the proposed technique is implemented together with an iterative window-deformation technique. On the basis of the results of the present work, the proposed technique is recommended to be used for initial velocity field calculation, with further correction using more accurate techniques.

A reduced complexity highly power/bandwidth efficient coded FQPSK system with iterative decoding

NASA Technical Reports Server (NTRS)

Simon, M. K.; Divsalar, D.

2001-01-01

Based on a representation of FQPSK as a trellis-coded modulation, this paper investigates the potential improvement in power efficiency obtained from the application of simple outer codes to form a concatenated coding arrangement with iterative decoding.

Fast in-memory elastic full-waveform inversion using consumer-grade GPUs

NASA Astrophysics Data System (ADS)

Sivertsen Bergslid, Tore; Birger Raknes, Espen; Arntsen, Børge

2017-04-01

Full-waveform inversion (FWI) is a technique to estimate subsurface properties by using the recorded waveform produced by a seismic source and applying inverse theory. This is done through an iterative optimization procedure, where each iteration requires solving the wave equation many times, then trying to minimize the difference between the modeled and the measured seismic data. Having to model many of these seismic sources per iteration means that this is a highly computationally demanding procedure, which usually involves writing a lot of data to disk. We have written code that does forward modeling and inversion entirely in memory. A typical HPC cluster has many more CPUs than GPUs. Since FWI involves modeling many seismic sources per iteration, the obvious approach is to parallelize the code on a source-by-source basis, where each core of the CPU performs one modeling, and do all modelings simultaneously. With this approach, the GPU is already at a major disadvantage in pure numbers. Fortunately, GPUs can more than make up for this hardware disadvantage by performing each modeling much faster than a CPU. Another benefit of parallelizing each individual modeling is that it lets each modeling use a lot more RAM. If one node has 128 GB of RAM and 20 CPU cores, each modeling can use only 6.4 GB RAM if one is running the node at full capacity with source-by-source parallelization on the CPU. A parallelized per-source code using GPUs can use 64 GB RAM per modeling. Whenever a modeling uses more RAM than is available and has to start using regular disk space the runtime increases dramatically, due to slow file I/O. The extremely high computational speed of the GPUs combined with the large amount of RAM available for each modeling lets us do high frequency FWI for fairly large models very quickly. For a single modeling, our GPU code outperforms the single-threaded CPU-code by a factor of about 75. Successful inversions have been run on data with frequencies up to 40 Hz for a model of 2001 by 600 grid points with 5 m grid spacing and 5000 time steps, in less than 2.5 minutes per source. In practice, using 15 nodes (30 GPUs) to model 101 sources, each iteration took approximately 9 minutes. For reference, the same inversion run with our CPU code uses two hours per iteration. This was done using only a very simple wavefield interpolation technique, saving every second timestep. Using a more sophisticated checkpointing or wavefield reconstruction method would allow us to increase this model size significantly. Our results show that ordinary gaming GPUs are a viable alternative to the expensive professional GPUs often used today, when performing large scale modeling and inversion in geophysics.

Parallel processing in finite element structural analysis

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.

1987-01-01

A brief review is made of the fundamental concepts and basic issues of parallel processing. Discussion focuses on parallel numerical algorithms, performance evaluation of machines and algorithms, and parallelism in finite element computations. A computational strategy is proposed for maximizing the degree of parallelism at different levels of the finite element analysis process including: 1) formulation level (through the use of mixed finite element models); 2) analysis level (through additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms); 3) numerical algorithm level (through the use of operator splitting techniques and application of iterative processes); and 4) implementation level (through the effective combination of vectorization, multitasking and microtasking, whenever available).

Space-Filling Supercapacitor Carpets: Highly scalable fractal architecture for energy storage

NASA Astrophysics Data System (ADS)

Tiliakos, Athanasios; Trefilov, Alexandra M. I.; Tanasǎ, Eugenia; Balan, Adriana; Stamatin, Ioan

2018-04-01

Revamping ground-breaking ideas from fractal geometry, we propose an alternative micro-supercapacitor configuration realized by laser-induced graphene (LIG) foams produced via laser pyrolysis of inexpensive commercial polymers. The Space-Filling Supercapacitor Carpet (SFSC) architecture introduces the concept of nested electrodes based on the pre-fractal Peano space-filling curve, arranged in a symmetrical equilateral setup that incorporates multiple parallel capacitor cells sharing common electrodes for maximum efficiency and optimal length-to-area distribution. We elucidate on the theoretical foundations of the SFSC architecture, and we introduce innovations (high-resolution vector-mode printing) in the LIG method that allow for the realization of flexible and scalable devices based on low iterations of the Peano algorithm. SFSCs exhibit distributed capacitance properties, leading to capacitance, energy, and power ratings proportional to the number of nested electrodes (up to 4.3 mF, 0.4 μWh, and 0.2 mW for the largest tested model of low iteration using aqueous electrolytes), with competitively high energy and power densities. This can pave the road for full scalability in energy storage, reaching beyond the scale of micro-supercapacitors for incorporating into larger and more demanding applications.

Shedding New Light on Exploding Stars: Terascale Simulations of Nuetrino-Dreiven Supernovas and Their Nucleosynthesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dennis C. Smolarski, S.J.

Project Abstract This project was a continuation of work begun under a subcontract issued off of TSI-DOE Grant 1528746, awarded to the University of Illinois Urbana-Champaign. Dr. Anthony Mezzacappa is the Principal Investigator on the Illinois award. A separate award was issued to Santa Clara University to continue the collaboration during the time period May 2003 ? 2004. Smolarski continued to work on preconditioner technology and its interface with various iterative methods. He worked primarily with F. Dough Swesty (SUNY-Stony Brook) in continuing software development started in the 2002-03 academic year. Special attention was paid to the development and testingmore » of difference sparse approximate inverse preconditioners and their use in the solution of linear systems arising from radiation transport equations. The target was a high performance platform on which efficient implementation is a critical component of the overall effort. Smolarski also focused on the integration of the adaptive iterative algorithm, Chebycode, developed by Tom Manteuffel and Steve Ashby and adapted by Ryan Szypowski for parallel platforms, into the radiation transport code being developed at SUNY-Stony Brook.« less

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.

PubMed

Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

Anti-alias filter in AORSA for modeling ICRF heating of DT plasmas in ITER

NASA Astrophysics Data System (ADS)

Berry, L. A.; Batchelor, D. B.; Jaeger, E. F.; RF SciDAC Team

2011-10-01

The spectral wave solver AORSA has been used extensively to model full-field, ICRF heating scenarios for DT plasmas in ITER. In these scenarios, the tritium (T) second harmonic cyclotron resonance is positioned near the magnetic axis, where fast magnetosonic waves are efficiently absorbed by tritium ions. In some cases, a fundamental deuterium (D) cyclotron layer can also be located within the plasma, but close to the high field boundary. In this case, the existence of multiple ion cyclotron resonances presents a serious challenge for numerical simulation because short-wavelength, mode-converted waves can be excited close to the plasma edge at the ion-ion hybrid layer. Although the left hand circularly polarized component of the wave field is partially shielded from the fundamental D resonance, some power penetrates, and a small fraction (typically <10%) can be absorbed by the D ions. We find that an anti-aliasing filter is required in AORSA to calculate this fraction correctly while including up-shift and down-shift in the parallel wave spectrum. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S.; Genovese, L.

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and themore » linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.« less

Automated Software Acceleration in Programmable Logic for an Efficient NFFT Algorithm Implementation: A Case Study.

PubMed

Rodríguez, Manuel; Magdaleno, Eduardo; Pérez, Fernando; García, Cristhian

2017-03-28

Non-equispaced Fast Fourier transform (NFFT) is a very important algorithm in several technological and scientific areas such as synthetic aperture radar, computational photography, medical imaging, telecommunications, seismic analysis and so on. However, its computation complexity is high. In this paper, we describe an efficient NFFT implementation with a hardware coprocessor using an All-Programmable System-on-Chip (APSoC). This is a hybrid device that employs an Advanced RISC Machine (ARM) as Processing System with Programmable Logic for high-performance digital signal processing through parallelism and pipeline techniques. The algorithm has been coded in C language with pragma directives to optimize the architecture of the system. We have used the very novel Software Develop System-on-Chip (SDSoC) evelopment tool that simplifies the interface and partitioning between hardware and software. This provides shorter development cycles and iterative improvements by exploring several architectures of the global system. The computational results shows that hardware acceleration significantly outperformed the software based implementation.

Automated Software Acceleration in Programmable Logic for an Efficient NFFT Algorithm Implementation: A Case Study

PubMed Central

Rodríguez, Manuel; Magdaleno, Eduardo; Pérez, Fernando; García, Cristhian

2017-01-01

Non-equispaced Fast Fourier transform (NFFT) is a very important algorithm in several technological and scientific areas such as synthetic aperture radar, computational photography, medical imaging, telecommunications, seismic analysis and so on. However, its computation complexity is high. In this paper, we describe an efficient NFFT implementation with a hardware coprocessor using an All-Programmable System-on-Chip (APSoC). This is a hybrid device that employs an Advanced RISC Machine (ARM) as Processing System with Programmable Logic for high-performance digital signal processing through parallelism and pipeline techniques. The algorithm has been coded in C language with pragma directives to optimize the architecture of the system. We have used the very novel Software Develop System-on-Chip (SDSoC) evelopment tool that simplifies the interface and partitioning between hardware and software. This provides shorter development cycles and iterative improvements by exploring several architectures of the global system. The computational results shows that hardware acceleration significantly outperformed the software based implementation. PMID:28350358

A Comparison of Solver Performance for Complex Gastric Electrophysiology Models

PubMed Central

Sathar, Shameer; Cheng, Leo K.; Trew, Mark L.

2016-01-01

Computational techniques for solving systems of equations arising in gastric electrophysiology have not been studied for efficient solution process. We present a computationally challenging problem of simulating gastric electrophysiology in anatomically realistic stomach geometries with multiple intracellular and extracellular domains. The multiscale nature of the problem and mesh resolution required to capture geometric and functional features necessitates efficient solution methods if the problem is to be tractable. In this study, we investigated and compared several parallel preconditioners for the linear systems arising from tetrahedral discretisation of electrically isotropic and anisotropic problems, with and without stimuli. The results showed that the isotropic problem was computationally less challenging than the anisotropic problem and that the application of extracellular stimuli increased workload considerably. Preconditioning based on block Jacobi and algebraic multigrid solvers were found to have the best overall solution times and least iteration counts, respectively. The algebraic multigrid preconditioner would be expected to perform better on large problems. PMID:26736543

Real-time depth camera tracking with geometrically stable weight algorithm

NASA Astrophysics Data System (ADS)

Fu, Xingyin; Zhu, Feng; Qi, Feng; Wang, Mingming

2017-03-01

We present an approach for real-time camera tracking with depth stream. Existing methods are prone to drift in sceneries without sufficient geometric information. First, we propose a new weight method for an iterative closest point algorithm commonly used in real-time dense mapping and tracking systems. By detecting uncertainty in pose and increasing weight of points that constrain unstable transformations, our system achieves accurate and robust trajectory estimation results. Our pipeline can be fully parallelized with GPU and incorporated into the current real-time depth camera tracking system seamlessly. Second, we compare the state-of-the-art weight algorithms and propose a weight degradation algorithm according to the measurement characteristics of a consumer depth camera. Third, we use Nvidia Kepler Shuffle instructions during warp and block reduction to improve the efficiency of our system. Results on the public TUM RGB-D database benchmark demonstrate that our camera tracking system achieves state-of-the-art results both in accuracy and efficiency.

SIAM Conference on Parallel Processing for Scientific Computing, 4th, Chicago, IL, Dec. 11-13, 1989, Proceedings

NASA Technical Reports Server (NTRS)

Dongarra, Jack (Editor); Messina, Paul (Editor); Sorensen, Danny C. (Editor); Voigt, Robert G. (Editor)

1990-01-01

Attention is given to such topics as an evaluation of block algorithm variants in LAPACK and presents a large-grain parallel sparse system solver, a multiprocessor method for the solution of the generalized Eigenvalue problem on an interval, and a parallel QR algorithm for iterative subspace methods on the CM2. A discussion of numerical methods includes the topics of asynchronous numerical solutions of PDEs on parallel computers, parallel homotopy curve tracking on a hypercube, and solving Navier-Stokes equations on the Cedar Multi-Cluster system. A section on differential equations includes a discussion of a six-color procedure for the parallel solution of elliptic systems using the finite quadtree structure, data parallel algorithms for the finite element method, and domain decomposition methods in aerodynamics. Topics dealing with massively parallel computing include hypercube vs. 2-dimensional meshes and massively parallel computation of conservation laws. Performance and tools are also discussed.

The novel high-performance 3-D MT inverse solver

NASA Astrophysics Data System (ADS)

Kruglyakov, Mikhail; Geraskin, Alexey; Kuvshinov, Alexey

2016-04-01

We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse solver. The solver is written in multi-language paradigm to make it as efficient, readable and maintainable as possible. Separation of concerns and single responsibility concepts go through implementation of the solver. As a forward modelling engine a modern scalable solver extrEMe, based on contracting integral equation approach, is used. Iterative gradient-type (quasi-Newton) optimization scheme is invoked to search for (regularized) inverse problem solution, and adjoint source approach is used to calculate efficiently the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT responses, and supports massive parallelization. Moreover, different parallelization strategies implemented in the code allow optimal usage of available computational resources for a given problem statement. To parameterize an inverse domain the so-called mask parameterization is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to HPC Piz Daint (6th supercomputer in the world) demonstrate practically linear scalability of the code up to thousands of nodes.

Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez

2015-11-01

Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

Iterative nonlinear joint transform correlation for the detection of objects in cluttered scenes

NASA Astrophysics Data System (ADS)

Haist, Tobias; Tiziani, Hans J.

1999-03-01

An iterative correlation technique with digital image processing in the feedback loop for the detection of small objects in cluttered scenes is proposed. A scanning aperture is combined with the method in order to improve the immunity against noise and clutter. Multiple reference objects or different views of one object are processed in parallel. We demonstrate the method by detecting a noisy and distorted face in a crowd with a nonlinear joint transform correlator.

A parallel Jacobson-Oksman optimization algorithm. [parallel processing (computers)

NASA Technical Reports Server (NTRS)

Straeter, T. A.; Markos, A. T.

1975-01-01

A gradient-dependent optimization technique which exploits the vector-streaming or parallel-computing capabilities of some modern computers is presented. The algorithm, derived by assuming that the function to be minimized is homogeneous, is a modification of the Jacobson-Oksman serial minimization method. In addition to describing the algorithm, conditions insuring the convergence of the iterates of the algorithm and the results of numerical experiments on a group of sample test functions are presented. The results of these experiments indicate that this algorithm will solve optimization problems in less computing time than conventional serial methods on machines having vector-streaming or parallel-computing capabilities.

Communications oriented programming of parallel iterative solutions of sparse linear systems

NASA Technical Reports Server (NTRS)

Patrick, M. L.; Pratt, T. W.

1986-01-01

Parallel algorithms are developed for a class of scientific computational problems by partitioning the problems into smaller problems which may be solved concurrently. The effectiveness of the resulting parallel solutions is determined by the amount and frequency of communication and synchronization and the extent to which communication can be overlapped with computation. Three different parallel algorithms for solving the same class of problems are presented, and their effectiveness is analyzed from this point of view. The algorithms are programmed using a new programming environment. Run-time statistics and experience obtained from the execution of these programs assist in measuring the effectiveness of these algorithms.

High-Order Methods for Incompressible Fluid Flow

NASA Astrophysics Data System (ADS)

Deville, M. O.; Fischer, P. F.; Mund, E. H.

2002-08-01

High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular sttention given to enforcement of imcompressibility. Advanced discretizations. implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications.

New developments in optical coherence tomography

PubMed Central

Kostanyan, Tigran; Wollstein, Gadi; Schuman, Joel S.

2017-01-01

Purpose of review Optical coherence tomography (OCT) has become the cornerstone technology for clinical ocular imaging in the past few years. The technology is still rapidly evolving with newly developed applications. This manuscript reviews recent innovative OCT applications for glaucoma diagnosis and management. Recent findings The improvements made in the technology have resulted in increased scanning speed, axial and transverse resolution, and more effective use of the OCT technology as a component of multimodal imaging tools. At the same time, the parallel evolution in novel algorithms makes it possible to efficiently analyze the increased volume of acquired data. Summary The innovative iterations of OCT technology have the potential to further improve the performance of the technology in evaluating ocular structural and functional characteristics and longitudinal changes in glaucoma. PMID:25594766

A Parallel Fast Sweeping Method for the Eikonal Equation

NASA Astrophysics Data System (ADS)

Baker, B.

2017-12-01

Recently, there has been an exciting emergence of probabilistic methods for travel time tomography. Unlike gradient-based optimization strategies, probabilistic tomographic methods are resistant to becoming trapped in a local minimum and provide a much better quantification of parameter resolution than, say, appealing to ray density or performing checkerboard reconstruction tests. The benefits associated with random sampling methods however are only realized by successive computation of predicted travel times in, potentially, strongly heterogeneous media. To this end this abstract is concerned with expediting the solution of the Eikonal equation. While many Eikonal solvers use a fast marching method, the proposed solver will use the iterative fast sweeping method because the eight fixed sweep orderings in each iteration are natural targets for parallelization. To reduce the number of iterations and grid points required the high-accuracy finite difference stencil of Nobel et al., 2014 is implemented. A directed acyclic graph (DAG) is created with a priori knowledge of the sweep ordering and finite different stencil. By performing a topological sort of the DAG sets of independent nodes are identified as candidates for concurrent updating. Additionally, the proposed solver will also address scalability during earthquake relocation, a necessary step in local and regional earthquake tomography and a barrier to extending probabilistic methods from active source to passive source applications, by introducing an asynchronous parallel forward solve phase for all receivers in the network. Synthetic examples using the SEG over-thrust model will be presented.

Marine Controlled-Source Electromagnetic 2D Inversion for synthetic models.

NASA Astrophysics Data System (ADS)

Liu, Y.; Li, Y.

2016-12-01

We present a 2D inverse algorithm for frequency domain marine controlled-source electromagnetic (CSEM) data, which is based on the regularized Gauss-Newton approach. As a forward solver, our parallel adaptive finite element forward modeling program is employed. It is a self-adaptive, goal-oriented grid refinement algorithm in which a finite element analysis is performed on a sequence of refined meshes. The mesh refinement process is guided by a dual error estimate weighting to bias refinement towards elements that affect the solution at the EM receiver locations. With the use of the direct solver (MUMPS), we can effectively compute the electromagnetic fields for multi-sources and parametric sensitivities. We also implement the parallel data domain decomposition approach of Key and Ovall (2011), with the goal of being able to compute accurate responses in parallel for complicated models and a full suite of data parameters typical of offshore CSEM surveys. All minimizations are carried out by using the Gauss-Newton algorithm and model perturbations at each iteration step are obtained by using the Inexact Conjugate Gradient iteration method. Synthetic test inversions are presented.

Summer Proceedings 2016: The Center for Computing Research at Sandia National Laboratories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carleton, James Brian; Parks, Michael L.

Solving sparse linear systems from the discretization of elliptic partial differential equations (PDEs) is an important building block in many engineering applications. Sparse direct solvers can solve general linear systems, but are usually slower and use much more memory than effective iterative solvers. To overcome these two disadvantages, a hierarchical solver (LoRaSp) based on H2-matrices was introduced in [22]. Here, we have developed a parallel version of the algorithm in LoRaSp to solve large sparse matrices on distributed memory machines. On a single processor, the factorization time of our parallel solver scales almost linearly with the problem size for three-dimensionalmore » problems, as opposed to the quadratic scalability of many existing sparse direct solvers. Moreover, our solver leads to almost constant numbers of iterations, when used as a preconditioner for Poisson problems. On more than one processor, our algorithm has significant speedups compared to sequential runs. With this parallel algorithm, we are able to solve large problems much faster than many existing packages as demonstrated by the numerical experiments.« less

Data and Workflow Management Challenges in Global Adjoint Tomography

NASA Astrophysics Data System (ADS)

Lei, W.; Ruan, Y.; Smith, J. A.; Modrak, R. T.; Orsvuran, R.; Krischer, L.; Chen, Y.; Balasubramanian, V.; Hill, J.; Turilli, M.; Bozdag, E.; Lefebvre, M. P.; Jha, S.; Tromp, J.

2017-12-01

It is crucial to take the complete physics of wave propagation into account in seismic tomography to further improve the resolution of tomographic images. The adjoint method is an efficient way of incorporating 3D wave simulations in seismic tomography. However, global adjoint tomography is computationally expensive, requiring thousands of wavefield simulations and massive data processing. Through our collaboration with the Oak Ridge National Laboratory (ORNL) computing group and an allocation on Titan, ORNL's GPU-accelerated supercomputer, we are now performing our global inversions by assimilating waveform data from over 1,000 earthquakes. The first challenge we encountered is dealing with the sheer amount of seismic data. Data processing based on conventional data formats and processing tools (such as SAC), which are not designed for parallel systems, becomes our major bottleneck. To facilitate the data processing procedures, we designed the Adaptive Seismic Data Format (ASDF) and developed a set of Python-based processing tools to replace legacy FORTRAN-based software. These tools greatly enhance reproducibility and accountability while taking full advantage of highly parallel system and showing superior scaling on modern computational platforms. The second challenge is that the data processing workflow contains more than 10 sub-procedures, making it delicate to handle and prone to human mistakes. To reduce human intervention as much as possible, we are developing a framework specifically designed for seismic inversion based on the state-of-the art workflow management research, specifically the Ensemble Toolkit (EnTK), in collaboration with the RADICAL team from Rutgers University. Using the initial developments of the EnTK, we are able to utilize the full computing power of the data processing cluster RHEA at ORNL while keeping human interaction to a minimum and greatly reducing the data processing time. Thanks to all the improvements, we are now able to perform iterations fast enough on more than a 1,000 earthquakes dataset. Starting from model GLAD-M15 (Bozdag et al., 2016), an elastic 3D model with a transversely isotropic upper mantle, we have successfully performed 5 iterations. Our goal is to finish 10 iterations, i.e., generating GLAD M25* by the end of this year.

Iterative image reconstruction for PROPELLER-MRI using the nonuniform fast fourier transform.

PubMed

Tamhane, Ashish A; Anastasio, Mark A; Gui, Minzhi; Arfanakis, Konstantinos

2010-07-01

To investigate an iterative image reconstruction algorithm using the nonuniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) MRI. Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it with that of conventional gridding. The trade-off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated. It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased signal to noise ratio, reduced artifacts, for similar spatial resolution, compared with gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER-MRI was maintained when using the iterative reconstruction approach. An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter, the new reconstruction technique may provide PROPELLER images with improved image quality compared with conventional gridding. (c) 2010 Wiley-Liss, Inc.

Iterative Image Reconstruction for PROPELLER-MRI using the NonUniform Fast Fourier Transform

PubMed Central

Tamhane, Ashish A.; Anastasio, Mark A.; Gui, Minzhi; Arfanakis, Konstantinos

2013-01-01

Purpose To investigate an iterative image reconstruction algorithm using the non-uniform fast Fourier transform (NUFFT) for PROPELLER (Periodically Rotated Overlapping parallEL Lines with Enhanced Reconstruction) MRI. Materials and Methods Numerical simulations, as well as experiments on a phantom and a healthy human subject were used to evaluate the performance of the iterative image reconstruction algorithm for PROPELLER, and compare it to that of conventional gridding. The trade-off between spatial resolution, signal to noise ratio, and image artifacts, was investigated for different values of the regularization parameter. The performance of the iterative image reconstruction algorithm in the presence of motion was also evaluated. Results It was demonstrated that, for a certain range of values of the regularization parameter, iterative reconstruction produced images with significantly increased SNR, reduced artifacts, for similar spatial resolution, compared to gridding. Furthermore, the ability to reduce the effects of motion in PROPELLER-MRI was maintained when using the iterative reconstruction approach. Conclusion An iterative image reconstruction technique based on the NUFFT was investigated for PROPELLER MRI. For a certain range of values of the regularization parameter the new reconstruction technique may provide PROPELLER images with improved image quality compared to conventional gridding. PMID:20578028

Exploring the Ability of a Coarse-grained Potential to Describe the Stress-strain Response of Glassy Polystyrene

DTIC Science & Technology

2012-10-01

using the open-source code Large-scale Atomic/Molecular Massively Parallel Simulator ( LAMMPS ) (http://lammps.sandia.gov) (23). The commercial...parameters are proprietary and cannot be ported to the LAMMPS 4 simulation code. In our molecular dynamics simulations at the atomistic resolution, we...IBI iterative Boltzmann inversion LAMMPS Large-scale Atomic/Molecular Massively Parallel Simulator MAPS Materials Processes and Simulations MS

Real-Time, Multiple, Pan/Tilt/Zoom, Computer Vision Tracking, and 3D Position Estimating System for Unmanned Aerial System Metrology

DTIC Science & Technology

2013-10-18

of the enclosed tasks plus the last parallel task for a total of five parallel tasks for one iteration, i). for j = 1…N for i = 1… 8 Figure...drizzling juices culminating in a state of salivating desire to cut a piece and enjoy. On the other hand, the smell could be that of a pungent, unpleasant

An efficient iteration strategy for the solution of the Euler equations

NASA Technical Reports Server (NTRS)

Walters, R. W.; Dwoyer, D. L.

1985-01-01

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two-dimensions is described. The basic algorithm has the property that convergence to the steady-state is quadratic for fully supersonic flows and linear otherwise. This is in contrast to the block ADI methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented here is easily enhanced to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, thus yielding a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing both oblique and normal shock waves which confirm the efficiency of the iteration strategy.

High performance computing for deformable image registration: towards a new paradigm in adaptive radiotherapy.

PubMed

Samant, Sanjiv S; Xia, Junyi; Muyan-Ozcelik, Pinar; Owens, John D

2008-08-01

The advent of readily available temporal imaging or time series volumetric (4D) imaging has become an indispensable component of treatment planning and adaptive radiotherapy (ART) at many radiotherapy centers. Deformable image registration (DIR) is also used in other areas of medical imaging, including motion corrected image reconstruction. Due to long computation time, clinical applications of DIR in radiation therapy and elsewhere have been limited and consequently relegated to offline analysis. With the recent advances in hardware and software, graphics processing unit (GPU) based computing is an emerging technology for general purpose computation, including DIR, and is suitable for highly parallelized computing. However, traditional general purpose computation on the GPU is limited because the constraints of the available programming platforms. As well, compared to CPU programming, the GPU currently has reduced dedicated processor memory, which can limit the useful working data set for parallelized processing. We present an implementation of the demons algorithm using the NVIDIA 8800 GTX GPU and the new CUDA programming language. The GPU performance will be compared with single threading and multithreading CPU implementations on an Intel dual core 2.4 GHz CPU using the C programming language. CUDA provides a C-like language programming interface, and allows for direct access to the highly parallel compute units in the GPU. Comparisons for volumetric clinical lung images acquired using 4DCT were carried out. Computation time for 100 iterations in the range of 1.8-13.5 s was observed for the GPU with image size ranging from 2.0 x 10(6) to 14.2 x 10(6) pixels. The GPU registration was 55-61 times faster than the CPU for the single threading implementation, and 34-39 times faster for the multithreading implementation. For CPU based computing, the computational time generally has a linear dependence on image size for medical imaging data. Computational efficiency is characterized in terms of time per megapixels per iteration (TPMI) with units of seconds per megapixels per iteration (or spmi). For the demons algorithm, our CPU implementation yielded largely invariant values of TPMI. The mean TPMIs were 0.527 spmi and 0.335 spmi for the single threading and multithreading cases, respectively, with <2% variation over the considered image data range. For GPU computing, we achieved TPMI =0.00916 spmi with 3.7% variation, indicating optimized memory handling under CUDA. The paradigm of GPU based real-time DIR opens up a host of clinical applications for medical imaging.

Memory-Scalable GPU Spatial Hierarchy Construction.

PubMed

Qiming Hou; Xin Sun; Kun Zhou; Lauterbach, C; Manocha, D

2011-04-01

Recent GPU algorithms for constructing spatial hierarchies have achieved promising performance for moderately complex models by using the breadth-first search (BFS) construction order. While being able to exploit the massive parallelism on the GPU, the BFS order also consumes excessive GPU memory, which becomes a serious issue for interactive applications involving very complex models with more than a few million triangles. In this paper, we propose to use the partial breadth-first search (PBFS) construction order to control memory consumption while maximizing performance. We apply the PBFS order to two hierarchy construction algorithms. The first algorithm is for kd-trees that automatically balances between the level of parallelism and intermediate memory usage. With PBFS, peak memory consumption during construction can be efficiently controlled without costly CPU-GPU data transfer. We also develop memory allocation strategies to effectively limit memory fragmentation. The resulting algorithm scales well with GPU memory and constructs kd-trees of models with millions of triangles at interactive rates on GPUs with 1 GB memory. Compared with existing algorithms, our algorithm is an order of magnitude more scalable for a given GPU memory bound. The second algorithm is for out-of-core bounding volume hierarchy (BVH) construction for very large scenes based on the PBFS construction order. At each iteration, all constructed nodes are dumped to the CPU memory, and the GPU memory is freed for the next iteration's use. In this way, the algorithm is able to build trees that are too large to be stored in the GPU memory. Experiments show that our algorithm can construct BVHs for scenes with up to 20 M triangles, several times larger than previous GPU algorithms.

Iterative-method performance evaluation for multiple vectors associated with a large-scale sparse matrix

NASA Astrophysics Data System (ADS)

Imamura, Seigo; Ono, Kenji; Yokokawa, Mitsuo

2016-07-01

Ensemble computing, which is an instance of capacity computing, is an effective computing scenario for exascale parallel supercomputers. In ensemble computing, there are multiple linear systems associated with a common coefficient matrix. We improve the performance of iterative solvers for multiple vectors by solving them at the same time, that is, by solving for the product of the matrices. We implemented several iterative methods and compared their performance. The maximum performance on Sparc VIIIfx was 7.6 times higher than that of a naïve implementation. Finally, to deal with the different convergence processes of linear systems, we introduced a control method to eliminate the calculation of already converged vectors.

Methodes iteratives paralleles: Applications en neutronique et en mecanique des fluides

NASA Astrophysics Data System (ADS)

Qaddouri, Abdessamad

Dans cette these, le calcul parallele est applique successivement a la neutronique et a la mecanique des fluides. Dans chacune de ces deux applications, des methodes iteratives sont utilisees pour resoudre le systeme d'equations algebriques resultant de la discretisation des equations du probleme physique. Dans le probleme de neutronique, le calcul des matrices des probabilites de collision (PC) ainsi qu'un schema iteratif multigroupe utilisant une methode inverse de puissance sont parallelises. Dans le probleme de mecanique des fluides, un code d'elements finis utilisant un algorithme iteratif du type GMRES preconditionne est parallelise. Cette these est presentee sous forme de six articles suivis d'une conclusion. Les cinq premiers articles traitent des applications en neutronique, articles qui representent l'evolution de notre travail dans ce domaine. Cette evolution passe par un calcul parallele des matrices des PC et un algorithme multigroupe parallele teste sur un probleme unidimensionnel (article 1), puis par deux algorithmes paralleles l'un mutiregion l'autre multigroupe, testes sur des problemes bidimensionnels (articles 2--3). Ces deux premieres etapes sont suivies par l'application de deux techniques d'acceleration, le rebalancement neutronique et la minimisation du residu aux deux algorithmes paralleles (article 4). Finalement, on a mis en oeuvre l'algorithme multigroupe et le calcul parallele des matrices des PC sur un code de production DRAGON ou les tests sont plus realistes et peuvent etre tridimensionnels (article 5). Le sixieme article (article 6), consacre a l'application a la mecanique des fluides, traite la parallelisation d'un code d'elements finis FES ou le partitionneur de graphe METIS et la librairie PSPARSLIB sont utilises.

Generalizations of the Alternating Direction Method of Multipliers for Large-Scale and Distributed Optimization

DTIC Science & Technology

2014-05-01

exact one is solved later — as- signed as step 5 of Algorithm 2 — because at each iteration , the ADMM updates the variables in the Gauss - Seidel ...Jacobi ADMM (see Algo- rithm 5 below). Unlike the Gauss - Seidel ADMM, the Jacobi ADMM updates all the 70 blocks in parallel at every iteration : xk+1i...that extending ADMM straightforwardly from the classic Gauss - Seidel setting to the Jacobi setting, from two blocks to multiple blocks, will preserve

Inversion of potential field data using the finite element method on parallel computers

NASA Astrophysics Data System (ADS)

Gross, L.; Altinay, C.; Shaw, S.

2015-11-01

In this paper we present a formulation of the joint inversion of potential field anomaly data as an optimization problem with partial differential equation (PDE) constraints. The problem is solved using the iterative Broyden-Fletcher-Goldfarb-Shanno (BFGS) method with the Hessian operator of the regularization and cross-gradient component of the cost function as preconditioner. We will show that each iterative step requires the solution of several PDEs namely for the potential fields, for the adjoint defects and for the application of the preconditioner. In extension to the traditional discrete formulation the BFGS method is applied to continuous descriptions of the unknown physical properties in combination with an appropriate integral form of the dot product. The PDEs can easily be solved using standard conforming finite element methods (FEMs) with potentially different resolutions. For two examples we demonstrate that the number of PDE solutions required to reach a given tolerance in the BFGS iteration is controlled by weighting regularization and cross-gradient but is independent of the resolution of PDE discretization and that as a consequence the method is weakly scalable with the number of cells on parallel computers. We also show a comparison with the UBC-GIF GRAV3D code.

Performance evaluation of canny edge detection on a tiled multicore architecture

NASA Astrophysics Data System (ADS)

Brethorst, Andrew Z.; Desai, Nehal; Enright, Douglas P.; Scrofano, Ronald

2011-01-01

In the last few years, a variety of multicore architectures have been used to parallelize image processing applications. In this paper, we focus on assessing the parallel speed-ups of different Canny edge detection parallelization strategies on the Tile64, a tiled multicore architecture developed by the Tilera Corporation. Included in these strategies are different ways Canny edge detection can be parallelized, as well as differences in data management. The two parallelization strategies examined were loop-level parallelism and domain decomposition. Loop-level parallelism is achieved through the use of OpenMP,1 and it is capable of parallelization across the range of values over which a loop iterates. Domain decomposition is the process of breaking down an image into subimages, where each subimage is processed independently, in parallel. The results of the two strategies show that for the same number of threads, programmer implemented, domain decomposition exhibits higher speed-ups than the compiler managed, loop-level parallelism implemented with OpenMP.

The wave-based substructuring approach for the efficient description of interface dynamics in substructuring

NASA Astrophysics Data System (ADS)

Donders, S.; Pluymers, B.; Ragnarsson, P.; Hadjit, R.; Desmet, W.

2010-04-01

In the vehicle design process, design decisions are more and more based on virtual prototypes. Due to competitive and regulatory pressure, vehicle manufacturers are forced to improve product quality, to reduce time-to-market and to launch an increasing number of design variants on the global market. To speed up the design iteration process, substructuring and component mode synthesis (CMS) methods are commonly used, involving the analysis of substructure models and the synthesis of the substructure analysis results. Substructuring and CMS enable efficient decentralized collaboration across departments and allow to benefit from the availability of parallel computing environments. However, traditional CMS methods become prohibitively inefficient when substructures are coupled along large interfaces, i.e. with a large number of degrees of freedom (DOFs) at the interface between substructures. The reason is that the analysis of substructures involves the calculation of a number of enrichment vectors, one for each interface degree of freedom (DOF). Since large interfaces are common in vehicles (e.g. the continuous line connections to connect the body with the windshield, roof or floor), this interface bottleneck poses a clear limitation in the vehicle noise, vibration and harshness (NVH) design process. Therefore there is a need to describe the interface dynamics more efficiently. This paper presents a wave-based substructuring (WBS) approach, which allows reducing the interface representation between substructures in an assembly by expressing the interface DOFs in terms of a limited set of basis functions ("waves"). As the number of basis functions can be much lower than the number of interface DOFs, this greatly facilitates the substructure analysis procedure and results in faster design predictions. The waves are calculated once from a full nominal assembly analysis, but these nominal waves can be re-used for the assembly of modified components. The WBS approach thus enables efficient structural modification predictions of the global modes, so that efficient vibro-acoustic design modification, optimization and robust design become possible. The results show that wave-based substructuring offers a clear benefit for vehicle design modifications, by improving both the speed of component reduction processes and the efficiency and accuracy of design iteration predictions, as compared to conventional substructuring approaches.

3-D inversion of airborne electromagnetic data parallelized and accelerated by local mesh and adaptive soundings

NASA Astrophysics Data System (ADS)

Yang, Dikun; Oldenburg, Douglas W.; Haber, Eldad

2014-03-01

Airborne electromagnetic (AEM) methods are highly efficient tools for assessing the Earth's conductivity structures in a large area at low cost. However, the configuration of AEM measurements, which typically have widely distributed transmitter-receiver pairs, makes the rigorous modelling and interpretation extremely time-consuming in 3-D. Excessive overcomputing can occur when working on a large mesh covering the entire survey area and inverting all soundings in the data set. We propose two improvements. The first is to use a locally optimized mesh for each AEM sounding for the forward modelling and calculation of sensitivity. This dedicated local mesh is small with fine cells near the sounding location and coarse cells far away in accordance with EM diffusion and the geometric decay of the signals. Once the forward problem is solved on the local meshes, the sensitivity for the inversion on the global mesh is available through quick interpolation. Using local meshes for AEM forward modelling avoids unnecessary computing on fine cells on a global mesh that are far away from the sounding location. Since local meshes are highly independent, the forward modelling can be efficiently parallelized over an array of processors. The second improvement is random and dynamic down-sampling of the soundings. Each inversion iteration only uses a random subset of the soundings, and the subset is reselected for every iteration. The number of soundings in the random subset, determined by an adaptive algorithm, is tied to the degree of model regularization. This minimizes the overcomputing caused by working with redundant soundings. Our methods are compared against conventional methods and tested with a synthetic example. We also invert a field data set that was previously considered to be too large to be practically inverted in 3-D. These examples show that our methodology can dramatically reduce the processing time of 3-D inversion to a practical level without losing resolution. Any existing modelling technique can be included into our framework of mesh decoupling and adaptive sampling to accelerate large-scale 3-D EM inversions.

WE-G-18A-04: 3D Dictionary Learning Based Statistical Iterative Reconstruction for Low-Dose Cone Beam CT Imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bai, T; UT Southwestern Medical Center, Dallas, TX; Yan, H

2014-06-15

Purpose: To develop a 3D dictionary learning based statistical reconstruction algorithm on graphic processing units (GPU), to improve the quality of low-dose cone beam CT (CBCT) imaging with high efficiency. Methods: A 3D dictionary containing 256 small volumes (atoms) of 3x3x3 voxels was trained from a high quality volume image. During reconstruction, we utilized a Cholesky decomposition based orthogonal matching pursuit algorithm to find a sparse representation on this dictionary basis of each patch in the reconstructed image, in order to regularize the image quality. To accelerate the time-consuming sparse coding in the 3D case, we implemented our algorithm inmore » a parallel fashion by taking advantage of the tremendous computational power of GPU. Evaluations are performed based on a head-neck patient case. FDK reconstruction with full dataset of 364 projections is used as the reference. We compared the proposed 3D dictionary learning based method with a tight frame (TF) based one using a subset data of 121 projections. The image qualities under different resolutions in z-direction, with or without statistical weighting are also studied. Results: Compared to the TF-based CBCT reconstruction, our experiments indicated that 3D dictionary learning based CBCT reconstruction is able to recover finer structures, to remove more streaking artifacts, and is less susceptible to blocky artifacts. It is also observed that statistical reconstruction approach is sensitive to inconsistency between the forward and backward projection operations in parallel computing. Using high a spatial resolution along z direction helps improving the algorithm robustness. Conclusion: 3D dictionary learning based CBCT reconstruction algorithm is able to sense the structural information while suppressing noise, and hence to achieve high quality reconstruction. The GPU realization of the whole algorithm offers a significant efficiency enhancement, making this algorithm more feasible for potential clinical application. A high zresolution is preferred to stabilize statistical iterative reconstruction. This work was supported in part by NIH(1R01CA154747-01), NSFC((No. 61172163), Research Fund for the Doctoral Program of Higher Education of China (No. 20110201110011), China Scholarship Council.« less

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

NASA Technical Reports Server (NTRS)

Turc, Catalin; Anand, Akash; Bruno, Oscar; Chaubell, Julian

2011-01-01

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

NASA Astrophysics Data System (ADS)

Wang, Yi-Hong; Wu, Guo-Cheng; Baleanu, Dumitru

2013-10-01

The variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method's new role.

Exploiting loop level parallelism in nonprocedural dataflow programs

NASA Technical Reports Server (NTRS)

Gokhale, Maya B.

1987-01-01

Discussed are how loop level parallelism is detected in a nonprocedural dataflow program, and how a procedural program with concurrent loops is scheduled. Also discussed is a program restructuring technique which may be applied to recursive equations so that concurrent loops may be generated for a seemingly iterative computation. A compiler which generates C code for the language described below has been implemented. The scheduling component of the compiler and the restructuring transformation are described.

Efficient Machine Learning Approach for Optimizing Scientific Computing Applications on Emerging HPC Architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arumugam, Kamesh

Efficient parallel implementations of scientific applications on multi-core CPUs with accelerators such as GPUs and Xeon Phis is challenging. This requires - exploiting the data parallel architecture of the accelerator along with the vector pipelines of modern x86 CPU architectures, load balancing, and efficient memory transfer between different devices. It is relatively easy to meet these requirements for highly structured scientific applications. In contrast, a number of scientific and engineering applications are unstructured. Getting performance on accelerators for these applications is extremely challenging because many of these applications employ irregular algorithms which exhibit data-dependent control-ow and irregular memory accesses. Furthermore,more » these applications are often iterative with dependency between steps, and thus making it hard to parallelize across steps. As a result, parallelism in these applications is often limited to a single step. Numerical simulation of charged particles beam dynamics is one such application where the distribution of work and memory access pattern at each time step is irregular. Applications with these properties tend to present significant branch and memory divergence, load imbalance between different processor cores, and poor compute and memory utilization. Prior research on parallelizing such irregular applications have been focused around optimizing the irregular, data-dependent memory accesses and control-ow during a single step of the application independent of the other steps, with the assumption that these patterns are completely unpredictable. We observed that the structure of computation leading to control-ow divergence and irregular memory accesses in one step is similar to that in the next step. It is possible to predict this structure in the current step by observing the computation structure of previous steps. In this dissertation, we present novel machine learning based optimization techniques to address the parallel implementation challenges of such irregular applications on different HPC architectures. In particular, we use supervised learning to predict the computation structure and use it to address the control-ow and memory access irregularities in the parallel implementation of such applications on GPUs, Xeon Phis, and heterogeneous architectures composed of multi-core CPUs with GPUs or Xeon Phis. We use numerical simulation of charged particles beam dynamics simulation as a motivating example throughout the dissertation to present our new approach, though they should be equally applicable to a wide range of irregular applications. The machine learning approach presented here use predictive analytics and forecasting techniques to adaptively model and track the irregular memory access pattern at each time step of the simulation to anticipate the future memory access pattern. Access pattern forecasts can then be used to formulate optimization decisions during application execution which improves the performance of the application at a future time step based on the observations from earlier time steps. In heterogeneous architectures, forecasts can also be used to improve the memory performance and resource utilization of all the processing units to deliver a good aggregate performance. We used these optimization techniques and anticipation strategy to design a cache-aware, memory efficient parallel algorithm to address the irregularities in the parallel implementation of charged particles beam dynamics simulation on different HPC architectures. Experimental result using a diverse mix of HPC architectures shows that our approach in using anticipation strategy is effective in maximizing data reuse, ensuring workload balance, minimizing branch and memory divergence, and in improving resource utilization.« less

GPU-accelerated iterative reconstruction for limited-data tomography in CBCT systems.

PubMed

de Molina, Claudia; Serrano, Estefania; Garcia-Blas, Javier; Carretero, Jesus; Desco, Manuel; Abella, Monica

2018-05-15

Standard cone-beam computed tomography (CBCT) involves the acquisition of at least 360 projections rotating through 360 degrees. Nevertheless, there are cases in which only a few projections can be taken in a limited angular span, such as during surgery, where rotation of the source-detector pair is limited to less than 180 degrees. Reconstruction of limited data with the conventional method proposed by Feldkamp, Davis and Kress (FDK) results in severe artifacts. Iterative methods may compensate for the lack of data by including additional prior information, although they imply a high computational burden and memory consumption. We present an accelerated implementation of an iterative method for CBCT following the Split Bregman formulation, which reduces computational time through GPU-accelerated kernels. The implementation enables the reconstruction of large volumes (>1024 3 pixels) using partitioning strategies in forward- and back-projection operations. We evaluated the algorithm on small-animal data for different scenarios with different numbers of projections, angular span, and projection size. Reconstruction time varied linearly with the number of projections and quadratically with projection size but remained almost unchanged with angular span. Forward- and back-projection operations represent 60% of the total computational burden. Efficient implementation using parallel processing and large-memory management strategies together with GPU kernels enables the use of advanced reconstruction approaches which are needed in limited-data scenarios. Our GPU implementation showed a significant time reduction (up to 48 ×) compared to a CPU-only implementation, resulting in a total reconstruction time from several hours to few minutes.

Fast iterative image reconstruction using sparse matrix factorization with GPU acceleration

NASA Astrophysics Data System (ADS)

Zhou, Jian; Qi, Jinyi

2011-03-01

Statistically based iterative approaches for image reconstruction have gained much attention in medical imaging. An accurate system matrix that defines the mapping from the image space to the data space is the key to high-resolution image reconstruction. However, an accurate system matrix is often associated with high computational cost and huge storage requirement. Here we present a method to address this problem by using sparse matrix factorization and parallel computing on a graphic processing unit (GPU).We factor the accurate system matrix into three sparse matrices: a sinogram blurring matrix, a geometric projection matrix, and an image blurring matrix. The sinogram blurring matrix models the detector response. The geometric projection matrix is based on a simple line integral model. The image blurring matrix is to compensate for the line-of-response (LOR) degradation due to the simplified geometric projection matrix. The geometric projection matrix is precomputed, while the sinogram and image blurring matrices are estimated by minimizing the difference between the factored system matrix and the original system matrix. The resulting factored system matrix has much less number of nonzero elements than the original system matrix and thus substantially reduces the storage and computation cost. The smaller size also allows an efficient implement of the forward and back projectors on GPUs, which have limited amount of memory. Our simulation studies show that the proposed method can dramatically reduce the computation cost of high-resolution iterative image reconstruction. The proposed technique is applicable to image reconstruction for different imaging modalities, including x-ray CT, PET, and SPECT.

Coarse mesh and one-cell block inversion based diffusion synthetic acceleration

NASA Astrophysics Data System (ADS)

Kim, Kang-Seog

DSA (Diffusion Synthetic Acceleration) has been developed to accelerate the SN transport iteration. We have developed solution techniques for the diffusion equations of FLBLD (Fully Lumped Bilinear Discontinuous), SCB (Simple Comer Balance) and UCB (Upstream Corner Balance) modified 4-step DSA in x-y geometry. Our first multi-level method includes a block Gauss-Seidel iteration for the discontinuous diffusion equation, uses the continuous diffusion equation derived from the asymptotic analysis, and avoids void cell calculation. We implemented this multi-level procedure and performed model problem calculations. The results showed that the FLBLD, SCB and UCB modified 4-step DSA schemes with this multi-level technique are unconditionally stable and rapidly convergent. We suggested a simplified multi-level technique for FLBLD, SCB and UCB modified 4-step DSA. This new procedure does not include iterations on the diffusion calculation or the residual calculation. Fourier analysis results showed that this new procedure was as rapidly convergent as conventional modified 4-step DSA. We developed new DSA procedures coupled with 1-CI (Cell Block Inversion) transport which can be easily parallelized. We showed that 1-CI based DSA schemes preceded by SI (Source Iteration) are efficient and rapidly convergent for LD (Linear Discontinuous) and LLD (Lumped Linear Discontinuous) in slab geometry and for BLD (Bilinear Discontinuous) and FLBLD in x-y geometry. For 1-CI based DSA without SI in slab geometry, the results showed that this procedure is very efficient and effective for all cases. We also showed that 1-CI based DSA in x-y geometry was not effective for thin mesh spacings, but is effective and rapidly convergent for intermediate and thick mesh spacings. We demonstrated that the diffusion equation discretized on a coarse mesh could be employed to accelerate the transport equation. Our results showed that coarse mesh DSA is unconditionally stable and is as rapidly convergent as fine mesh DSA in slab geometry. For x-y geometry our coarse mesh DSA is very effective for thin and intermediate mesh spacings independent of the scattering ratio, but is not effective for purely scattering problems and high aspect ratio zoning. However, if the scattering ratio is less than about 0.95, this procedure is very effective for all mesh spacing.

Evaluating Multi-core Architectures through Accelerating the Three-Dimensional Lax–Wendroff Correction

DOE Office of Scientific and Technical Information (OSTI.GOV)

You, Yang; Fu, Haohuan; Song, Shuaiwen

2014-07-18

Wave propagation forward modeling is a widely used computational method in oil and gas exploration. The iterative stencil loops in such problems have broad applications in scientific computing. However, executing such loops can be highly time time-consuming, which greatly limits application’s performance and power efficiency. In this paper, we accelerate the forward modeling technique on the latest multi-core and many-core architectures such as Intel Sandy Bridge CPUs, NVIDIA Fermi C2070 GPU, NVIDIA Kepler K20x GPU, and the Intel Xeon Phi Co-processor. For the GPU platforms, we propose two parallel strategies to explore the performance optimization opportunities for our stencil kernels.more » For Sandy Bridge CPUs and MIC, we also employ various optimization techniques in order to achieve the best.« less

Domain decomposition algorithms and computation fluid dynamics

NASA Technical Reports Server (NTRS)

Chan, Tony F.

1988-01-01

In the past several years, domain decomposition was a very popular topic, partly motivated by the potential of parallelization. While a large body of theory and algorithms were developed for model elliptic problems, they are only recently starting to be tested on realistic applications. The application of some of these methods to two model problems in computational fluid dynamics are investigated. Some examples are two dimensional convection-diffusion problems and the incompressible driven cavity flow problem. The construction and analysis of efficient preconditioners for the interface operator to be used in the iterative solution of the interface solution is described. For the convection-diffusion problems, the effect of the convection term and its discretization on the performance of some of the preconditioners is discussed. For the driven cavity problem, the effectiveness of a class of boundary probe preconditioners is discussed.

Iterated unscented Kalman filter for phase unwrapping of interferometric fringes.

PubMed

Xie, Xianming

2016-08-22

A fresh phase unwrapping algorithm based on iterated unscented Kalman filter is proposed to estimate unambiguous unwrapped phase of interferometric fringes. This method is the result of combining an iterated unscented Kalman filter with a robust phase gradient estimator based on amended matrix pencil model, and an efficient quality-guided strategy based on heap sort. The iterated unscented Kalman filter that is one of the most robust methods under the Bayesian theorem frame in non-linear signal processing so far, is applied to perform simultaneously noise suppression and phase unwrapping of interferometric fringes for the first time, which can simplify the complexity and the difficulty of pre-filtering procedure followed by phase unwrapping procedure, and even can remove the pre-filtering procedure. The robust phase gradient estimator is used to efficiently and accurately obtain phase gradient information from interferometric fringes, which is needed for the iterated unscented Kalman filtering phase unwrapping model. The efficient quality-guided strategy is able to ensure that the proposed method fast unwraps wrapped pixels along the path from the high-quality area to the low-quality area of wrapped phase images, which can greatly improve the efficiency of phase unwrapping. Results obtained from synthetic data and real data show that the proposed method can obtain better solutions with an acceptable time consumption, with respect to some of the most used algorithms.

Efficient Geometry Minimization and Transition Structure Optimization Using Interpolated Potential Energy Surfaces and Iteratively Updated Hessians.

PubMed

Zheng, Jingjing; Frisch, Michael J

2017-12-12

An efficient geometry optimization algorithm based on interpolated potential energy surfaces with iteratively updated Hessians is presented in this work. At each step of geometry optimization (including both minimization and transition structure search), an interpolated potential energy surface is properly constructed by using the previously calculated information (energies, gradients, and Hessians/updated Hessians), and Hessians of the two latest geometries are updated in an iterative manner. The optimized minimum or transition structure on the interpolated surface is used for the starting geometry of the next geometry optimization step. The cost of searching the minimum or transition structure on the interpolated surface and iteratively updating Hessians is usually negligible compared with most electronic structure single gradient calculations. These interpolated potential energy surfaces are often better representations of the true potential energy surface in a broader range than a local quadratic approximation that is usually used in most geometry optimization algorithms. Tests on a series of large and floppy molecules and transition structures both in gas phase and in solutions show that the new algorithm can significantly improve the optimization efficiency by using the iteratively updated Hessians and optimizations on interpolated surfaces.

Tinker-HP: a massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c7sc04531j

PubMed Central

Lagardère, Louis; Jolly, Luc-Henri; Lipparini, Filippo; Aviat, Félix; Stamm, Benjamin; Jing, Zhifeng F.; Harger, Matthew; Torabifard, Hedieh; Cisneros, G. Andrés; Schnieders, Michael J.; Gresh, Nohad; Maday, Yvon; Ren, Pengyu Y.; Ponder, Jay W.

2017-01-01

We present Tinker-HP, a massively MPI parallel package dedicated to classical molecular dynamics (MD) and to multiscale simulations, using advanced polarizable force fields (PFF) encompassing distributed multipoles electrostatics. Tinker-HP is an evolution of the popular Tinker package code that conserves its simplicity of use and its reference double precision implementation for CPUs. Grounded on interdisciplinary efforts with applied mathematics, Tinker-HP allows for long polarizable MD simulations on large systems up to millions of atoms. We detail in the paper the newly developed extension of massively parallel 3D spatial decomposition to point dipole polarizable models as well as their coupling to efficient Krylov iterative and non-iterative polarization solvers. The design of the code allows the use of various computer systems ranging from laboratory workstations to modern petascale supercomputers with thousands of cores. Tinker-HP proposes therefore the first high-performance scalable CPU computing environment for the development of next generation point dipole PFFs and for production simulations. Strategies linking Tinker-HP to Quantum Mechanics (QM) in the framework of multiscale polarizable self-consistent QM/MD simulations are also provided. The possibilities, performances and scalability of the software are demonstrated via benchmarks calculations using the polarizable AMOEBA force field on systems ranging from large water boxes of increasing size and ionic liquids to (very) large biosystems encompassing several proteins as well as the complete satellite tobacco mosaic virus and ribosome structures. For small systems, Tinker-HP appears to be competitive with the Tinker-OpenMM GPU implementation of Tinker. As the system size grows, Tinker-HP remains operational thanks to its access to distributed memory and takes advantage of its new algorithmic enabling for stable long timescale polarizable simulations. Overall, a several thousand-fold acceleration over a single-core computation is observed for the largest systems. The extension of the present CPU implementation of Tinker-HP to other computational platforms is discussed. PMID:29732110

Exploiting Vector and Multicore Parallelsim for Recursive, Data- and Task-Parallel Programs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ren, Bin; Krishnamoorthy, Sriram; Agrawal, Kunal

Modern hardware contains parallel execution resources that are well-suited for data-parallelism-vector units-and task parallelism-multicores. However, most work on parallel scheduling focuses on one type of hardware or the other. In this work, we present a scheduling framework that allows for a unified treatment of task- and data-parallelism. Our key insight is an abstraction, task blocks, that uniformly handles data-parallel iterations and task-parallel tasks, allowing them to be scheduled on vector units or executed independently as multicores. Our framework allows us to define schedulers that can dynamically select between executing task- blocks on vector units or multicores. We show that thesemore » schedulers are asymptotically optimal, and deliver the maximum amount of parallelism available in computation trees. To evaluate our schedulers, we develop program transformations that can convert mixed data- and task-parallel pro- grams into task block-based programs. Using a prototype instantiation of our scheduling framework, we show that, on an 8-core system, we can simultaneously exploit vector and multicore parallelism to achieve 14×-108× speedup over sequential baselines.« less

Development of a fully implicit particle-in-cell scheme for gyrokinetic electromagnetic turbulence simulation in XGC1

NASA Astrophysics Data System (ADS)

Ku, Seung-Hoe; Hager, R.; Chang, C. S.; Chacon, L.; Chen, G.; EPSI Team

2016-10-01

The cancelation problem has been a long-standing issue for long wavelengths modes in electromagnetic gyrokinetic PIC simulations in toroidal geometry. As an attempt of resolving this issue, we implemented a fully implicit time integration scheme in the full-f, gyrokinetic PIC code XGC1. The new scheme - based on the implicit Vlasov-Darwin PIC algorithm by G. Chen and L. Chacon - can potentially resolve cancelation problem. The time advance for the field and the particle equations is space-time-centered, with particle sub-cycling. The resulting system of equations is solved by a Picard iteration solver with fixed-point accelerator. The algorithm is implemented in the parallel velocity formalism instead of the canonical parallel momentum formalism. XGC1 specializes in simulating the tokamak edge plasma with magnetic separatrix geometry. A fully implicit scheme could be a way to accurate and efficient gyrokinetic simulations. We will test if this numerical scheme overcomes the cancelation problem, and reproduces the dispersion relation of Alfven waves and tearing modes in cylindrical geometry. Funded by US DOE FES and ASCR, and computing resources provided by OLCF through ALCC.

Acoustic 3D modeling by the method of integral equations

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2018-02-01

This paper presents a parallel algorithm for frequency-domain acoustic modeling by the method of integral equations (IE). The algorithm is applied to seismic simulation. The IE method reduces the size of the problem but leads to a dense system matrix. A tolerable memory consumption and numerical complexity were achieved by applying an iterative solver, accompanied by an effective matrix-vector multiplication operation, based on the fast Fourier transform (FFT). We demonstrate that, the IE system matrix is better conditioned than that of the finite-difference (FD) method, and discuss its relation to a specially preconditioned FD matrix. We considered several methods of matrix-vector multiplication for the free-space and layered host models. The developed algorithm and computer code were benchmarked against the FD time-domain solution. It was demonstrated that, the method could accurately calculate the seismic field for the models with sharp material boundaries and a point source and receiver located close to the free surface. We used OpenMP to speed up the matrix-vector multiplication, while MPI was used to speed up the solution of the system equations, and also for parallelizing across multiple sources. The practical examples and efficiency tests are presented as well.

An innovative hybrid 3D analytic-numerical model for air breathing parallel channel counter-flow PEM fuel cells.

PubMed

Tavčar, Gregor; Katrašnik, Tomaž

2014-01-01

The parallel straight channel PEM fuel cell model presented in this paper extends the innovative hybrid 3D analytic-numerical (HAN) approach previously published by the authors with capabilities to address ternary diffusion systems and counter-flow configurations. The model's core principle is modelling species transport by obtaining a 2D analytic solution for species concentration distribution in the plane perpendicular to the cannel gas-flow and coupling consecutive 2D solutions by means of a 1D numerical pipe-flow model. Electrochemical and other nonlinear phenomena are coupled to the species transport by a routine that uses derivative approximation with prediction-iteration. The latter is also the core of the counter-flow computation algorithm. A HAN model of a laboratory test fuel cell is presented and evaluated against a professional 3D CFD simulation tool showing very good agreement between results of the presented model and those of the CFD simulation. Furthermore, high accuracy results are achieved at moderate computational times, which is owed to the semi-analytic nature and to the efficient computational coupling of electrochemical kinetics and species transport.

A Single LiDAR-Based Feature Fusion Indoor Localization Algorithm.

PubMed

Wang, Yun-Ting; Peng, Chao-Chung; Ravankar, Ankit A; Ravankar, Abhijeet

2018-04-23

In past years, there has been significant progress in the field of indoor robot localization. To precisely recover the position, the robots usually relies on multiple on-board sensors. Nevertheless, this affects the overall system cost and increases computation. In this research work, we considered a light detection and ranging (LiDAR) device as the only sensor for detecting surroundings and propose an efficient indoor localization algorithm. To attenuate the computation effort and preserve localization robustness, a weighted parallel iterative closed point (WP-ICP) with interpolation is presented. As compared to the traditional ICP, the point cloud is first processed to extract corners and line features before applying point registration. Later, points labeled as corners are only matched with the corner candidates. Similarly, points labeled as lines are only matched with the lines candidates. Moreover, their ICP confidence levels are also fused in the algorithm, which make the pose estimation less sensitive to environment uncertainties. The proposed WP-ICP architecture reduces the probability of mismatch and thereby reduces the ICP iterations. Finally, based on given well-constructed indoor layouts, experiment comparisons are carried out under both clean and perturbed environments. It is shown that the proposed method is effective in significantly reducing computation effort and is simultaneously able to preserve localization precision.

A Single LiDAR-Based Feature Fusion Indoor Localization Algorithm

PubMed Central

Wang, Yun-Ting; Peng, Chao-Chung; Ravankar, Ankit A.; Ravankar, Abhijeet

2018-01-01

In past years, there has been significant progress in the field of indoor robot localization. To precisely recover the position, the robots usually relies on multiple on-board sensors. Nevertheless, this affects the overall system cost and increases computation. In this research work, we considered a light detection and ranging (LiDAR) device as the only sensor for detecting surroundings and propose an efficient indoor localization algorithm. To attenuate the computation effort and preserve localization robustness, a weighted parallel iterative closed point (WP-ICP) with interpolation is presented. As compared to the traditional ICP, the point cloud is first processed to extract corners and line features before applying point registration. Later, points labeled as corners are only matched with the corner candidates. Similarly, points labeled as lines are only matched with the lines candidates. Moreover, their ICP confidence levels are also fused in the algorithm, which make the pose estimation less sensitive to environment uncertainties. The proposed WP-ICP architecture reduces the probability of mismatch and thereby reduces the ICP iterations. Finally, based on given well-constructed indoor layouts, experiment comparisons are carried out under both clean and perturbed environments. It is shown that the proposed method is effective in significantly reducing computation effort and is simultaneously able to preserve localization precision. PMID:29690624

Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations.

PubMed

Negre, Christian F A; Mniszewski, Susan M; Cawkwell, Marc J; Bock, Nicolas; Wall, Michael E; Niklasson, Anders M N

2016-07-12

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive, iterative refinement of an initial guess of Z (inverse square root of the overlap matrix S). The initial guess of Z is obtained beforehand by using either an approximate divide-and-conquer technique or dynamical methods, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under the incomplete, approximate, iterative refinement of Z. Linear-scaling performance is obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables efficient shared-memory parallelization. As we show in this article using self-consistent density-functional-based tight-binding MD, our approach is faster than conventional methods based on the diagonalization of overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4158-atom water-solvated polyalanine system, we find an average speedup factor of 122 for the computation of Z in each MD step.

Air Force Maui Optical and Supercomputing Site (AMOS) Application Briefs 2004

DTIC Science & Technology

2004-01-01

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection...17. LIMITATION OF ABSTRACT Same as Report (SAR) 18. NUMBER OF PAGES 60 19a. NAME OF RESPONSIBLE PERSON a. REPORT unclassified b. ABSTRACT...SOR methods, the work in parallel matrix iterative methods is very relevant to the parallelization of a CA. The Moore neighborhood used in this work

Nonlinear study of the parallel velocity/tearing instability using an implicit, nonlinear resistive MHD solver

NASA Astrophysics Data System (ADS)

Chacon, L.; Finn, J. M.; Knoll, D. A.

2000-10-01

Recently, a new parallel velocity instability has been found.(J. M. Finn, Phys. Plasmas), 2, 12 (1995) This mode is a tearing mode driven unstable by curvature effects and sound wave coupling in the presence of parallel velocity shear. Under such conditions, linear theory predicts that tearing instabilities will grow even in situations in which the classical tearing mode is stable. This could then be a viable seed mechanism for the neoclassical tearing mode, and hence a non-linear study is of interest. Here, the linear and non-linear stages of this instability are explored using a fully implicit, fully nonlinear 2D reduced resistive MHD code,(L. Chacon et al), ``Implicit, Jacobian-free Newton-Krylov 2D reduced resistive MHD nonlinear solver,'' submitted to J. Comput. Phys. (2000) including viscosity and particle transport effects. The nonlinear implicit time integration is performed using the Newton-Raphson iterative algorithm. Krylov iterative techniques are employed for the required algebraic matrix inversions, implemented Jacobian-free (i.e., without ever forming and storing the Jacobian matrix), and preconditioned with a ``physics-based'' preconditioner. Nonlinear results indicate that, for large total plasma beta and large parallel velocity shear, the instability results in the generation of large poloidal shear flows and large magnetic islands even in regimes when the classical tearing mode is absolutely stable. For small viscosity, the time asymptotic state can be turbulent.

A communication-avoiding, hybrid-parallel, rank-revealing orthogonalization method.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hoemmen, Mark

2010-11-01

Orthogonalization consumes much of the run time of many iterative methods for solving sparse linear systems and eigenvalue problems. Commonly used algorithms, such as variants of Gram-Schmidt or Householder QR, have performance dominated by communication. Here, 'communication' includes both data movement between the CPU and memory, and messages between processors in parallel. Our Tall Skinny QR (TSQR) family of algorithms requires asymptotically fewer messages between processors and data movement between CPU and memory than typical orthogonalization methods, yet achieves the same accuracy as Householder QR factorization. Furthermore, in block orthogonalizations, TSQR is faster and more accurate than existing approaches formore » orthogonalizing the vectors within each block ('normalization'). TSQR's rank-revealing capability also makes it useful for detecting deflation in block iterative methods, for which existing approaches sacrifice performance, accuracy, or both. We have implemented a version of TSQR that exploits both distributed-memory and shared-memory parallelism, and supports real and complex arithmetic. Our implementation is optimized for the case of orthogonalizing a small number (5-20) of very long vectors. The shared-memory parallel component uses Intel's Threading Building Blocks, though its modular design supports other shared-memory programming models as well, including computation on the GPU. Our implementation achieves speedups of 2 times or more over competing orthogonalizations. It is available now in the development branch of the Trilinos software package, and will be included in the 10.8 release.« less

A parallel variable metric optimization algorithm

NASA Technical Reports Server (NTRS)

Straeter, T. A.

1973-01-01

An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.

Memory transfer optimization for a lattice Boltzmann solver on Kepler architecture nVidia GPUs

NASA Astrophysics Data System (ADS)

Mawson, Mark J.; Revell, Alistair J.

2014-10-01

The Lattice Boltzmann method (LBM) for solving fluid flow is naturally well suited to an efficient implementation for massively parallel computing, due to the prevalence of local operations in the algorithm. This paper presents and analyses the performance of a 3D lattice Boltzmann solver, optimized for third generation nVidia GPU hardware, also known as 'Kepler'. We provide a review of previous optimization strategies and analyse data read/write times for different memory types. In LBM, the time propagation step (known as streaming), involves shifting data to adjacent locations and is central to parallel performance; here we examine three approaches which make use of different hardware options. Two of which make use of 'performance enhancing' features of the GPU; shared memory and the new shuffle instruction found in Kepler based GPUs. These are compared to a standard transfer of data which relies instead on optimized storage to increase coalesced access. It is shown that the more simple approach is most efficient; since the need for large numbers of registers per thread in LBM limits the block size and thus the efficiency of these special features is reduced. Detailed results are obtained for a D3Q19 LBM solver, which is benchmarked on nVidia K5000M and K20C GPUs. In the latter case the use of a read-only data cache is explored, and peak performance of over 1036 Million Lattice Updates Per Second (MLUPS) is achieved. The appearance of a periodic bottleneck in the solver performance is also reported, believed to be hardware related; spikes in iteration-time occur with a frequency of around 11 Hz for both GPUs, independent of the size of the problem.

A novel iterative scheme and its application to differential equations.

PubMed

Khan, Yasir; Naeem, F; Šmarda, Zdeněk

2014-01-01

The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method.

Upgrade of the BATMAN test facility for H- source development

NASA Astrophysics Data System (ADS)

Heinemann, B.; Fröschle, M.; Falter, H.-D.; Fantz, U.; Franzen, P.; Kraus, W.; Nocentini, R.; Riedl, R.; Ruf, B.

2015-04-01

The development of a radio frequency (RF) driven source for negative hydrogen ions for the neutral beam heating devices of fusion experiments has been successfully carried out at IPP since 1996 on the test facility BATMAN. The required ITER parameters have been achieved with the prototype source consisting of a cylindrical driver on the back side of a racetrack like expansion chamber. The extraction system, called "Large Area Grid" (LAG) was derived from a positive ion accelerator from ASDEX Upgrade (AUG) using its aperture size (ø 8 mm) and pattern but replacing the first two electrodes and masking down the extraction area to 70 cm2. BATMAN is a well diagnosed and highly flexible test facility which will be kept operational in parallel to the half size ITER source test facility ELISE for further developments to improve the RF efficiency and the beam properties. It is therefore planned to upgrade BATMAN with a new ITER-like grid system (ILG) representing almost one ITER beamlet group, namely 5 × 14 apertures (ø 14 mm). Additionally to the standard three grid extraction system a repeller electrode upstream of the grounded grid can optionally be installed which is positively charged against it by 2 kV. This is designated to affect the onset of the space charge compensation downstream of the grounded grid and to reduce the backstreaming of positive ions from the drift space backwards into the ion source. For magnetic filter field studies a plasma grid current up to 3 kA will be available as well as permanent magnets embedded into a diagnostic flange or in an external magnet frame. Furthermore different source vessels and source configurations are under discussion for BATMAN, e.g. using the AUG type racetrack RF source as driver instead of the circular one or modifying the expansion chamber for a more flexible position of the external magnet frame.

FPGA implementation of low complexity LDPC iterative decoder

NASA Astrophysics Data System (ADS)

Verma, Shivani; Sharma, Sanjay

2016-07-01

Low-density parity-check (LDPC) codes, proposed by Gallager, emerged as a class of codes which can yield very good performance on the additive white Gaussian noise channel as well as on the binary symmetric channel. LDPC codes have gained lots of importance due to their capacity achieving property and excellent performance in the noisy channel. Belief propagation (BP) algorithm and its approximations, most notably min-sum, are popular iterative decoding algorithms used for LDPC and turbo codes. The trade-off between the hardware complexity and the decoding throughput is a critical factor in the implementation of the practical decoder. This article presents introduction to LDPC codes and its various decoding algorithms followed by realisation of LDPC decoder by using simplified message passing algorithm and partially parallel decoder architecture. Simplified message passing algorithm has been proposed for trade-off between low decoding complexity and decoder performance. It greatly reduces the routing and check node complexity of the decoder. Partially parallel decoder architecture possesses high speed and reduced complexity. The improved design of the decoder possesses a maximum symbol throughput of 92.95 Mbps and a maximum of 18 decoding iterations. The article presents implementation of 9216 bits, rate-1/2, (3, 6) LDPC decoder on Xilinx XC3D3400A device from Spartan-3A DSP family.

Drifts, currents, and power scrape-off width in SOLPS-ITER modeling of DIII-D

DOE PAGES

Meier, E. T.; Goldston, R. J.; Kaveeva, E. G.; ...

2016-12-27

The effects of drifts and associated flows and currents on the width of the parallel heat flux channel (λ q) in the tokamak scrape-off layer (SOL) are analyzed using the SOLPS-ITER 2D fluid transport code. Motivation is supplied by Goldston’s heuristic drift (HD) model for λ q, which yields the same approximately inverse poloidal magnetic field dependence seen in multi-machine regression. The analysis, focusing on a DIII-D H-mode discharge, reveals HD-like features, including comparable density and temperature fall-off lengths in the SOL, and up-down ion pressure asymmetry that allows net cross-separatrix ion magnetic drift flux to exceed net anomalous ionmore » flux. In experimentally relevant high-recycling cases, scans of both toroidal and poloidal magnetic field (B tor and B pol) are conducted, showing minimal λ q dependence on either component of the field. Insensitivity to B tor is expected, and suggests that SOLPS-ITER is effectively capturing some aspects of HD physics. Absence of λ q dependence on B pol, however, is inconsistent with both the HD model and experimental results. As a result, the inconsistency is attributed to strong variation in the parallel Mach number, which violates one of the premises of the HD model.« less

Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moryakov, A. V., E-mail: sailor@orc.ru

2016-12-15

An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

Acceleration of linear stationary iterative processes in multiprocessor computers. II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romm, Ya.E.

1982-05-01

For pt.I, see Kibernetika, vol.18, no.1, p.47 (1982). For pt.I, see Cybernetics, vol.18, no.1, p.54 (1982). Considers a reduced system of linear algebraic equations x=ax+b, where a=(a/sub ij/) is a real n*n matrix; b is a real vector with common euclidean norm >>>. It is supposed that the existence and uniqueness of solution det (0-a) not equal to e is given, where e is a unit matrix. The linear iterative process converging to x x/sup (k+1)/=fx/sup (k)/, k=0, 1, 2, ..., where the operator f translates r/sup n/ into r/sup n/. In considering implementation of the iterative process (ip) inmore » a multiprocessor system, it is assumed that the number of processors is constant, and are various values of the latter investigated; it is assumed in addition, that the processors perform elementary binary arithmetic operations of addition and multiestimates only include the time of execution of arithmetic operations. With any paralleling of individual iteration, the execution time of the ip is proportional to the number of sequential steps k+1. The author sets the task of reducing the number of sequential steps in the ip so as to execute it in a time proportional to a value smaller than k+1. He also sets the goal of formulating a method of accelerated bit serial-parallel execution of each successive step of the ip, with, in the modification sought, a reduced number of steps in a time comparable to the operation time of logical elements. 6 references.« less

Reconstruction of coded aperture images

NASA Technical Reports Server (NTRS)

Bielefeld, Michael J.; Yin, Lo I.

1987-01-01

Balanced correlation method and the Maximum Entropy Method (MEM) were implemented to reconstruct a laboratory X-ray source as imaged by a Uniformly Redundant Array (URA) system. Although the MEM method has advantages over the balanced correlation method, it is computationally time consuming because of the iterative nature of its solution. Massively Parallel Processing, with its parallel array structure is ideally suited for such computations. These preliminary results indicate that it is possible to use the MEM method in future coded-aperture experiments with the help of the MPP.

Research in Computational Aeroscience Applications Implemented on Advanced Parallel Computing Systems

NASA Technical Reports Server (NTRS)

Wigton, Larry

1996-01-01

Improving the numerical linear algebra routines for use in new Navier-Stokes codes, specifically Tim Barth's unstructured grid code, with spin-offs to TRANAIR is reported. A fast distance calculation routine for Navier-Stokes codes using the new one-equation turbulence models is written. The primary focus of this work was devoted to improving matrix-iterative methods. New algorithms have been developed which activate the full potential of classical Cray-class computers as well as distributed-memory parallel computers.

Recent Progress on ECH Technology for ITER

NASA Astrophysics Data System (ADS)

Sirigiri, Jagadishwar

2005-10-01

The Electron Cyclotron Heating and Current Drive (ECH&CD) system for ITER is a critical ITER system that must be available for use on Day 1 of the ITER experimental program. The applications of the system include plasma start-up, plasma heating and suppression of Neoclassical Tearing Modes (NTMs). These applications are accomplished using 27 one megawatt continuous wave gyrotrons: 24 at a frequency of 170 GHz and 3 at a frequency of 120 GHz. There are DC power supplies for the gyrotrons, a transmission line system, one launcher at the equatorial plane and three upper port launchers. The US will play a major role in delivering parts of the ECH&CD system to ITER. The present state-of-the-art includes major advances in all areas of ECH technology. In the US, a major effort is underway to supply gyrotrons of up to 1.5 MW power level at 110 GHz to General Atomics for use in heating the DIII-D tokamak. This presentation will include a brief review of the state-of-the-art, worldwide, in ECH technology. The requirements for the ITER ECH&CD system will then be reviewed. ITER calls for gyrotrons capable of operating from a 50 kV power supply, after potential depression, with a minimum of 50% overall efficiency. This is a very significant challenge and some approaches to meeting this goal will be presented. Recent experimental results at MIT showing improved efficiency of high frequency, 1.5 MW gyrotrons will be described. These results will be incorporated into the planned development of gyrotrons for ITER. The ITER ECH&CD system will also be a challenge to the transmission lines, which must operate at high average power at up to 1000 seconds and with high efficiency. The technology challenges and efforts in the US and other ITER parties to solve these problems will be reviewed. *In collaboration with E. Choi, C. Marchewka, I. Mastovosky, M. A. Shapiro and R. J. Temkin. This work is supported by the Office of Fusion Energy Sciences of the U. S. Department of Energy.

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Al-Nasra, M.; Zhang, Y.; Baddourah, M. A.; Agarwal, T. K.; Storaasli, O. O.; Carmona, E. A.

1991-01-01

Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

Test of prototype ITER vacuum ultraviolet spectrometer and its application to impurity study in KSTAR plasmas.

PubMed

Seon, C R; Hong, J H; Jang, J; Lee, S H; Choe, W; Lee, H H; Cheon, M S; Pak, S; Lee, H G; Biel, W; Barnsley, R

2014-11-01

To optimize the design of ITER vacuum ultraviolet (VUV) spectrometer, a prototype VUV spectrometer was developed. The sensitivity calibration curve of the spectrometer was calculated from the mirror reflectivity, the grating efficiency, and the detector efficiency. The calibration curve was consistent with the calibration points derived in the experiment using the calibrated hollow cathode lamp. For the application of the prototype ITER VUV spectrometer, the prototype spectrometer was installed at KSTAR, and various impurity emission lines could be measured. By analyzing about 100 shots, strong positive correlation between the O VI and the C IV emission intensities could be found.

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE PAGES

Bunting, Gregory; Prakash, Arun; Walsh, Timothy; ...

2018-01-26

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bunting, Gregory; Prakash, Arun; Walsh, Timothy

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Upwind relaxation methods for the Navier-Stokes equations using inner iterations

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Ng, Wing-Fai; Walters, Robert W.

1992-01-01

A subsonic and a supersonic problem are respectively treated by an upwind line-relaxation algorithm for the Navier-Stokes equations using inner iterations to accelerate steady-state solution convergence and thereby minimize CPU time. While the ability of the inner iterative procedure to mimic the quadratic convergence of the direct solver method is attested to in both test problems, some of the nonquadratic inner iterative results are noted to have been more efficient than the quadratic. In the more successful, supersonic test case, inner iteration required only about 65 percent of the line-relaxation method-entailed CPU time.

Multilevel acceleration of scattering-source iterations with application to electron transport

DOE PAGES

Drumm, Clif; Fan, Wesley

2017-08-18

Acceleration/preconditioning strategies available in the SCEPTRE radiation transport code are described. A flexible transport synthetic acceleration (TSA) algorithm that uses a low-order discrete-ordinates (S N) or spherical-harmonics (P N) solve to accelerate convergence of a high-order S N source-iteration (SI) solve is described. Convergence of the low-order solves can be further accelerated by applying off-the-shelf incomplete-factorization or algebraic-multigrid methods. Also available is an algorithm that uses a generalized minimum residual (GMRES) iterative method rather than SI for convergence, using a parallel sweep-based solver to build up a Krylov subspace. TSA has been applied as a preconditioner to accelerate the convergencemore » of the GMRES iterations. The methods are applied to several problems involving electron transport and problems with artificial cross sections with large scattering ratios. These methods were compared and evaluated by considering material discontinuities and scattering anisotropy. Observed accelerations obtained are highly problem dependent, but speedup factors around 10 have been observed in typical applications.« less

Iterative Importance Sampling Algorithms for Parameter Estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grout, Ray W; Morzfeld, Matthias; Day, Marcus S.

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov chain Monte Carlo (MCMC) is often used for the numerical solution of such problems. An alternative to MCMC is importance sampling, which can exhibit near perfect scaling with the number of cores on high performance computing systems because samples are drawn independently. However, finding a suitable proposal distribution is a challenging task. Several sampling algorithms have been proposed over the past years that take an iterative approach to constructing a proposal distribution. We investigate the applicabilitymore » of such algorithms by applying them to two realistic and challenging test problems, one in subsurface flow, and one in combustion modeling. More specifically, we implement importance sampling algorithms that iterate over the mean and covariance matrix of Gaussian or multivariate t-proposal distributions. Our implementation leverages massively parallel computers, and we present strategies to initialize the iterations using 'coarse' MCMC runs or Gaussian mixture models.« less

Approximate Computing Techniques for Iterative Graph Algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh

Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with lowmore » impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.« less

Real-space processing of helical filaments in SPARX

PubMed Central

Behrmann, Elmar; Tao, Guozhi; Stokes, David L.; Egelman, Edward H.; Raunser, Stefan; Penczek, Pawel A.

2012-01-01

We present a major revision of the iterative helical real-space refinement (IHRSR) procedure and its implementation in the SPARX single particle image processing environment. We built on over a decade of experience with IHRSR helical structure determination and we took advantage of the flexible SPARX infrastructure to arrive at an implementation that offers ease of use, flexibility in designing helical structure determination strategy, and high computational efficiency. We introduced the 3D projection matching code which now is able to work with non-cubic volumes, the geometry better suited for long helical filaments, we enhanced procedures for establishing helical symmetry parameters, and we parallelized the code using distributed memory paradigm. Additional feature includes a graphical user interface that facilitates entering and editing of parameters controlling the structure determination strategy of the program. In addition, we present a novel approach to detect and evaluate structural heterogeneity due to conformer mixtures that takes advantage of helical structure redundancy. PMID:22248449

Sierra/Solid Mechanics 4.48 User's Guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Merewether, Mark Thomas; Crane, Nathan K; de Frias, Gabriel Jose

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutionsmore » of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.« less

Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205

NASA Technical Reports Server (NTRS)

Kincaid, D. R.; Young, D. M.

1984-01-01

Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.

User's Guide for ENSAERO_FE Parallel Finite Element Solver

NASA Technical Reports Server (NTRS)

Eldred, Lloyd B.; Guruswamy, Guru P.

1999-01-01

A high fidelity parallel static structural analysis capability is created and interfaced to the multidisciplinary analysis package ENSAERO-MPI of Ames Research Center. This new module replaces ENSAERO's lower fidelity simple finite element and modal modules. Full aircraft structures may be more accurately modeled using the new finite element capability. Parallel computation is performed by breaking the full structure into multiple substructures. This approach is conceptually similar to ENSAERO's multizonal fluid analysis capability. The new substructure code is used to solve the structural finite element equations for each substructure in parallel. NASTRANKOSMIC is utilized as a front end for this code. Its full library of elements can be used to create an accurate and realistic aircraft model. It is used to create the stiffness matrices for each substructure. The new parallel code then uses an iterative preconditioned conjugate gradient method to solve the global structural equations for the substructure boundary nodes.

Comparison between iteration schemes for three-dimensional coordinate-transformed saturated-unsaturated flow model

NASA Astrophysics Data System (ADS)

An, Hyunuk; Ichikawa, Yutaka; Tachikawa, Yasuto; Shiiba, Michiharu

2012-11-01

SummaryThree different iteration methods for a three-dimensional coordinate-transformed saturated-unsaturated flow model are compared in this study. The Picard and Newton iteration methods are the common approaches for solving Richards' equation. The Picard method is simple to implement and cost-efficient (on an individual iteration basis). However it converges slower than the Newton method. On the other hand, although the Newton method converges faster, it is more complex to implement and consumes more CPU resources per iteration than the Picard method. The comparison of the two methods in finite-element model (FEM) for saturated-unsaturated flow has been well evaluated in previous studies. However, two iteration methods might exhibit different behavior in the coordinate-transformed finite-difference model (FDM). In addition, the Newton-Krylov method could be a suitable alternative for the coordinate-transformed FDM because it requires the evaluation of a 19-point stencil matrix. The formation of a 19-point stencil is quite a complex and laborious procedure. Instead, the Newton-Krylov method calculates the matrix-vector product, which can be easily approximated by calculating the differences of the original nonlinear function. In this respect, the Newton-Krylov method might be the most appropriate iteration method for coordinate-transformed FDM. However, this method involves the additional cost of taking an approximation at each Krylov iteration in the Newton-Krylov method. In this paper, we evaluated the efficiency and robustness of three iteration methods—the Picard, Newton, and Newton-Krylov methods—for simulating saturated-unsaturated flow through porous media using a three-dimensional coordinate-transformed FDM.

Trace: a high-throughput tomographic reconstruction engine for large-scale datasets

DOE PAGES

Bicer, Tekin; Gursoy, Doga; Andrade, Vincent De; ...

2017-01-28

Here, synchrotron light source and detector technologies enable scientists to perform advanced experiments. These scientific instruments and experiments produce data at such scale and complexity that large-scale computation is required to unleash their full power. One of the widely used data acquisition technique at light sources is Computed Tomography, which can generate tens of GB/s depending on x-ray range. A large-scale tomographic dataset, such as mouse brain, may require hours of computation time with a medium size workstation. In this paper, we present Trace, a data-intensive computing middleware we developed for implementation and parallelization of iterative tomographic reconstruction algorithms. Tracemore » provides fine-grained reconstruction of tomography datasets using both (thread level) shared memory and (process level) distributed memory parallelization. Trace utilizes a special data structure called replicated reconstruction object to maximize application performance. We also present the optimizations we have done on the replicated reconstruction objects and evaluate them using a shale and a mouse brain sinogram. Our experimental evaluations show that the applied optimizations and parallelization techniques can provide 158x speedup (using 32 compute nodes) over single core configuration, which decreases the reconstruction time of a sinogram (with 4501 projections and 22400 detector resolution) from 12.5 hours to less than 5 minutes per iteration.« less

Trace: a high-throughput tomographic reconstruction engine for large-scale datasets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bicer, Tekin; Gursoy, Doga; Andrade, Vincent De

Here, synchrotron light source and detector technologies enable scientists to perform advanced experiments. These scientific instruments and experiments produce data at such scale and complexity that large-scale computation is required to unleash their full power. One of the widely used data acquisition technique at light sources is Computed Tomography, which can generate tens of GB/s depending on x-ray range. A large-scale tomographic dataset, such as mouse brain, may require hours of computation time with a medium size workstation. In this paper, we present Trace, a data-intensive computing middleware we developed for implementation and parallelization of iterative tomographic reconstruction algorithms. Tracemore » provides fine-grained reconstruction of tomography datasets using both (thread level) shared memory and (process level) distributed memory parallelization. Trace utilizes a special data structure called replicated reconstruction object to maximize application performance. We also present the optimizations we have done on the replicated reconstruction objects and evaluate them using a shale and a mouse brain sinogram. Our experimental evaluations show that the applied optimizations and parallelization techniques can provide 158x speedup (using 32 compute nodes) over single core configuration, which decreases the reconstruction time of a sinogram (with 4501 projections and 22400 detector resolution) from 12.5 hours to less than 5 minutes per iteration.« less

Performance Models for the Spike Banded Linear System Solver

DOE PAGES

Manguoglu, Murat; Saied, Faisal; Sameh, Ahmed; ...

2011-01-01

With availability of large-scale parallel platforms comprised of tens-of-thousands of processors and beyond, there is significant impetus for the development of scalable parallel sparse linear system solvers and preconditioners. An integral part of this design process is the development of performance models capable of predicting performance and providing accurate cost models for the solvers and preconditioners. There has been some work in the past on characterizing performance of the iterative solvers themselves. In this paper, we investigate the problem of characterizing performance and scalability of banded preconditioners. Recent work has demonstrated the superior convergence properties and robustness of banded preconditioners,more » compared to state-of-the-art ILU family of preconditioners as well as algebraic multigrid preconditioners. Furthermore, when used in conjunction with efficient banded solvers, banded preconditioners are capable of significantly faster time-to-solution. Our banded solver, the Truncated Spike algorithm is specifically designed for parallel performance and tolerance to deep memory hierarchies. Its regular structure is also highly amenable to accurate performance characterization. Using these characteristics, we derive the following results in this paper: (i) we develop parallel formulations of the Truncated Spike solver, (ii) we develop a highly accurate pseudo-analytical parallel performance model for our solver, (iii) we show excellent predication capabilities of our model – based on which we argue the high scalability of our solver. Our pseudo-analytical performance model is based on analytical performance characterization of each phase of our solver. These analytical models are then parameterized using actual runtime information on target platforms. An important consequence of our performance models is that they reveal underlying performance bottlenecks in both serial and parallel formulations. All of our results are validated on diverse heterogeneous multiclusters – platforms for which performance prediction is particularly challenging. Finally, we provide predict the scalability of the Spike algorithm using up to 65,536 cores with our model. In this paper we extend the results presented in the Ninth International Symposium on Parallel and Distributed Computing.« less

Virtual fringe projection system with nonparallel illumination based on iteration

NASA Astrophysics Data System (ADS)

Zhou, Duo; Wang, Zhangying; Gao, Nan; Zhang, Zonghua; Jiang, Xiangqian

2017-06-01

Fringe projection profilometry has been widely applied in many fields. To set up an ideal measuring system, a virtual fringe projection technique has been studied to assist in the design of hardware configurations. However, existing virtual fringe projection systems use parallel illumination and have a fixed optical framework. This paper presents a virtual fringe projection system with nonparallel illumination. Using an iterative method to calculate intersection points between rays and reference planes or object surfaces, the proposed system can simulate projected fringe patterns and captured images. A new explicit calibration method has been presented to validate the precision of the system. Simulated results indicate that the proposed iterative method outperforms previous systems. Our virtual system can be applied to error analysis, algorithm optimization, and help operators to find ideal system parameter settings for actual measurements.

Variable aperture-based ptychographical iterative engine method

NASA Astrophysics Data System (ADS)

Sun, Aihui; Kong, Yan; Meng, Xin; He, Xiaoliang; Du, Ruijun; Jiang, Zhilong; Liu, Fei; Xue, Liang; Wang, Shouyu; Liu, Cheng

2018-02-01

A variable aperture-based ptychographical iterative engine (vaPIE) is demonstrated both numerically and experimentally to reconstruct the sample phase and amplitude rapidly. By adjusting the size of a tiny aperture under the illumination of a parallel light beam to change the illumination on the sample step by step and recording the corresponding diffraction patterns sequentially, both the sample phase and amplitude can be faithfully reconstructed with a modified ptychographical iterative engine (PIE) algorithm. Since many fewer diffraction patterns are required than in common PIE and the shape, the size, and the position of the aperture need not to be known exactly, this proposed vaPIE method remarkably reduces the data acquisition time and makes PIE less dependent on the mechanical accuracy of the translation stage; therefore, the proposed technique can be potentially applied for various scientific researches.

a Novel Approach of Indexing and Retrieving Spatial Polygons for Efficient Spatial Region Queries

NASA Astrophysics Data System (ADS)

Zhao, J. H.; Wang, X. Z.; Wang, F. Y.; Shen, Z. H.; Zhou, Y. C.; Wang, Y. L.

2017-10-01

Spatial region queries are more and more widely used in web-based applications. Mechanisms to provide efficient query processing over geospatial data are essential. However, due to the massive geospatial data volume, heavy geometric computation, and high access concurrency, it is difficult to get response in real time. Spatial indexes are usually used in this situation. In this paper, based on k-d tree, we introduce a distributed KD-Tree (DKD-Tree) suitbable for polygon data, and a two-step query algorithm. The spatial index construction is recursive and iterative, and the query is an in memory process. Both the index and query methods can be processed in parallel, and are implemented based on HDFS, Spark and Redis. Experiments on a large volume of Remote Sensing images metadata have been carried out, and the advantages of our method are investigated by comparing with spatial region queries executed on PostgreSQL and PostGIS. Results show that our approach not only greatly improves the efficiency of spatial region query, but also has good scalability, Moreover, the two-step spatial range query algorithm can also save cluster resources to support a large number of concurrent queries. Therefore, this method is very useful when building large geographic information systems.

MPF: A portable message passing facility for shared memory multiprocessors

NASA Technical Reports Server (NTRS)

Malony, Allen D.; Reed, Daniel A.; Mcguire, Patrick J.

1987-01-01

The design, implementation, and performance evaluation of a message passing facility (MPF) for shared memory multiprocessors are presented. The MPF is based on a message passing model conceptually similar to conversations. Participants (parallel processors) can enter or leave a conversation at any time. The message passing primitives for this model are implemented as a portable library of C function calls. The MPF is currently operational on a Sequent Balance 21000, and several parallel applications were developed and tested. Several simple benchmark programs are presented to establish interprocess communication performance for common patterns of interprocess communication. Finally, performance figures are presented for two parallel applications, linear systems solution, and iterative solution of partial differential equations.

Beyond ITER: neutral beams for a demonstration fusion reactor (DEMO) (invited).

PubMed

McAdams, R

2014-02-01

In the development of magnetically confined fusion as an economically sustainable power source, International Tokamak Experimental Reactor (ITER) is currently under construction. Beyond ITER is the demonstration fusion reactor (DEMO) programme in which the physics and engineering aspects of a future fusion power plant will be demonstrated. DEMO will produce net electrical power. The DEMO programme will be outlined and the role of neutral beams for heating and current drive will be described. In particular, the importance of the efficiency of neutral beam systems in terms of injected neutral beam power compared to wallplug power will be discussed. Options for improving this efficiency including advanced neutralisers and energy recovery are discussed.

Further investigation on "A multiplicative regularization for force reconstruction"

NASA Astrophysics Data System (ADS)

Aucejo, M.; De Smet, O.

2018-05-01

We have recently proposed a multiplicative regularization to reconstruct mechanical forces acting on a structure from vibration measurements. This method does not require any selection procedure for choosing the regularization parameter, since the amount of regularization is automatically adjusted throughout an iterative resolution process. The proposed iterative algorithm has been developed with performance and efficiency in mind, but it is actually a simplified version of a full iterative procedure not described in the original paper. The present paper aims at introducing the full resolution algorithm and comparing it with its simplified version in terms of computational efficiency and solution accuracy. In particular, it is shown that both algorithms lead to very similar identified solutions.

Regularization and computational methods for precise solution of perturbed orbit transfer problems

NASA Astrophysics Data System (ADS)

Woollands, Robyn Michele

The author has developed a suite of algorithms for solving the perturbed Lambert's problem in celestial mechanics. These algorithms have been implemented as a parallel computation tool that has broad applicability. This tool is composed of four component algorithms and each provides unique benefits for solving a particular type of orbit transfer problem. The first one utilizes a Keplerian solver (a-iteration) for solving the unperturbed Lambert's problem. This algorithm not only provides a "warm start" for solving the perturbed problem but is also used to identify which of several perturbed solvers is best suited for the job. The second algorithm solves the perturbed Lambert's problem using a variant of the modified Chebyshev-Picard iteration initial value solver that solves two-point boundary value problems. This method converges over about one third of an orbit and does not require a Newton-type shooting method and thus no state transition matrix needs to be computed. The third algorithm makes use of regularization of the differential equations through the Kustaanheimo-Stiefel transformation and extends the domain of convergence over which the modified Chebyshev-Picard iteration two-point boundary value solver will converge, from about one third of an orbit to almost a full orbit. This algorithm also does not require a Newton-type shooting method. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver to solve the perturbed two-impulse Lambert problem over multiple revolutions. The method of particular solutions is a shooting method but differs from the Newton-type shooting methods in that it does not require integration of the state transition matrix. The mathematical developments that underlie these four algorithms are derived in the chapters of this dissertation. For each of the algorithms, some orbit transfer test cases are included to provide insight on accuracy and efficiency of these individual algorithms. Following this discussion, the combined parallel algorithm, known as the unified Lambert tool, is presented and an explanation is given as to how it automatically selects which of the three perturbed solvers to compute the perturbed solution for a particular orbit transfer. The unified Lambert tool may be used to determine a single orbit transfer or for generating of an extremal field map. A case study is presented for a mission that is required to rendezvous with two pieces of orbit debris (spent rocket boosters). The unified Lambert tool software developed in this dissertation is already being utilized by several industrial partners and we are confident that it will play a significant role in practical applications, including solution of Lambert problems that arise in the current applications focused on enhanced space situational awareness.

Unsupervised iterative detection of land mines in highly cluttered environments.

PubMed

Batman, Sinan; Goutsias, John

2003-01-01

An unsupervised iterative scheme is proposed for land mine detection in heavily cluttered scenes. This scheme is based on iterating hybrid multispectral filters that consist of a decorrelating linear transform coupled with a nonlinear morphological detector. Detections extracted from the first pass are used to improve results in subsequent iterations. The procedure stops after a predetermined number of iterations. The proposed scheme addresses several weaknesses associated with previous adaptations of morphological approaches to land mine detection. Improvement in detection performance, robustness with respect to clutter inhomogeneities, a completely unsupervised operation, and computational efficiency are the main highlights of the method. Experimental results reveal excellent performance.

Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

DOE PAGES

Till, Andrew T.; Warsa, James S.; Morel, Jim E.

2018-06-15

The thermal radiative transfer (TRT) equations comprise a radiation equation coupled to the material internal energy equation. Linearization of these equations produces effective, thermally-redistributed scattering through absorption-reemission. In this paper, we investigate the effectiveness and efficiency of Linear-Multi-Frequency-Grey (LMFG) acceleration that has been reformulated for use as a preconditioner to Krylov iterative solution methods. We introduce two general frameworks, the scalar flux formulation (SFF) and the absorption rate formulation (ARF), and investigate their iterative properties in the absence and presence of true scattering. SFF has a group-dependent state size but may be formulated without inner iterations in the presence ofmore » scattering, while ARF has a group-independent state size but requires inner iterations when scattering is present. We compare and evaluate the computational cost and efficiency of LMFG applied to these two formulations using a direct solver for the preconditioners. Finally, this work is novel because the use of LMFG for the radiation transport equation, in conjunction with Krylov methods, involves special considerations not required for radiation diffusion.« less

Probing soil C metabolism in response to temperature: results from experiments and modeling

NASA Astrophysics Data System (ADS)

Dijkstra, P.; Dalder, J.; Blankinship, J.; Selmants, P. C.; Schwartz, E.; Koch, G. W.; Hart, S.; Hungate, B. A.

2010-12-01

C use efficiency (CUE) is one of the least understood aspects of soil C cycling, has a very large effect on soil respiration and C sequestration, and decreases with elevated temperature. CUE is directly related to substrate partitioning over energy production and biosynthesis. The production of energy and metabolic precursors occurs in well-known processes such as glycolysis and Krebs cycle. We have developed a new stable isotope approach using position-specific 13C-labeled metabolic tracers to measure these fundamental metabolic processes in intact soil communities (1). We use this new approach, combined with models of soil metabolic flux patterns, to analyze the response of microbial energy production, biosynthesis, and CUE to temperature. The method consists of adding small but precise amounts of position-specific 13C -labeled metabolic tracers to parallel soil incubations, in this case 1-13C and 2,3-13C pyruvate and 1-13C and U-13C glucose. The measurement of CO2 released from the labeled tracers is used to calculate the C flux rates through various metabolic pathways. A simplified metabolic model consisting of 23 reactions is iteratively solved using results of the metabolic tracer experiments and information on microbial precursor demand under different temperatures. This new method enables direct study of fundamental aspects of microbial energy production, C use efficiency, and soil organic matter formation in response to temperature. (1) Dijkstra P, Blankinship JC, Selmants PC, Hart SC, Koch GW, Schwarz E and Hungate BA. Probing metabolic flux patterns of soil microbial communities using parallel position-specific tracer labeling. Soil Biology and Biochemistry (accepted)

Efficient entanglement distillation without quantum memory.

PubMed

Abdelkhalek, Daniela; Syllwasschy, Mareike; Cerf, Nicolas J; Fiurášek, Jaromír; Schnabel, Roman

2016-05-31

Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibres are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to date. Here, we present the theory for an efficient iterative entanglement distillation protocol without quantum memories and provide a proof-of-principle experimental demonstration. The scheme is applied to phase-diffused two-mode-squeezed states and proven to distil entanglement for up to three iteration steps. The data are indistinguishable from those that an efficient scheme using quantum memories would produce. Since our protocol includes the final measurement it is particularly promising for enhancing continuous-variable quantum key distribution.

Efficient entanglement distillation without quantum memory

PubMed Central

Abdelkhalek, Daniela; Syllwasschy, Mareike; Cerf, Nicolas J.; Fiurášek, Jaromír; Schnabel, Roman

2016-01-01

Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibres are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to date. Here, we present the theory for an efficient iterative entanglement distillation protocol without quantum memories and provide a proof-of-principle experimental demonstration. The scheme is applied to phase-diffused two-mode-squeezed states and proven to distil entanglement for up to three iteration steps. The data are indistinguishable from those that an efficient scheme using quantum memories would produce. Since our protocol includes the final measurement it is particularly promising for enhancing continuous-variable quantum key distribution. PMID:27241946

A frequency dependent preconditioned wavelet method for atmospheric tomography

NASA Astrophysics Data System (ADS)

Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny

2013-12-01

Atmospheric tomography, i.e. the reconstruction of the turbulence in the atmosphere, is a main task for the adaptive optics systems of the next generation telescopes. For extremely large telescopes, such as the European Extremely Large Telescope, this problem becomes overly complex and an efficient algorithm is needed to reduce numerical costs. Recently, a conjugate gradient method based on wavelet parametrization of turbulence layers was introduced [5]. An iterative algorithm can only be numerically efficient when the number of iterations required for a sufficient reconstruction is low. A way to achieve this is to design an efficient preconditioner. In this paper we propose a new frequency-dependent preconditioner for the wavelet method. In the context of a multi conjugate adaptive optics (MCAO) system simulated on the official end-to-end simulation tool OCTOPUS of the European Southern Observatory we demonstrate robustness and speed of the preconditioned algorithm. We show that three iterations are sufficient for a good reconstruction.

Efficient solutions to the Euler equations for supersonic flow with embedded subsonic regions

NASA Technical Reports Server (NTRS)

Walters, Robert W.; Dwoyer, Douglas L.

1987-01-01

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two dimensions is described. Convergence of the basic algorithm to the steady state is quadratic for fully supersonic flows and is linear for other flows. This is in contrast to the block alternating direction implicit methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented herein is easily coupled with methods to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, and yields a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Optimization and validation of accelerated golden-angle radial sparse MRI reconstruction with self-calibrating GRAPPA operator gridding.

PubMed

Benkert, Thomas; Tian, Ye; Huang, Chenchan; DiBella, Edward V R; Chandarana, Hersh; Feng, Li

2018-07-01

Golden-angle radial sparse parallel (GRASP) MRI reconstruction requires gridding and regridding to transform data between radial and Cartesian k-space. These operations are repeatedly performed in each iteration, which makes the reconstruction computationally demanding. This work aimed to accelerate GRASP reconstruction using self-calibrating GRAPPA operator gridding (GROG) and to validate its performance in clinical imaging. GROG is an alternative gridding approach based on parallel imaging, in which k-space data acquired on a non-Cartesian grid are shifted onto a Cartesian k-space grid using information from multicoil arrays. For iterative non-Cartesian image reconstruction, GROG is performed only once as a preprocessing step. Therefore, the subsequent iterative reconstruction can be performed directly in Cartesian space, which significantly reduces computational burden. Here, a framework combining GROG with GRASP (GROG-GRASP) is first optimized and then compared with standard GRASP reconstruction in 22 prostate patients. GROG-GRASP achieved approximately 4.2-fold reduction in reconstruction time compared with GRASP (∼333 min versus ∼78 min) while maintaining image quality (structural similarity index ≈ 0.97 and root mean square error ≈ 0.007). Visual image quality assessment by two experienced radiologists did not show significant differences between the two reconstruction schemes. With a graphics processing unit implementation, image reconstruction time can be further reduced to approximately 14 min. The GRASP reconstruction can be substantially accelerated using GROG. This framework is promising toward broader clinical application of GRASP and other iterative non-Cartesian reconstruction methods. Magn Reson Med 80:286-293, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Analysis of surface wave propagation in a grounded dielectric slab covered by a resistive sheet

NASA Technical Reports Server (NTRS)

Shively, David G.

1992-01-01

Both parallel and perpendicular polarized surface waves are known to propagate on lossless and lossy grounded dielectric slabs. Surface wave propagation on a grounded dielectric slab covered with a resistive sheet is considered. Both parallel and perpendicular polarizations are examined. Transcendental equations are derived for each polarization and are solved using iterative techniques. Attenuation and phase velocity are shown for representative geometries. The results are applicable to both a grounded slab with a resistive sheet and an ungrounded slab covered on each side with a resistive sheet.

Robust parallel iterative solvers for linear and least-squares problems, Final Technical Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saad, Yousef

2014-01-16

The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners formore » solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.« less

Novel techniques for data decomposition and load balancing for parallel processing of vision systems: Implementation and evaluation using a motion estimation system

NASA Technical Reports Server (NTRS)

Choudhary, Alok Nidhi; Leung, Mun K.; Huang, Thomas S.; Patel, Janak H.

1989-01-01

Computer vision systems employ a sequence of vision algorithms in which the output of an algorithm is the input of the next algorithm in the sequence. Algorithms that constitute such systems exhibit vastly different computational characteristics, and therefore, require different data decomposition techniques and efficient load balancing techniques for parallel implementation. However, since the input data for a task is produced as the output data of the previous task, this information can be exploited to perform knowledge based data decomposition and load balancing. Presented here are algorithms for a motion estimation system. The motion estimation is based on the point correspondence between the involved images which are a sequence of stereo image pairs. Researchers propose algorithms to obtain point correspondences by matching feature points among stereo image pairs at any two consecutive time instants. Furthermore, the proposed algorithms employ non-iterative procedures, which results in saving considerable amounts of computation time. The system consists of the following steps: (1) extraction of features; (2) stereo match of images in one time instant; (3) time match of images from consecutive time instants; (4) stereo match to compute final unambiguous points; and (5) computation of motion parameters.

Development and study of a parallel algorithm of iteratively forming latent functionally-determined structures for classification and analysis of meteorological data

NASA Astrophysics Data System (ADS)

Sorokin, V. A.; Volkov, Yu V.; Sherstneva, A. I.; Botygin, I. A.

2016-11-01

This paper overviews a method of generating climate regions based on an analytic signal theory. When applied to atmospheric surface layer temperature data sets, the method allows forming climatic structures with the corresponding changes in the temperature to make conclusions on the uniformity of climate in an area and to trace the climate changes in time by analyzing the type group shifts. The algorithm is based on the fact that the frequency spectrum of the thermal oscillation process is narrow-banded and has only one mode for most weather stations. This allows using the analytic signal theory, causality conditions and introducing an oscillation phase. The annual component of the phase, being a linear function, was removed by the least squares method. The remaining phase fluctuations allow consistent studying of their coordinated behavior and timing, using the Pearson correlation coefficient for dependence evaluation. This study includes program experiments to evaluate the calculation efficiency in the phase grouping task. The paper also overviews some single-threaded and multi-threaded computing models. It is shown that the phase grouping algorithm for meteorological data can be parallelized and that a multi-threaded implementation leads to a 25-30% increase in the performance.

Computational Challenges of 3D Radiative Transfer in Atmospheric Models

NASA Astrophysics Data System (ADS)

Jakub, Fabian; Bernhard, Mayer

2017-04-01

The computation of radiative heating and cooling rates is one of the most expensive components in todays atmospheric models. The high computational cost stems not only from the laborious integration over a wide range of the electromagnetic spectrum but also from the fact that solving the integro-differential radiative transfer equation for monochromatic light is already rather involved. This lead to the advent of numerous approximations and parameterizations to reduce the cost of the solver. One of the most prominent one is the so called independent pixel approximations (IPA) where horizontal energy transfer is neglected whatsoever and radiation may only propagate in the vertical direction (1D). Recent studies implicate that the IPA introduces significant errors in high resolution simulations and affects the evolution and development of convective systems. However, using fully 3D solvers such as for example MonteCarlo methods is not even on state of the art supercomputers feasible. The parallelization of atmospheric models is often realized by a horizontal domain decomposition, and hence, horizontal transfer of energy necessitates communication. E.g. a cloud's shadow at a low zenith angle will cast a long shadow and potentially needs to communication through a multitude of processors. Especially light in the solar spectral range may travel long distances through the atmosphere. Concerning highly parallel simulations, it is vital that 3D radiative transfer solvers put a special emphasis on parallel scalability. We will present an introduction to intricacies computing 3D radiative heating and cooling rates as well as report on the parallel performance of the TenStream solver. The TenStream is a 3D radiative transfer solver using the PETSc framework to iteratively solve a set of partial differential equation. We investigate two matrix preconditioners, (a) geometric algebraic multigrid preconditioning(MG+GAMG) and (b) block Jacobi incomplete LU (ILU) factorization. The TenStream solver is tested for up to 4096 cores and shows a parallel scaling efficiency of 80-90% on various supercomputers.

SciSpark: Highly Interactive and Scalable Model Evaluation and Climate Metrics

NASA Astrophysics Data System (ADS)

Wilson, B. D.; Mattmann, C. A.; Waliser, D. E.; Kim, J.; Loikith, P.; Lee, H.; McGibbney, L. J.; Whitehall, K. D.

2014-12-01

Remote sensing data and climate model output are multi-dimensional arrays of massive sizes locked away in heterogeneous file formats (HDF5/4, NetCDF 3/4) and metadata models (HDF-EOS, CF) making it difficult to perform multi-stage, iterative science processing since each stage requires writing and reading data to and from disk. We are developing a lightning fast Big Data technology called SciSpark based on ApacheTM Spark. Spark implements the map-reduce paradigm for parallel computing on a cluster, but emphasizes in-memory computation, "spilling" to disk only as needed, and so outperforms the disk-based ApacheTM Hadoop by 100x in memory and by 10x on disk, and makes iterative algorithms feasible. SciSpark will enable scalable model evaluation by executing large-scale comparisons of A-Train satellite observations to model grids on a cluster of 100 to 1000 compute nodes. This 2nd generation capability for NASA's Regional Climate Model Evaluation System (RCMES) will compute simple climate metrics at interactive speeds, and extend to quite sophisticated iterative algorithms such as machine-learning (ML) based clustering of temperature PDFs, and even graph-based algorithms for searching for Mesocale Convective Complexes. The goals of SciSpark are to: (1) Decrease the time to compute comparison statistics and plots from minutes to seconds; (2) Allow for interactive exploration of time-series properties over seasons and years; (3) Decrease the time for satellite data ingestion into RCMES to hours; (4) Allow for Level-2 comparisons with higher-order statistics or PDF's in minutes to hours; and (5) Move RCMES into a near real time decision-making platform. We will report on: the architecture and design of SciSpark, our efforts to integrate climate science algorithms in Python and Scala, parallel ingest and partitioning (sharding) of A-Train satellite observations from HDF files and model grids from netCDF files, first parallel runs to compute comparison statistics and PDF's, and first metrics quantifying parallel speedups and memory & disk usage.

An improved 3D MoF method based on analytical partial derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2016-12-01

MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.

Evaluation of power transfer efficiency for a high power inductively coupled radio-frequency hydrogen ion source

NASA Astrophysics Data System (ADS)

Jain, P.; Recchia, M.; Cavenago, M.; Fantz, U.; Gaio, E.; Kraus, W.; Maistrello, A.; Veltri, P.

2018-04-01

Neutral beam injection (NBI) for plasma heating and current drive is necessary for International Thermonuclear Experimental reactor (ITER) tokamak. Due to its various advantages, a radio frequency (RF) driven plasma source type was selected as a reference ion source for the ITER heating NBI. The ITER relevant RF negative ion sources are inductively coupled (IC) devices whose operational working frequency has been chosen to be 1 MHz and are characterized by high RF power density (˜9.4 W cm-3) and low operational pressure (around 0.3 Pa). The RF field is produced by a coil in a cylindrical chamber leading to a plasma generation followed by its expansion inside the chamber. This paper recalls different concepts based on which a methodology is developed to evaluate the efficiency of the RF power transfer to hydrogen plasma. This efficiency is then analyzed as a function of the working frequency and in dependence of other operating source and plasma parameters. The study is applied to a high power IC RF hydrogen ion source which is similar to one simplified driver of the ELISE source (half the size of the ITER NBI source).

Implicit methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Yoon, S.; Kwak, D.

1990-01-01

Numerical solutions of the Navier-Stokes equations using explicit schemes can be obtained at the expense of efficiency. Conventional implicit methods which often achieve fast convergence rates suffer high cost per iteration. A new implicit scheme based on lower-upper factorization and symmetric Gauss-Seidel relaxation offers very low cost per iteration as well as fast convergence. High efficiency is achieved by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.

Solving Upwind-Biased Discretizations: Defect-Correction Iterations

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

1999-01-01

This paper considers defect-correction solvers for a second order upwind-biased discretization of the 2D convection equation. The following important features are reported: (1) The asymptotic convergence rate is about 0.5 per defect-correction iteration. (2) If the operators involved in defect-correction iterations have different approximation order, then the initial convergence rates may be very slow. The number of iterations required to get into the asymptotic convergence regime might grow on fine grids as a negative power of h. In the case of a second order target operator and a first order driver operator, this number of iterations is roughly proportional to h-1/3. (3) If both the operators have the second approximation order, the defect-correction solver demonstrates the asymptotic convergence rate after three iterations at most. The same three iterations are required to converge algebraic error below the truncation error level. A novel comprehensive half-space Fourier mode analysis (which, by the way, can take into account the influence of discretized outflow boundary conditions as well) for the defect-correction method is developed. This analysis explains many phenomena observed in solving non-elliptic equations and provides a close prediction of the actual solution behavior. It predicts the convergence rate for each iteration and the asymptotic convergence rate. As a result of this analysis, a new very efficient adaptive multigrid algorithm solving the discrete problem to within a given accuracy is proposed. Numerical simulations confirm the accuracy of the analysis and the efficiency of the proposed algorithm. The results of the numerical tests are reported.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1992-01-01

The development of efficient iterative solution methods for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations is discussed. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. In this work, another approach based on the classical conjugate gradient method, known as the Generalized Minimum Residual (GMRES) algorithm is investigated. The GMRES algorithm has been used in the past by a number of researchers for solving steady viscous and inviscid flow problems. Here, we investigate the suitability of this algorithm for solving the system of non-linear equations that arise in unsteady Navier-Stokes solvers at each time step.

High resolution x-ray CMT: Reconstruction methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, J.K.

This paper qualitatively discusses the primary characteristics of methods for reconstructing tomographic images from a set of projections. These reconstruction methods can be categorized as either {open_quotes}analytic{close_quotes} or {open_quotes}iterative{close_quotes} techniques. Analytic algorithms are derived from the formal inversion of equations describing the imaging process, while iterative algorithms incorporate a model of the imaging process and provide a mechanism to iteratively improve image estimates. Analytic reconstruction algorithms are typically computationally more efficient than iterative methods; however, analytic algorithms are available for a relatively limited set of imaging geometries and situations. Thus, the framework of iterative reconstruction methods is better suited formore » high accuracy, tomographic reconstruction codes.« less

Variable aperture-based ptychographical iterative engine method.

PubMed

Sun, Aihui; Kong, Yan; Meng, Xin; He, Xiaoliang; Du, Ruijun; Jiang, Zhilong; Liu, Fei; Xue, Liang; Wang, Shouyu; Liu, Cheng

2018-02-01

A variable aperture-based ptychographical iterative engine (vaPIE) is demonstrated both numerically and experimentally to reconstruct the sample phase and amplitude rapidly. By adjusting the size of a tiny aperture under the illumination of a parallel light beam to change the illumination on the sample step by step and recording the corresponding diffraction patterns sequentially, both the sample phase and amplitude can be faithfully reconstructed with a modified ptychographical iterative engine (PIE) algorithm. Since many fewer diffraction patterns are required than in common PIE and the shape, the size, and the position of the aperture need not to be known exactly, this proposed vaPIE method remarkably reduces the data acquisition time and makes PIE less dependent on the mechanical accuracy of the translation stage; therefore, the proposed technique can be potentially applied for various scientific researches. (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

On iterative processes in the Krylov-Sonneveld subspaces

NASA Astrophysics Data System (ADS)

Ilin, Valery P.

2016-10-01

The iterative Induced Dimension Reduction (IDR) methods are considered for solving large systems of linear algebraic equations (SLAEs) with nonsingular nonsymmetric matrices. These approaches are investigated by many authors and are charachterized sometimes as the alternative to the classical processes of Krylov type. The key moments of the IDR algorithms consist in the construction of the embedded Sonneveld subspaces, which have the decreasing dimensions and use the orthogonalization to some fixed subspace. Other independent approaches for research and optimization of the iterations are based on the augmented and modified Krylov subspaces by using the aggregation and deflation procedures with present various low rank approximations of the original matrices. The goal of this paper is to show, that IDR method in Sonneveld subspaces present an original interpretation of the modified algorithms in the Krylov subspaces. In particular, such description is given for the multi-preconditioned semi-conjugate direction methods which are actual for the parallel algebraic domain decomposition approaches.

Iterated reaction graphs: simulating complex Maillard reaction pathways.

PubMed

Patel, S; Rabone, J; Russell, S; Tissen, J; Klaffke, W

2001-01-01

This study investigates a new method of simulating a complex chemical system including feedback loops and parallel reactions. The practical purpose of this approach is to model the actual reactions that take place in the Maillard process, a set of food browning reactions, in sufficient detail to be able to predict the volatile composition of the Maillard products. The developed framework, called iterated reaction graphs, consists of two main elements: a soup of molecules and a reaction base of Maillard reactions. An iterative process loops through the reaction base, taking reactants from and feeding products back to the soup. This produces a reaction graph, with molecules as nodes and reactions as arcs. The iterated reaction graph is updated and validated by comparing output with the main products found by classical gas-chromatographic/mass spectrometric analysis. To ensure a realistic output and convergence to desired volatiles only, the approach contains a number of novel elements: rate kinetics are treated as reaction probabilities; only a subset of the true chemistry is modeled; and the reactions are blocked into groups.

Selection of Thermal Worst-Case Orbits via Modified Efficient Global Optimization

NASA Technical Reports Server (NTRS)

Moeller, Timothy M.; Wilhite, Alan W.; Liles, Kaitlin A.

2014-01-01

Efficient Global Optimization (EGO) was used to select orbits with worst-case hot and cold thermal environments for the Stratospheric Aerosol and Gas Experiment (SAGE) III. The SAGE III system thermal model changed substantially since the previous selection of worst-case orbits (which did not use the EGO method), so the selections were revised to ensure the worst cases are being captured. The EGO method consists of first conducting an initial set of parametric runs, generated with a space-filling Design of Experiments (DoE) method, then fitting a surrogate model to the data and searching for points of maximum Expected Improvement (EI) to conduct additional runs. The general EGO method was modified by using a multi-start optimizer to identify multiple new test points at each iteration. This modification facilitates parallel computing and decreases the burden of user interaction when the optimizer code is not integrated with the model. Thermal worst-case orbits for SAGE III were successfully identified and shown by direct comparison to be more severe than those identified in the previous selection. The EGO method is a useful tool for this application and can result in computational savings if the initial Design of Experiments (DoE) is selected appropriately.

Fast segmentation of satellite images using SLIC, WebGL and Google Earth Engine

NASA Astrophysics Data System (ADS)

Donchyts, Gennadii; Baart, Fedor; Gorelick, Noel; Eisemann, Elmar; van de Giesen, Nick

2017-04-01

Google Earth Engine (GEE) is a parallel geospatial processing platform, which harmonizes access to petabytes of freely available satellite images. It provides a very rich API, allowing development of dedicated algorithms to extract useful geospatial information from these images. At the same time, modern GPUs provide thousands of computing cores, which are mostly not utilized in this context. In the last years, WebGL became a popular and well-supported API, allowing fast image processing directly in web browsers. In this work, we will evaluate the applicability of WebGL to enable fast segmentation of satellite images. A new implementation of a Simple Linear Iterative Clustering (SLIC) algorithm using GPU shaders will be presented. SLIC is a simple and efficient method to decompose an image in visually homogeneous regions. It adapts a k-means clustering approach to generate superpixels efficiently. While this approach will be hard to scale, due to a significant amount of data to be transferred to the client, it should significantly improve exploratory possibilities and simplify development of dedicated algorithms for geoscience applications. Our prototype implementation will be used to improve surface water detection of the reservoirs using multispectral satellite imagery.

Parallelization of a blind deconvolution algorithm

NASA Astrophysics Data System (ADS)

Matson, Charles L.; Borelli, Kathy J.

2006-09-01

Often it is of interest to deblur imagery in order to obtain higher-resolution images. Deblurring requires knowledge of the blurring function - information that is often not available separately from the blurred imagery. Blind deconvolution algorithms overcome this problem by jointly estimating both the high-resolution image and the blurring function from the blurred imagery. Because blind deconvolution algorithms are iterative in nature, they can take minutes to days to deblur an image depending how many frames of data are used for the deblurring and the platforms on which the algorithms are executed. Here we present our progress in parallelizing a blind deconvolution algorithm to increase its execution speed. This progress includes sub-frame parallelization and a code structure that is not specialized to a specific computer hardware architecture.

Picard Trajectory Approximation Iteration for Efficient Orbit Propagation

DTIC Science & Technology

2015-07-21

Eqn (8)) for an iterative ap- proximation of eccentric anomaly, and is transformed back to . The Lambert/ Kepler time – eccentric anomaly relationship...of Kepler motion based on spinor regulari- zation, Journal fur die Reine und Angewandt Mathematik 218, 204-219, 1965. [3] Levi-Civita T., Sur la...transformed back to  , ,x y z . The Lambert/ Kepler time – eccentric anomaly relationship is iterated by a Newton/Secant method to converge on the

Parallel CE/SE Computations via Domain Decomposition

NASA Technical Reports Server (NTRS)

Himansu, Ananda; Jorgenson, Philip C. E.; Wang, Xiao-Yen; Chang, Sin-Chung

2000-01-01

This paper describes the parallelization strategy and achieved parallel efficiency of an explicit time-marching algorithm for solving conservation laws. The Space-Time Conservation Element and Solution Element (CE/SE) algorithm for solving the 2D and 3D Euler equations is parallelized with the aid of domain decomposition. The parallel efficiency of the resultant algorithm on a Silicon Graphics Origin 2000 parallel computer is checked.

Fine‐resolution conservation planning with limited climate‐change information

USGS Publications Warehouse

Shah, Payal; Mallory, Mindy L.; Ando , Amy W.; Guntenspergen, Glenn R.

2017-01-01

Climate‐change induced uncertainties in future spatial patterns of conservation‐related outcomes make it difficult to implement standard conservation‐planning paradigms. A recent study translates Markowitz's risk‐diversification strategy from finance to conservation settings, enabling conservation agents to use this diversification strategy for allocating conservation and restoration investments across space to minimize the risk associated with such uncertainty. However, this method is information intensive and requires a large number of forecasts of ecological outcomes associated with possible climate‐change scenarios for carrying out fine‐resolution conservation planning. We developed a technique for iterative, spatial portfolio analysis that can be used to allocate scarce conservation resources across a desired level of subregions in a planning landscape in the absence of a sufficient number of ecological forecasts. We applied our technique to the Prairie Pothole Region in central North America. A lack of sufficient future climate information prevented attainment of the most efficient risk‐return conservation outcomes in the Prairie Pothole Region. The difference in expected conservation returns between conservation planning with limited climate‐change information and full climate‐change information was as large as 30% for the Prairie Pothole Region even when the most efficient iterative approach was used. However, our iterative approach allowed finer resolution portfolio allocation with limited climate‐change forecasts such that the best possible risk‐return combinations were obtained. With our most efficient iterative approach, the expected loss in conservation outcomes owing to limited climate‐change information could be reduced by 17% relative to other iterative approaches.

Characterization of onset of parametric decay instability of lower hybrid waves

NASA Astrophysics Data System (ADS)

Baek, S. G.; Bonoli, P. T.; Parker, R. R.; Shiraiwa, S.; Wallace, G. M.; Porkolab, M.; Takase, Y.; Brunner, D.; Faust, I. C.; Hubbard, A. E.; LaBombard, B. L.; Lau, C.

2014-02-01

The goal of the lower hybrid current drive (LHCD) program on Alcator C-Mod is to develop and optimize ITER-relevant steady-state plasmas by controlling the current density profile. Using a 4×16 waveguide array, over 1 MW of LH power at 4.6 GHz has been successfully coupled to the plasmas. However, current drive efficiency precipitously drops as the line averaged density (n¯e) increases above 1020m-3. Previous numerical work shows that the observed loss of current drive efficiency in high density plasmas stems from the interactions of LH waves with edge/scrape-off layer (SOL) plasmas [Wallace et al., Physics of Plasmas 19, 062505 (2012)]. Recent observations of parametric decay instability (PDI) suggest that non-linear effects should be also taken into account to fully characterize the parasitic loss mechanisms [Baek et al., Plasma Phys. Control Fusion 55, 052001 (2013)]. In particular, magnetic configuration dependent ion cyclotron PDIs are observed using the probes near n¯e≈1.2×1020m-3. In upper single null plasmas, ion cyclotron PDI is excited near the low field side separatrix with no apparent indications of pump depletion. The observed ion cyclotron PDI becomes weaker in inner wall limited plasmas, which exhibit enhanced current drive effects. In lower single null plasmas, the dominant ion cyclotron PDI is excited near the high field side (HFS) separatrix. In this case, the onset of PDI is correlated with the decrease in pump power, indicating that pump wave power propagates to the HFS and is absorbed locally near the HFS separatrix. Comparing the observed spectra with the homogeneous growth rate calculation indicates that the observed ion cyclotron instability is excited near the plasma periphery. The incident pump power density is high enough to overcome the collisional homogeneous threshold. For C-Mod plasma parameters, the growth rate of ion sound quasi-modes is found to be typically smaller by an order of magnitude than that of ion cyclotron quasi-modes. When considering the convective threshold near the plasma edge, convective growth due to parallel coupling rather than perpendicular coupling is likely to be responsible for the observed strength of the sidebands. To demonstrate the improved LHCD efficiency in high density plasmas, an additional launcher has been designed. In conjunction with the existing launcher, this new launcher will allow access to an ITER-like high single pass absorption regime, replicating the JLH(r) expected in ITER. The predictions from the time domain discharge scenarios, in which the two launchers are used, will be also presented.

Research on material removal accuracy analysis and correction of removal function during ion beam figuring

NASA Astrophysics Data System (ADS)

Wu, Weibin; Dai, Yifan; Zhou, Lin; Xu, Mingjin

2016-09-01

Material removal accuracy has a direct impact on the machining precision and efficiency of ion beam figuring. By analyzing the factors suppressing the improvement of material removal accuracy, we conclude that correcting the removal function deviation and reducing the removal material amount during each iterative process could help to improve material removal accuracy. Removal function correcting principle can effectively compensate removal function deviation between actual figuring and simulated processes, while experiments indicate that material removal accuracy decreases with a long machining time, so a small amount of removal material in each iterative process is suggested. However, more clamping and measuring steps will be introduced in this way, which will also generate machining errors and suppress the improvement of material removal accuracy. On this account, a free-measurement iterative process method is put forward to improve material removal accuracy and figuring efficiency by using less measuring and clamping steps. Finally, an experiment on a φ 100-mm Zerodur planar is preformed, which shows that, in similar figuring time, three free-measurement iterative processes could improve the material removal accuracy and the surface error convergence rate by 62.5% and 17.6%, respectively, compared with a single iterative process.

Optimal Iterative Task Scheduling for Parallel Simulations.

DTIC Science & Technology

1991-03-01

State University, Pullman, Washington. November 1976. 19. Grimaldi , Ralph P . Discrete and Combinatorial Mathematics. Addison-Wesley. June 1989. 20...2 4.8.1 Problem Description .. .. .. .. ... .. ... .... 4-25 4.8.2 Reasons for Level-Strate- p Failure. .. .. .. .. ... 4-26...f- I CA A* overview................................ C-1 C .2 Sample A* r......................... .... C-I C-3 Evaluation P

Turbo Trellis Coded Modulation With Iterative Decoding for Mobile Satellite Communications

NASA Technical Reports Server (NTRS)

Divsalar, D.; Pollara, F.

1997-01-01

In this paper, analytical bounds on the performance of parallel concatenation of two codes, known as turbo codes, and serial concatenation of two codes over fading channels are obtained. Based on this analysis, design criteria for the selection of component trellis codes for MPSK modulation, and a suitable bit-by-bit iterative decoding structure are proposed. Examples are given for throughput of 2 bits/sec/Hz with 8PSK modulation. The parallel concatenation example uses two rate 4/5 8-state convolutional codes with two interleavers. The convolutional codes' outputs are then mapped to two 8PSK modulations. The serial concatenated code example uses an 8-state outer code with rate 4/5 and a 4-state inner trellis code with 5 inputs and 2 x 8PSK outputs per trellis branch. Based on the above mentioned design criteria for fading channels, a method to obtain he structure of the trellis code with maximum diversity is proposed. Simulation results are given for AWGN and an independent Rayleigh fading channel with perfect Channel State Information (CSI).

HeinzelCluster: accelerated reconstruction for FORE and OSEM3D.

PubMed

Vollmar, S; Michel, C; Treffert, J T; Newport, D F; Casey, M; Knöss, C; Wienhard, K; Liu, X; Defrise, M; Heiss, W D

2002-08-07

Using iterative three-dimensional (3D) reconstruction techniques for reconstruction of positron emission tomography (PET) is not feasible on most single-processor machines due to the excessive computing time needed, especially so for the large sinogram sizes of our high-resolution research tomograph (HRRT). In our first approach to speed up reconstruction time we transform the 3D scan into the format of a two-dimensional (2D) scan with sinograms that can be reconstructed independently using Fourier rebinning (FORE) and a fast 2D reconstruction method. On our dedicated reconstruction cluster (seven four-processor systems, Intel PIII@700 MHz, switched fast ethernet and Myrinet, Windows NT Server), we process these 2D sinograms in parallel. We have achieved a speedup > 23 using 26 processors and also compared results for different communication methods (RPC, Syngo, Myrinet GM). The other approach is to parallelize OSEM3D (implementation of C Michel), which has produced the best results for HRRT data so far and is more suitable for an adequate treatment of the sinogram gaps that result from the detector geometry of the HRRT. We have implemented two levels of parallelization for four dedicated cluster (a shared memory fine-grain level on each node utilizing all four processors and a coarse-grain level allowing for 15 nodes) reducing the time for one core iteration from over 7 h to about 35 min.

An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

NASA Technical Reports Server (NTRS)

Williams, S. D.; Curry, D. M.

1977-01-01

For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

An efficient algorithm using matrix methods to solve wind tunnel force-balance equations

NASA Technical Reports Server (NTRS)

Smith, D. L.

1972-01-01

An iterative procedure applying matrix methods to accomplish an efficient algorithm for automatic computer reduction of wind-tunnel force-balance data has been developed. Balance equations are expressed in a matrix form that is convenient for storing balance sensitivities and interaction coefficient values for online or offline batch data reduction. The convergence of the iterative values to a unique solution of this system of equations is investigated, and it is shown that for balances which satisfy the criteria discussed, this type of solution does occur. Methods for making sensitivity adjustments and initial load effect considerations in wind-tunnel applications are also discussed, and the logic for determining the convergence accuracy limits for the iterative solution is given. This more efficient data reduction program is compared with the technique presently in use at the NASA Langley Research Center, and computational times on the order of one-third or less are demonstrated by use of this new program.

Evaluation of the effects of patient arm attenuation in SPECT cardiac perfusion imaging

NASA Astrophysics Data System (ADS)

Luo, Dershan; King, M. A.; Pan, Tin-Su; Xia, Weishi

1996-12-01

It was hypothesized that the use of attenuation correction could compensate for degradation in the uniformity of apparent localization of imaging agents seen in cardiac walls when patients are imaged with arms at their sides. Noise-free simulations of the digital MCAT phantom were employed to investigate this hypothesis. Four variations in camera size and collimation scheme were investigated. We observed that: 1) without attenuation correction, the arms had little additional influences on the uniformity of the heart for 180/spl deg/ reconstructions and caused a small increase in nonuniformity for 360/spl deg/ reconstructions, where the impact of both arms was included; 2) change in patient size had more of an impact on count uniformity than the presence of the arms, either with or without attenuation correction; 3) for a low number of iterations and large patient size, slightly better uniformity was obtained from parallel emission data than from fan-beam emission data, independent of whether parallel or fan-beam transmission data was used to reconstruct the attenuation maps; and 4) for all camera configurations, uniformity was improved with attenuation correction and, given sufficient number of iterations, it was compatible among different imaging geometry combinations. Thus, iterative algorithms can compensate for the additional attenuation imposed by larger patients or having the arms on the sides. When the arms are at the sides of the patient, however, a larger radius of rotation may be required, resulting in decreased spatial resolution.

Evaluation of the effects of patient arm attenuation in SPECT cardiac perfusion imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, D.; King, M.A.; Pan, T.S.

1996-12-01

It was hypothesized that the use of attenuation correction could compensate for degradation in the uniformity of apparent localization of imaging agents seen in cardiac walls when patients are imaged with arms at their sides. Noise-free simulations of the digital MCAT phantom were employed to investigate this hypothesis. Four variations in camera size and collimation scheme were investigated. The authors observed that: (1) without attenuation correction, the arms had little additional influences on the uniformity of the heart for 180{degree} reconstructions and caused a small increase in nonuniformity for 360{degree} reconstructions, where the impact of both arms was included; (2)more » change in patient size had more of an impact on count uniformity than the presence of the arms, either with or without attenuation correction; (3) for a low number of iterations and large patient size, slightly better uniformity was obtained from parallel emission data than from fan-beam emission data, independent of whether parallel or fan-beam transmission data was used to reconstruct the attenuation maps; and (4) for all camera configurations, uniformity was improved with attenuation correction and, given sufficient number of iterations, it was compatible among different imaging geometry combinations. Thus, iterative algorithms can compensate for the additional attenuation imposed by larger patients or having the arms on the sides. When the arms are at the sides of the patient, however, a larger radius of rotation may be required, resulting in decreased spatial resolution.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Azevedo, Eduardo; Abbott, Stephen; Koskela, Tuomas

The XGC fusion gyrokinetic code combines state-of-the-art, portable computational and algorithmic technologies to enable complicated multiscale simulations of turbulence and transport dynamics in ITER edge plasma on the largest US open-science computer, the CRAY XK7 Titan, at its maximal heterogeneous capability, which have not been possible before due to a factor of over 10 shortage in the time-to-solution for less than 5 days of wall-clock time for one physics case. Frontier techniques such as nested OpenMP parallelism, adaptive parallel I/O, staging I/O and data reduction using dynamic and asynchronous applications interactions, dynamic repartitioning.

A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chatterjee, Kausik, E-mail: kausik.chatterjee@aggiemail.usu.edu; Center for Atmospheric and Space Sciences, Utah State University, Logan, UT 84322; Roadcap, John R., E-mail: john.roadcap@us.af.mil

The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals ofmore » the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.« less

A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson-Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

NASA Astrophysics Data System (ADS)

Chatterjee, Kausik; Roadcap, John R.; Singh, Surendra

2014-11-01

The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson-Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.

Parallel architectures for iterative methods on adaptive, block structured grids

NASA Technical Reports Server (NTRS)

Gannon, D.; Vanrosendale, J.

1983-01-01

A parallel computer architecture well suited to the solution of partial differential equations in complicated geometries is proposed. Algorithms for partial differential equations contain a great deal of parallelism. But this parallelism can be difficult to exploit, particularly on complex problems. One approach to extraction of this parallelism is the use of special purpose architectures tuned to a given problem class. The architecture proposed here is tuned to boundary value problems on complex domains. An adaptive elliptic algorithm which maps effectively onto the proposed architecture is considered in detail. Two levels of parallelism are exploited by the proposed architecture. First, by making use of the freedom one has in grid generation, one can construct grids which are locally regular, permitting a one to one mapping of grids to systolic style processor arrays, at least over small regions. All local parallelism can be extracted by this approach. Second, though there may be a regular global structure to the grids constructed, there will be parallelism at this level. One approach to finding and exploiting this parallelism is to use an architecture having a number of processor clusters connected by a switching network. The use of such a network creates a highly flexible architecture which automatically configures to the problem being solved.

Framework for analysis of guaranteed QOS systems

NASA Astrophysics Data System (ADS)

Chaudhry, Shailender; Choudhary, Alok

1997-01-01

Multimedia data is isochronous in nature and entails managing and delivering high volumes of data. Multiprocessors with their large processing power, vast memory, and fast interconnects, are an ideal candidate for the implementation of multimedia applications. Initially, multiprocessors were designed to execute scientific programs and thus their architecture was optimized to provide low message latency and efficiently support regular communication patterns. Hence, they have a regular network topology and most use wormhole routing. The design offers the benefits of a simple router, small buffer size, and network latency that is almost independent of path length. Among the various multimedia applications, video on demand (VOD) server is well-suited for implementation using parallel multiprocessors. Logical models for VOD servers are presently mapped onto multiprocessors. Our paper provides a framework for calculating bounds on utilization of system resources with which QoS parameters for each isochronous stream can be guaranteed. Effects of the architecture of multiprocessors, and efficiency of various local models and mapping on particular architectures can be investigated within our framework. Our framework is based on rigorous proofs and provides tight bounds. The results obtained may be used as the basis for admission control tests. To illustrate the versatility of our framework, we provide bounds on utilization for various logical models applied to mesh connected architectures for a video on demand server. Our results show that worm hole routing can lead to packets waiting for transmission of other packets that apparently share no common resources. This situation is analogous to head-of-the-line blocking. We find that the provision of multiple VCs per link and multiple flit buffers improves utilization (even under guaranteed QoS parameters). This analogous to parallel iterative matching.

An 81.6 μW FastICA processor for epileptic seizure detection.

PubMed

Yang, Chia-Hsiang; Shih, Yi-Hsin; Chiueh, Herming

2015-02-01

To improve the performance of epileptic seizure detection, independent component analysis (ICA) is applied to multi-channel signals to separate artifacts and signals of interest. FastICA is an efficient algorithm to compute ICA. To reduce the energy dissipation, eigenvalue decomposition (EVD) is utilized in the preprocessing stage to reduce the convergence time of iterative calculation of ICA components. EVD is computed efficiently through an array structure of processing elements running in parallel. Area-efficient EVD architecture is realized by leveraging the approximate Jacobi algorithm, leading to a 77.2% area reduction. By choosing proper memory element and reduced wordlength, the power and area of storage memory are reduced by 95.6% and 51.7%, respectively. The chip area is minimized through fixed-point implementation and architectural transformations. Given a latency constraint of 0.1 s, an 86.5% area reduction is achieved compared to the direct-mapped architecture. Fabricated in 90 nm CMOS, the core area of the chip is 0.40 mm(2). The FastICA processor, part of an integrated epileptic control SoC, dissipates 81.6 μW at 0.32 V. The computation delay of a frame of 256 samples for 8 channels is 84.2 ms. Compared to prior work, 0.5% power dissipation, 26.7% silicon area, and 3.4 × computation speedup are achieved. The performance of the chip was verified by human dataset.

An iterative method for the localization of a neutron source in a large box (container)

NASA Astrophysics Data System (ADS)

Dubinski, S.; Presler, O.; Alfassi, Z. B.

2007-12-01

The localization of an unknown neutron source in a bulky box was studied. This can be used for the inspection of cargo, to prevent the smuggling of neutron and α emitters. It is important to localize the source from the outside for safety reasons. Source localization is necessary in order to determine its activity. A previous study showed that, by using six detectors, three on each parallel face of the box (460×420×200 mm 3), the location of the source can be found with an average distance of 4.73 cm between the real source position and the calculated one and a maximal distance of about 9 cm. Accuracy was improved in this work by applying an iteration method based on four fixed detectors and the successive iteration of positioning of an external calibrating source. The initial positioning of the calibrating source is the plane of detectors 1 and 2. This method finds the unknown source location with an average distance of 0.78 cm between the real source position and the calculated one and a maximum distance of 3.66 cm for the same box. For larger boxes, localization without iterations requires an increase in the number of detectors, while localization with iterations requires only an increase in the number of iteration steps. In addition to source localization, two methods for determining the activity of the unknown source were also studied.

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.

1990-01-01

The compressible Navier-Stokes equations are solved for a variety of two-dimensional inviscid and viscous problems by preconditioned conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. The system of linear equations which arises out of the linearization of a fully implicit scheme is solved iteratively by the well known methods of GMRES (Generalized Minimum Residual technique) and Chebyschev iteration. Incomplete LU factorization and block diagonal factorization are used as preconditioners. The resulting algorithm is competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

Domain decomposition methods in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Gropp, William D.; Keyes, David E.

1991-01-01

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

Efficient solution of the simplified P N equations

DOE PAGES

Hamilton, Steven P.; Evans, Thomas M.

2014-12-23

We show new solver strategies for the multigroup SPN equations for nuclear reactor analysis. By forming the complete matrix over space, moments, and energy a robust set of solution strategies may be applied. Moreover, power iteration, shifted power iteration, Rayleigh quotient iteration, Arnoldi's method, and a generalized Davidson method, each using algebraic and physics-based multigrid preconditioners, have been compared on C5G7 MOX test problem as well as an operational PWR model. These results show that the most ecient approach is the generalized Davidson method, that is 30-40 times faster than traditional power iteration and 6-10 times faster than Arnoldi's method.

Thermo-mechanical analysis of ITER first mirrors and its use for the ITER equatorial visible∕infrared wide angle viewing system optical design.

PubMed

Joanny, M; Salasca, S; Dapena, M; Cantone, B; Travère, J M; Thellier, C; Fermé, J J; Marot, L; Buravand, O; Perrollaz, G; Zeile, C

2012-10-01

ITER first mirrors (FMs), as the first components of most ITER optical diagnostics, will be exposed to high plasma radiation flux and neutron load. To reduce the FMs heating and optical surface deformation induced during ITER operation, the use of relevant materials and cooling system are foreseen. The calculations led on different materials and FMs designs and geometries (100 mm and 200 mm) show that the use of CuCrZr and TZM, and a complex integrated cooling system can limit efficiently the FMs heating and reduce their optical surface deformation under plasma radiation flux and neutron load. These investigations were used to evaluate, for the ITER equatorial port visible∕infrared wide angle viewing system, the impact of the FMs properties change during operation on the instrument main optical performances. The results obtained are presented and discussed.

Parallel approach for bioinspired algorithms

NASA Astrophysics Data System (ADS)

Zaporozhets, Dmitry; Zaruba, Daria; Kulieva, Nina

2018-05-01

In the paper, a probabilistic parallel approach based on the population heuristic, such as a genetic algorithm, is suggested. The authors proposed using a multithreading approach at the micro level at which new alternative solutions are generated. On each iteration, several threads that independently used the same population to generate new solutions can be started. After the work of all threads, a selection operator combines obtained results in the new population. To confirm the effectiveness of the suggested approach, the authors have developed software on the basis of which experimental computations can be carried out. The authors have considered a classic optimization problem – finding a Hamiltonian cycle in a graph. Experiments show that due to the parallel approach at the micro level, increment of running speed can be obtained on graphs with 250 and more vertices.

Nonnegative least-squares image deblurring: improved gradient projection approaches

NASA Astrophysics Data System (ADS)

Benvenuto, F.; Zanella, R.; Zanni, L.; Bertero, M.

2010-02-01

The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the ill-posedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.

Fine-resolution conservation planning with limited climate-change information.

PubMed

Shah, Payal; Mallory, Mindy L; Ando, Amy W; Guntenspergen, Glenn R

2017-04-01

Climate-change induced uncertainties in future spatial patterns of conservation-related outcomes make it difficult to implement standard conservation-planning paradigms. A recent study translates Markowitz's risk-diversification strategy from finance to conservation settings, enabling conservation agents to use this diversification strategy for allocating conservation and restoration investments across space to minimize the risk associated with such uncertainty. However, this method is information intensive and requires a large number of forecasts of ecological outcomes associated with possible climate-change scenarios for carrying out fine-resolution conservation planning. We developed a technique for iterative, spatial portfolio analysis that can be used to allocate scarce conservation resources across a desired level of subregions in a planning landscape in the absence of a sufficient number of ecological forecasts. We applied our technique to the Prairie Pothole Region in central North America. A lack of sufficient future climate information prevented attainment of the most efficient risk-return conservation outcomes in the Prairie Pothole Region. The difference in expected conservation returns between conservation planning with limited climate-change information and full climate-change information was as large as 30% for the Prairie Pothole Region even when the most efficient iterative approach was used. However, our iterative approach allowed finer resolution portfolio allocation with limited climate-change forecasts such that the best possible risk-return combinations were obtained. With our most efficient iterative approach, the expected loss in conservation outcomes owing to limited climate-change information could be reduced by 17% relative to other iterative approaches. © 2016 Society for Conservation Biology.

ITER Central Solenoid Module Fabrication

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, John

The fabrication of the modules for the ITER Central Solenoid (CS) has started in a dedicated production facility located in Poway, California, USA. The necessary tools have been designed, built, installed, and tested in the facility to enable the start of production. The current schedule has first module fabrication completed in 2017, followed by testing and subsequent shipment to ITER. The Central Solenoid is a key component of the ITER tokamak providing the inductive voltage to initiate and sustain the plasma current and to position and shape the plasma. The design of the CS has been a collaborative effort betweenmore » the US ITER Project Office (US ITER), the international ITER Organization (IO) and General Atomics (GA). GA’s responsibility includes: completing the fabrication design, developing and qualifying the fabrication processes and tools, and then completing the fabrication of the seven 110 tonne CS modules. The modules will be shipped separately to the ITER site, and then stacked and aligned in the Assembly Hall prior to insertion in the core of the ITER tokamak. A dedicated facility in Poway, California, USA has been established by GA to complete the fabrication of the seven modules. Infrastructure improvements included thick reinforced concrete floors, a diesel generator for backup power, along with, cranes for moving the tooling within the facility. The fabrication process for a single module requires approximately 22 months followed by five months of testing, which includes preliminary electrical testing followed by high current (48.5 kA) tests at 4.7K. The production of the seven modules is completed in a parallel fashion through ten process stations. The process stations have been designed and built with most stations having completed testing and qualification for carrying out the required fabrication processes. The final qualification step for each process station is achieved by the successful production of a prototype coil. Fabrication of the first ITER module is in progress. The seven modules will be individually shipped to Cadarache, France upon their completion. This paper describes the processes and status of the fabrication of the CS Modules for ITER.« less

Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Lin; Shao, Sihong; E, Weinan

2012-11-06

We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Ptmore » $$_{2}$$, Au$$_{2}$$, TlF, and Bi$$_{2}$$Se$$_{3}$$ indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.« less

Parallel Symmetric Eigenvalue Problem Solvers

DTIC Science & Technology

2015-05-01

get research, tutoring, and mentoring experience as an undergraduate. Last but not least, I thank my family for their love and support. v TABLE OF...32 4.6.2 Choice of the Ritz shifts . . . . . . . . . . . . . . . . . . . . 37 4.7 Relationship between...pencil. I will conclude with a discussion of the relationship between Trace- Min and simultaneous iteration. If both methods solve the linear systems

Tokamak und Stellarator - zwei Wege zur Fusionsenergie: Fusionsforschung

NASA Astrophysics Data System (ADS)

Milch, Isabella

2006-07-01

Im Laufe der Fusionsforschung haben sich zwei Bautypen für ein zukünftiges Kraftwerk als besonders aussichtsreich erwiesen: Tokamak und Stellarator. Mit dem geplanten Tokamak-Experimentalreaktor ITER steht die internationale Fusionsforschung vor der Demonstration eines Energie liefernden Plasmas. Parallel soll die in Greifswald entstehende Forschungsanlage Wendelstein 7-X die Kraftwerkstauglichkeit des alternativen Bauprinzips der Stellaratoren zeigen.

Input-output-controlled nonlinear equation solvers

NASA Technical Reports Server (NTRS)

Padovan, Joseph

1988-01-01

To upgrade the efficiency and stability of the successive substitution (SS) and Newton-Raphson (NR) schemes, the concept of input-output-controlled solvers (IOCS) is introduced. By employing the formal properties of the constrained version of the SS and NR schemes, the IOCS algorithm can handle indefiniteness of the system Jacobian, can maintain iterate monotonicity, and provide for separate control of load incrementation and iterate excursions, as well as having other features. To illustrate the algorithmic properties, the results for several benchmark examples are presented. These define the associated numerical efficiency and stability of the IOCS.

Programmable logic construction kits for hyper-real-time neuronal modeling.

PubMed

Guerrero-Rivera, Ruben; Morrison, Abigail; Diesmann, Markus; Pearce, Tim C

2006-11-01

Programmable logic designs are presented that achieve exact integration of leaky integrate-and-fire soma and dynamical synapse neuronal models and incorporate spike-time dependent plasticity and axonal delays. Highly accurate numerical performance has been achieved by modifying simpler forward-Euler-based circuitry requiring minimal circuit allocation, which, as we show, behaves equivalently to exact integration. These designs have been implemented and simulated at the behavioral and physical device levels, demonstrating close agreement with both numerical and analytical results. By exploiting finely grained parallelism and single clock cycle numerical iteration, these designs achieve simulation speeds at least five orders of magnitude faster than the nervous system, termed here hyper-real-time operation, when deployed on commercially available field-programmable gate array (FPGA) devices. Taken together, our designs form a programmable logic construction kit of commonly used neuronal model elements that supports the building of large and complex architectures of spiking neuron networks for real-time neuromorphic implementation, neurophysiological interfacing, or efficient parameter space investigations.

Simulation of Electrical Characteristics of a Solar Panel

NASA Astrophysics Data System (ADS)

Obukhov, S.; Plotnikov, I.; Kryuchkova, M.

2016-06-01

The fast-growing photovoltaic system market leads to the necessity of the informed choice of major energy components and optimization of operating conditions in order to improve energy efficiency. Development of mathematical models of the main components of photovoltaic systems to ensure their comprehensive study is an urgent problem of improving and practical using of the technology of electrical energy production. The paper presents a mathematical model of the solar module implemented in the popular software MATLAB/Simulink. Equivalent circuit of the solar cell with a diode parallel without derived resistance is used for modelling. The serie8s resistance of the solar module is calculated by Newton's iterative method using the data of its technical specifications. It ensures high precision of simulation. Model validity was evaluated by the well-known technical characteristics of the module Solarex MSX 60. The calculation results of the experiment showed that the obtained current-voltage and current-watt characteristics of the model are compatible with those of the manufacturer.

HO2 rovibrational eigenvalue studies for nonzero angular momentum

NASA Astrophysics Data System (ADS)

Wu, Xudong T.; Hayes, Edward F.

1997-08-01

An efficient parallel algorithm is reported for determining all bound rovibrational energy levels for the HO2 molecule for nonzero angular momentum values, J=1, 2, and 3. Performance tests on the CRAY T3D indicate that the algorithm scales almost linearly when up to 128 processors are used. Sustained performance levels of up to 3.8 Gflops have been achieved using 128 processors for J=3. The algorithm uses a direct product discrete variable representation (DVR) basis and the implicitly restarted Lanczos method (IRLM) of Sorensen to compute the eigenvalues of the polyatomic Hamiltonian. Since the IRLM is an iterative method, it does not require storage of the full Hamiltonian matrix—it only requires the multiplication of the Hamiltonian matrix by a vector. When the IRLM is combined with a formulation such as DVR, which produces a very sparse matrix, both memory and computation times can be reduced dramatically. This algorithm has the potential to achieve even higher performance levels for larger values of the total angular momentum.

Solving lattice QCD systems of equations using mixed precision solvers on GPUs

NASA Astrophysics Data System (ADS)

Clark, M. A.; Babich, R.; Barros, K.; Brower, R. C.; Rebbi, C.

2010-09-01

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodynamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40, 135 and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.

Implementation of an effective hybrid GA for large-scale traveling salesman problems.

PubMed

Nguyen, Hung Dinh; Yoshihara, Ikuo; Yamamori, Kunihito; Yasunaga, Moritoshi

2007-02-01

This correspondence describes a hybrid genetic algorithm (GA) to find high-quality solutions for the traveling salesman problem (TSP). The proposed method is based on a parallel implementation of a multipopulation steady-state GA involving local search heuristics. It uses a variant of the maximal preservative crossover and the double-bridge move mutation. An effective implementation of the Lin-Kernighan heuristic (LK) is incorporated into the method to compensate for the GA's lack of local search ability. The method is validated by comparing it with the LK-Helsgaun method (LKH), which is one of the most effective methods for the TSP. Experimental results with benchmarks having up to 316228 cities show that the proposed method works more effectively and efficiently than LKH when solving large-scale problems. Finally, the method is used together with the implementation of the iterated LK to find a new best tour (as of June 2, 2003) for a 1904711-city TSP challenge.

Aeroelastic optimization methodology for viscous and turbulent flows

NASA Astrophysics Data System (ADS)

Barcelos Junior, Manuel Nascimento Dias

2007-12-01

In recent years, the development of faster computers and parallel processing allowed the application of high-fidelity analysis methods to the aeroelastic design of aircraft. However, these methods are restricted to the final design verification, mainly due to the computational cost involved in iterative design processes. Therefore, this work is concerned with the creation of a robust and efficient aeroelastic optimization methodology for inviscid, viscous and turbulent flows by using high-fidelity analysis and sensitivity analysis techniques. Most of the research in aeroelastic optimization, for practical reasons, treat the aeroelastic system as a quasi-static inviscid problem. In this work, as a first step toward the creation of a more complete aeroelastic optimization methodology for realistic problems, an analytical sensitivity computation technique was developed and tested for quasi-static aeroelastic viscous and turbulent flow configurations. Viscous and turbulent effects are included by using an averaged discretization of the Navier-Stokes equations, coupled with an eddy viscosity turbulence model. For quasi-static aeroelastic problems, the traditional staggered solution strategy has unsatisfactory performance when applied to cases where there is a strong fluid-structure coupling. Consequently, this work also proposes a solution methodology for aeroelastic and sensitivity analyses of quasi-static problems, which is based on the fixed point of an iterative nonlinear block Gauss-Seidel scheme. The methodology can also be interpreted as the solution of the Schur complement of the aeroelastic and sensitivity analyses linearized systems of equations. The methodologies developed in this work are tested and verified by using realistic aeroelastic systems.

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

PubMed

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-15

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries

PubMed Central

Asgharzadeh, Hafez; Borazjani, Iman

2016-01-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 – 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80–90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future. PMID:28042172

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42-74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

Multi-GPU Acceleration of Branchless Distance Driven Projection and Backprojection for Clinical Helical CT.

PubMed

Mitra, Ayan; Politte, David G; Whiting, Bruce R; Williamson, Jeffrey F; O'Sullivan, Joseph A

2017-01-01

Model-based image reconstruction (MBIR) techniques have the potential to generate high quality images from noisy measurements and a small number of projections which can reduce the x-ray dose in patients. These MBIR techniques rely on projection and backprojection to refine an image estimate. One of the widely used projectors for these modern MBIR based technique is called branchless distance driven (DD) projection and backprojection. While this method produces superior quality images, the computational cost of iterative updates keeps it from being ubiquitous in clinical applications. In this paper, we provide several new parallelization ideas for concurrent execution of the DD projectors in multi-GPU systems using CUDA programming tools. We have introduced some novel schemes for dividing the projection data and image voxels over multiple GPUs to avoid runtime overhead and inter-device synchronization issues. We have also reduced the complexity of overlap calculation of the algorithm by eliminating the common projection plane and directly projecting the detector boundaries onto image voxel boundaries. To reduce the time required for calculating the overlap between the detector edges and image voxel boundaries, we have proposed a pre-accumulation technique to accumulate image intensities in perpendicular 2D image slabs (from a 3D image) before projection and after backprojection to ensure our DD kernels run faster in parallel GPU threads. For the implementation of our iterative MBIR technique we use a parallel multi-GPU version of the alternating minimization (AM) algorithm with penalized likelihood update. The time performance using our proposed reconstruction method with Siemens Sensation 16 patient scan data shows an average of 24 times speedup using a single TITAN X GPU and 74 times speedup using 3 TITAN X GPUs in parallel for combined projection and backprojection.

Data decomposition method for parallel polygon rasterization considering load balancing

NASA Astrophysics Data System (ADS)

Zhou, Chen; Chen, Zhenjie; Liu, Yongxue; Li, Feixue; Cheng, Liang; Zhu, A.-xing; Li, Manchun

2015-12-01

It is essential to adopt parallel computing technology to rapidly rasterize massive polygon data. In parallel rasterization, it is difficult to design an effective data decomposition method. Conventional methods ignore load balancing of polygon complexity in parallel rasterization and thus fail to achieve high parallel efficiency. In this paper, a novel data decomposition method based on polygon complexity (DMPC) is proposed. First, four factors that possibly affect the rasterization efficiency were investigated. Then, a metric represented by the boundary number and raster pixel number in the minimum bounding rectangle was developed to calculate the complexity of each polygon. Using this metric, polygons were rationally allocated according to the polygon complexity, and each process could achieve balanced loads of polygon complexity. To validate the efficiency of DMPC, it was used to parallelize different polygon rasterization algorithms and tested on different datasets. Experimental results showed that DMPC could effectively parallelize polygon rasterization algorithms. Furthermore, the implemented parallel algorithms with DMPC could achieve good speedup ratios of at least 15.69 and generally outperformed conventional decomposition methods in terms of parallel efficiency and load balancing. In addition, the results showed that DMPC exhibited consistently better performance for different spatial distributions of polygons.

Multi-GPU three dimensional Stokes solver for simulating glacier flow

NASA Astrophysics Data System (ADS)

Licul, Aleksandar; Herman, Frédéric; Podladchikov, Yuri; Räss, Ludovic; Omlin, Samuel

2016-04-01

Here we present how we have recently developed a three-dimensional Stokes solver on the GPUs and apply it to a glacier flow. We numerically solve the Stokes momentum balance equations together with the incompressibility equation, while also taking into account strong nonlinearities for ice rheology. We have developed a fully three-dimensional numerical MATLAB application based on an iterative finite difference scheme with preconditioning of residuals. Differential equations are discretized on a regular staggered grid. We have ported it to C-CUDA to run it on GPU's in parallel, using MPI. We demonstrate the accuracy and efficiency of our developed model by manufactured analytical solution test for three-dimensional Stokes ice sheet models (Leng et al.,2013) and by comparison with other well-established ice sheet models on diagnostic ISMIP-HOM benchmark experiments (Pattyn et al., 2008). The results show that our developed model is capable to accurately and efficiently solve Stokes system of equations in a variety of different test scenarios, while preserving good parallel efficiency on up to 80 GPU's. For example, in 3D test scenarios with 250000 grid points our solver converges in around 3 minutes for single precision computations and around 10 minutes for double precision computations. We have also optimized the developed code to efficiently run on our newly acquired state-of-the-art GPU cluster octopus. This allows us to solve our problem on more than 20 million grid points, by just increasing the number of GPU used, while keeping the computation time the same. In future work we will apply our solver to real world applications and implement the free surface evolution capabilities. REFERENCES Leng,W.,Ju,L.,Gunzburger,M. & Price,S., 2013. Manufactured solutions and the verification of three-dimensional stokes ice-sheet models. Cryosphere 7,19-29. Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson,G.H., Hindmarsh, R.C.A., Hubbard, A., Johnson, J.V., Kleiner, T., Konovalov,Y., Martin, C., Payne, A.J., Pollard, D., Price, S., Rckamp, M., Saito, F., Souk, O.,Sugiyama, S. & Zwinger, T., 2008. Benchmark experiments for higher-order and full-stokes ice sheet models (ismiphom). The Cryosphere 2, 95-108.

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

Parallel processors and nonlinear structural dynamics algorithms and software

NASA Technical Reports Server (NTRS)

Belytschko, Ted

1990-01-01

Techniques are discussed for the implementation and improvement of vectorization and concurrency in nonlinear explicit structural finite element codes. In explicit integration methods, the computation of the element internal force vector consumes the bulk of the computer time. The program can be efficiently vectorized by subdividing the elements into blocks and executing all computations in vector mode. The structuring of elements into blocks also provides a convenient way to implement concurrency by creating tasks which can be assigned to available processors for evaluation. The techniques were implemented in a 3-D nonlinear program with one-point quadrature shell elements. Concurrency and vectorization were first implemented in a single time step version of the program. Techniques were developed to minimize processor idle time and to select the optimal vector length. A comparison of run times between the program executed in scalar, serial mode and the fully vectorized code executed concurrently using eight processors shows speed-ups of over 25. Conjugate gradient methods for solving nonlinear algebraic equations are also readily adapted to a parallel environment. A new technique for improving convergence properties of conjugate gradients in nonlinear problems is developed in conjunction with other techniques such as diagonal scaling. A significant reduction in the number of iterations required for convergence is shown for a statically loaded rigid bar suspended by three equally spaced springs.

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

DOE PAGES

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

2017-10-30

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

Error Control Coding Techniques for Space and Satellite Communications

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.; Takeshita, Oscar Y.; Cabral, Hermano A.; He, Jiali; White, Gregory S.

1997-01-01

Turbo coding using iterative SOVA decoding and M-ary differentially coherent or non-coherent modulation can provide an effective coding modulation solution: (1) Energy efficient with relatively simple SOVA decoding and small packet lengths, depending on BEP required; (2) Low number of decoding iterations required; and (3) Robustness in fading with channel interleaving.

FBILI method for multi-level line transfer

NASA Astrophysics Data System (ADS)

Kuzmanovska, O.; Atanacković, O.; Faurobert, M.

2017-07-01

Efficient non-LTE multilevel radiative transfer calculations are needed for a proper interpretation of astrophysical spectra. In particular, realistic simulations of time-dependent processes or multi-dimensional phenomena require that the iterative method used to solve such non-linear and non-local problem is as fast as possible. There are several multilevel codes based on efficient iterative schemes that provide a very high convergence rate, especially when combined with mathematical acceleration techniques. The Forth-and-Back Implicit Lambda Iteration (FBILI) developed by Atanacković-Vukmanović et al. [1] is a Gauss-Seidel-type iterative scheme that is characterized by a very high convergence rate without the need of complementing it with additional acceleration techniques. In this paper we make the implementation of the FBILI method to the multilevel atom line transfer in 1D more explicit. We also consider some of its variants and investigate their convergence properties by solving the benchmark problem of CaII line formation in the solar atmosphere. Finally, we compare our solutions with results obtained with the well known code MULTI.

Energy Efficiency Maximization for WSNs with Simultaneous Wireless Information and Power Transfer

PubMed Central

Yu, Hongyan; Zhang, Yongqiang; Yang, Yuanyuan; Ji, Luyue

2017-01-01

Recently, the simultaneous wireless information and power transfer (SWIPT) technique has been regarded as a promising approach to enhance performance of wireless sensor networks with limited energy supply. However, from a green communication perspective, energy efficiency optimization for SWIPT system design has not been investigated in Wireless Rechargeable Sensor Networks (WRSNs). In this paper, we consider the tradeoffs between energy efficiency and three factors including spectral efficiency, the transmit power and outage target rate for two different modes, i.e., power splitting (PS) and time switching modes (TS), at the receiver. Moreover, we formulate the energy efficiency maximization problem subject to the constraints of minimum Quality of Service (QoS), minimum harvested energy and maximum transmission power as non-convex optimization problem. In particular, we focus on optimizing power control and power allocation policy in PS and TS modes to maximize energy efficiency of data transmission. For PS and TS modes, we propose the corresponding algorithm to characterize a non-convex optimization problem that takes into account the circuit power consumption and the harvested energy. By exploiting nonlinear fractional programming and Lagrangian dual decomposition, we propose suboptimal iterative algorithms to obtain the solutions of non-convex optimization problems. Furthermore, we derive the outage probability and effective throughput from the scenarios that the transmitter does not or partially know the channel state information (CSI) of the receiver. Simulation results illustrate that the proposed optimal iterative algorithm can achieve optimal solutions within a small number of iterations and various tradeoffs between energy efficiency and spectral efficiency, transmit power and outage target rate, respectively. PMID:28820496

Energy Efficiency Maximization for WSNs with Simultaneous Wireless Information and Power Transfer.

PubMed

Yu, Hongyan; Zhang, Yongqiang; Guo, Songtao; Yang, Yuanyuan; Ji, Luyue

2017-08-18

Recently, the simultaneous wireless information and power transfer (SWIPT) technique has been regarded as a promising approach to enhance performance of wireless sensor networks with limited energy supply. However, from a green communication perspective, energy efficiency optimization for SWIPT system design has not been investigated in Wireless Rechargeable Sensor Networks (WRSNs). In this paper, we consider the tradeoffs between energy efficiency and three factors including spectral efficiency, the transmit power and outage target rate for two different modes, i.e., power splitting (PS) and time switching modes (TS), at the receiver. Moreover, we formulate the energy efficiency maximization problem subject to the constraints of minimum Quality of Service (QoS), minimum harvested energy and maximum transmission power as non-convex optimization problem. In particular, we focus on optimizing power control and power allocation policy in PS and TS modes to maximize energy efficiency of data transmission. For PS and TS modes, we propose the corresponding algorithm to characterize a non-convex optimization problem that takes into account the circuit power consumption and the harvested energy. By exploiting nonlinear fractional programming and Lagrangian dual decomposition, we propose suboptimal iterative algorithms to obtain the solutions of non-convex optimization problems. Furthermore, we derive the outage probability and effective throughput from the scenarios that the transmitter does not or partially know the channel state information (CSI) of the receiver. Simulation results illustrate that the proposed optimal iterative algorithm can achieve optimal solutions within a small number of iterations and various tradeoffs between energy efficiency and spectral efficiency, transmit power and outage target rate, respectively.

Region of interest processing for iterative reconstruction in x-ray computed tomography

NASA Astrophysics Data System (ADS)

Kopp, Felix K.; Nasirudin, Radin A.; Mei, Kai; Fehringer, Andreas; Pfeiffer, Franz; Rummeny, Ernst J.; Noël, Peter B.

2015-03-01

The recent advancements in the graphics card technology raised the performance of parallel computing and contributed to the introduction of iterative reconstruction methods for x-ray computed tomography in clinical CT scanners. Iterative maximum likelihood (ML) based reconstruction methods are known to reduce image noise and to improve the diagnostic quality of low-dose CT. However, iterative reconstruction of a region of interest (ROI), especially ML based, is challenging. But for some clinical procedures, like cardiac CT, only a ROI is needed for diagnostics. A high-resolution reconstruction of the full field of view (FOV) consumes unnecessary computation effort that results in a slower reconstruction than clinically acceptable. In this work, we present an extension and evaluation of an existing ROI processing algorithm. Especially improvements for the equalization between regions inside and outside of a ROI are proposed. The evaluation was done on data collected from a clinical CT scanner. The performance of the different algorithms is qualitatively and quantitatively assessed. Our solution to the ROI problem provides an increase in signal-to-noise ratio and leads to visually less noise in the final reconstruction. The reconstruction speed of our technique was observed to be comparable with other previous proposed techniques. The development of ROI processing algorithms in combination with iterative reconstruction will provide higher diagnostic quality in the near future.

astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Jennings, E.; Madigan, M.

2017-04-01

Given the complexity of modern cosmological parameter inference where we are faced with non-Gaussian data and noise, correlated systematics and multi-probe correlated datasets,the Approximate Bayesian Computation (ABC) method is a promising alternative to traditional Markov Chain Monte Carlo approaches in the case where the Likelihood is intractable or unknown. The ABC method is called "Likelihood free" as it avoids explicit evaluation of the Likelihood by using a forward model simulation of the data which can include systematics. We introduce astroABC, an open source ABC Sequential Monte Carlo (SMC) sampler for parameter estimation. A key challenge in astrophysics is the efficient use of large multi-probe datasets to constrain high dimensional, possibly correlated parameter spaces. With this in mind astroABC allows for massive parallelization using MPI, a framework that handles spawning of processes across multiple nodes. A key new feature of astroABC is the ability to create MPI groups with different communicators, one for the sampler and several others for the forward model simulation, which speeds up sampling time considerably. For smaller jobs the Python multiprocessing option is also available. Other key features of this new sampler include: a Sequential Monte Carlo sampler; a method for iteratively adapting tolerance levels; local covariance estimate using scikit-learn's KDTree; modules for specifying optimal covariance matrix for a component-wise or multivariate normal perturbation kernel and a weighted covariance metric; restart files output frequently so an interrupted sampling run can be resumed at any iteration; output and restart files are backed up at every iteration; user defined distance metric and simulation methods; a module for specifying heterogeneous parameter priors including non-standard prior PDFs; a module for specifying a constant, linear, log or exponential tolerance level; well-documented examples and sample scripts. This code is hosted online at https://github.com/EliseJ/astroABC.

Reducing Design Cycle Time and Cost Through Process Resequencing

NASA Technical Reports Server (NTRS)

Rogers, James L.

2004-01-01

In today's competitive environment, companies are under enormous pressure to reduce the time and cost of their design cycle. One method for reducing both time and cost is to develop an understanding of the flow of the design processes and the effects of the iterative subcycles that are found in complex design projects. Once these aspects are understood, the design manager can make decisions that take advantage of decomposition, concurrent engineering, and parallel processing techniques to reduce the total time and the total cost of the design cycle. One software tool that can aid in this decision-making process is the Design Manager's Aid for Intelligent Decomposition (DeMAID). The DeMAID software minimizes the feedback couplings that create iterative subcycles, groups processes into iterative subcycles, and decomposes the subcycles into a hierarchical structure. The real benefits of producing the best design in the least time and at a minimum cost are obtained from sequencing the processes in the subcycles.

Solution of partial differential equations on vector and parallel computers

NASA Technical Reports Server (NTRS)

Ortega, J. M.; Voigt, R. G.

1985-01-01

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

Diverse power iteration embeddings: Theory and practice

DOE PAGES

Huang, Hao; Yoo, Shinjae; Yu, Dantong; ...

2015-11-09

Manifold learning, especially spectral embedding, is known as one of the most effective learning approaches on high dimensional data, but for real-world applications it raises a serious computational burden in constructing spectral embeddings for large datasets. To overcome this computational complexity, we propose a novel efficient embedding construction, Diverse Power Iteration Embedding (DPIE). DPIE shows almost the same effectiveness of spectral embeddings and yet is three order of magnitude faster than spectral embeddings computed from eigen-decomposition. Our DPIE is unique in that (1) it finds linearly independent embeddings and thus shows diverse aspects of dataset; (2) the proposed regularized DPIEmore » is effective if we need many embeddings; (3) we show how to efficiently orthogonalize DPIE if one needs; and (4) Diverse Power Iteration Value (DPIV) provides the importance of each DPIE like an eigen value. As a result, such various aspects of DPIE and DPIV ensure that our algorithm is easy to apply to various applications, and we also show the effectiveness and efficiency of DPIE on clustering, anomaly detection, and feature selection as our case studies.« less

Scientific and technical challenges on the road towards fusion electricity

NASA Astrophysics Data System (ADS)

Donné, A. J. H.; Federici, G.; Litaudon, X.; McDonald, D. C.

2017-10-01

The goal of the European Fusion Roadmap is to deliver fusion electricity to the grid early in the second half of this century. It breaks the quest for fusion energy into eight missions, and for each of them it describes a research and development programme to address all the open technical gaps in physics and technology and estimates the required resources. It points out the needs to intensify industrial involvement and to seek all opportunities for collaboration outside Europe. The roadmap covers three periods: the short term, which runs parallel to the European Research Framework Programme Horizon 2020, the medium term and the long term. ITER is the key facility of the roadmap as it is expected to achieve most of the important milestones on the path to fusion power. Thus, the vast majority of present resources are dedicated to ITER and its accompanying experiments. The medium term is focussed on taking ITER into operation and bringing it to full power, as well as on preparing the construction of a demonstration power plant DEMO, which will for the first time demonstrate fusion electricity to the grid around the middle of this century. Building and operating DEMO is the subject of the last roadmap phase: the long term. Clearly, the Fusion Roadmap is tightly connected to the ITER schedule. Three key milestones are the first operation of ITER, the start of the DT operation in ITER and reaching the full performance at which the thermal fusion power is 10 times the power put in to the plasma. The Engineering Design Activity of DEMO needs to start a few years after the first ITER plasma, while the start of the construction phase will be a few years after ITER reaches full performance. In this way ITER can give viable input to the design and development of DEMO. Because the neutron fluence in DEMO will be much higher than in ITER, it is important to develop and validate materials that can handle these very high neutron loads. For the testing of the materials, a dedicated 14 MeV neutron source is needed. This DEMO Oriented Neutron Source (DONES) is therefore an important facility to support the fusion roadmap.

Nonperturbative measurement of the local magnetic field using pulsed polarimetry for fusion reactor conditions (invited).

PubMed

Smith, Roger J

2008-10-01

A novel diagnostic technique for the remote and nonperturbative sensing of the local magnetic field in reactor relevant plasmas is presented. Pulsed polarimetry [Patent No. 12/150,169 (pending)] combines optical scattering with the Faraday effect. The polarimetric light detection and ranging (LIDAR)-like diagnostic has the potential to be a local B(pol) diagnostic on ITER and can achieve spatial resolutions of millimeters on high energy density (HED) plasmas using existing lasers. The pulsed polarimetry method is based on nonlocal measurements and subtle effects are introduced that are not present in either cw polarimetry or Thomson scattering LIDAR. Important features include the capability of simultaneously measuring local T(e), n(e), and B(parallel) along the line of sight, a resiliency to refractive effects, a short measurement duration providing near instantaneous data in time, and location for real-time feedback and control of magnetohydrodynamic (MHD) instabilities and the realization of a widely applicable internal magnetic field diagnostic for the magnetic fusion energy program. The technique improves for higher n(e)B(parallel) product and higher n(e) and is well suited for diagnosing the transient plasmas in the HED program. Larger devices such as ITER and DEMO are also better suited to the technique, allowing longer pulse lengths and thereby relaxing key technology constraints making pulsed polarimetry a valuable asset for next step devices. The pulsed polarimetry technique is clarified by way of illustration on the ITER tokamak and plasmas within the magnetized target fusion program within present technological means.

An improved parallel fuzzy connected image segmentation method based on CUDA.

PubMed

Wang, Liansheng; Li, Dong; Huang, Shaohui

2016-05-12

Fuzzy connectedness method (FC) is an effective method for extracting fuzzy objects from medical images. However, when FC is applied to large medical image datasets, its running time will be greatly expensive. Therefore, a parallel CUDA version of FC (CUDA-kFOE) was proposed by Ying et al. to accelerate the original FC. Unfortunately, CUDA-kFOE does not consider the edges between GPU blocks, which causes miscalculation of edge points. In this paper, an improved algorithm is proposed by adding a correction step on the edge points. The improved algorithm can greatly enhance the calculation accuracy. In the improved method, an iterative manner is applied. In the first iteration, the affinity computation strategy is changed and a look up table is employed for memory reduction. In the second iteration, the error voxels because of asynchronism are updated again. Three different CT sequences of hepatic vascular with different sizes were used in the experiments with three different seeds. NVIDIA Tesla C2075 is used to evaluate our improved method over these three data sets. Experimental results show that the improved algorithm can achieve a faster segmentation compared to the CPU version and higher accuracy than CUDA-kFOE. The calculation results were consistent with the CPU version, which demonstrates that it corrects the edge point calculation error of the original CUDA-kFOE. The proposed method has a comparable time cost and has less errors compared to the original CUDA-kFOE as demonstrated in the experimental results. In the future, we will focus on automatic acquisition method and automatic processing.

Accelerating Computation of DCM for ERP in MATLAB by External Function Calls to the GPU.

PubMed

Wang, Wei-Jen; Hsieh, I-Fan; Chen, Chun-Chuan

2013-01-01

This study aims to improve the performance of Dynamic Causal Modelling for Event Related Potentials (DCM for ERP) in MATLAB by using external function calls to a graphics processing unit (GPU). DCM for ERP is an advanced method for studying neuronal effective connectivity. DCM utilizes an iterative procedure, the expectation maximization (EM) algorithm, to find the optimal parameters given a set of observations and the underlying probability model. As the EM algorithm is computationally demanding and the analysis faces possible combinatorial explosion of models to be tested, we propose a parallel computing scheme using the GPU to achieve a fast estimation of DCM for ERP. The computation of DCM for ERP is dynamically partitioned and distributed to threads for parallel processing, according to the DCM model complexity and the hardware constraints. The performance efficiency of this hardware-dependent thread arrangement strategy was evaluated using the synthetic data. The experimental data were used to validate the accuracy of the proposed computing scheme and quantify the time saving in practice. The simulation results show that the proposed scheme can accelerate the computation by a factor of 155 for the parallel part. For experimental data, the speedup factor is about 7 per model on average, depending on the model complexity and the data. This GPU-based implementation of DCM for ERP gives qualitatively the same results as the original MATLAB implementation does at the group level analysis. In conclusion, we believe that the proposed GPU-based implementation is very useful for users as a fast screen tool to select the most likely model and may provide implementation guidance for possible future clinical applications such as online diagnosis.

3D streamers simulation in a pin to plane configuration using massively parallel computing

NASA Astrophysics Data System (ADS)

Plewa, J.-M.; Eichwald, O.; Ducasse, O.; Dessante, P.; Jacobs, C.; Renon, N.; Yousfi, M.

2018-03-01

This paper concerns the 3D simulation of corona discharge using high performance computing (HPC) managed with the message passing interface (MPI) library. In the field of finite volume methods applied on non-adaptive mesh grids and in the case of a specific 3D dynamic benchmark test devoted to streamer studies, the great efficiency of the iterative R&B SOR and BiCGSTAB methods versus the direct MUMPS method was clearly demonstrated in solving the Poisson equation using HPC resources. The optimization of the parallelization and the resulting scalability was undertaken as a function of the HPC architecture for a number of mesh cells ranging from 8 to 512 million and a number of cores ranging from 20 to 1600. The R&B SOR method remains at least about four times faster than the BiCGSTAB method and requires significantly less memory for all tested situations. The R&B SOR method was then implemented in a 3D MPI parallelized code that solves the classical first order model of an atmospheric pressure corona discharge in air. The 3D code capabilities were tested by following the development of one, two and four coplanar streamers generated by initial plasma spots for 6 ns. The preliminary results obtained allowed us to follow in detail the formation of the tree structure of a corona discharge and the effects of the mutual interactions between the streamers in terms of streamer velocity, trajectory and diameter. The computing time for 64 million of mesh cells distributed over 1000 cores using the MPI procedures is about 30 min ns-1, regardless of the number of streamers.

Accelerating Computation of DCM for ERP in MATLAB by External Function Calls to the GPU

PubMed Central

Wang, Wei-Jen; Hsieh, I-Fan; Chen, Chun-Chuan

2013-01-01

This study aims to improve the performance of Dynamic Causal Modelling for Event Related Potentials (DCM for ERP) in MATLAB by using external function calls to a graphics processing unit (GPU). DCM for ERP is an advanced method for studying neuronal effective connectivity. DCM utilizes an iterative procedure, the expectation maximization (EM) algorithm, to find the optimal parameters given a set of observations and the underlying probability model. As the EM algorithm is computationally demanding and the analysis faces possible combinatorial explosion of models to be tested, we propose a parallel computing scheme using the GPU to achieve a fast estimation of DCM for ERP. The computation of DCM for ERP is dynamically partitioned and distributed to threads for parallel processing, according to the DCM model complexity and the hardware constraints. The performance efficiency of this hardware-dependent thread arrangement strategy was evaluated using the synthetic data. The experimental data were used to validate the accuracy of the proposed computing scheme and quantify the time saving in practice. The simulation results show that the proposed scheme can accelerate the computation by a factor of 155 for the parallel part. For experimental data, the speedup factor is about 7 per model on average, depending on the model complexity and the data. This GPU-based implementation of DCM for ERP gives qualitatively the same results as the original MATLAB implementation does at the group level analysis. In conclusion, we believe that the proposed GPU-based implementation is very useful for users as a fast screen tool to select the most likely model and may provide implementation guidance for possible future clinical applications such as online diagnosis. PMID:23840507

Parallel computing for automated model calibration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burke, John S.; Danielson, Gary R.; Schulz, Douglas A.

2002-07-29

Natural resources model calibration is a significant burden on computing and staff resources in modeling efforts. Most assessments must consider multiple calibration objectives (for example magnitude and timing of stream flow peak). An automated calibration process that allows real time updating of data/models, allowing scientists to focus effort on improving models is needed. We are in the process of building a fully featured multi objective calibration tool capable of processing multiple models cheaply and efficiently using null cycle computing. Our parallel processing and calibration software routines have been generically, but our focus has been on natural resources model calibration. Somore » far, the natural resources models have been friendly to parallel calibration efforts in that they require no inter-process communication, only need a small amount of input data and only output a small amount of statistical information for each calibration run. A typical auto calibration run might involve running a model 10,000 times with a variety of input parameters and summary statistical output. In the past model calibration has been done against individual models for each data set. The individual model runs are relatively fast, ranging from seconds to minutes. The process was run on a single computer using a simple iterative process. We have completed two Auto Calibration prototypes and are currently designing a more feature rich tool. Our prototypes have focused on running the calibration in a distributed computing cross platform environment. They allow incorporation of?smart? calibration parameter generation (using artificial intelligence processing techniques). Null cycle computing similar to SETI@Home has also been a focus of our efforts. This paper details the design of the latest prototype and discusses our plans for the next revision of the software.« less

Optimal parallel solution of sparse triangular systems

NASA Technical Reports Server (NTRS)

Alvarado, Fernando L.; Schreiber, Robert

1990-01-01

A method for the parallel solution of triangular sets of equations is described that is appropriate when there are many right-handed sides. By preprocessing, the method can reduce the number of parallel steps required to solve Lx = b compared to parallel forward or backsolve. Applications are to iterative solvers with triangular preconditioners, to structural analysis, or to power systems applications, where there may be many right-handed sides (not all available a priori). The inverse of L is represented as a product of sparse triangular factors. The problem is to find a factored representation of this inverse of L with the smallest number of factors (or partitions), subject to the requirement that no new nonzero elements be created in the formation of these inverse factors. A method from an earlier reference is shown to solve this problem. This method is improved upon by constructing a permutation of the rows and columns of L that preserves triangularity and allow for the best possible such partition. A number of practical examples and algorithmic details are presented. The parallelism attainable is illustrated by means of elimination trees and clique trees.

The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science.

PubMed

Marek, A; Blum, V; Johanni, R; Havu, V; Lang, B; Auckenthaler, T; Heinecke, A; Bungartz, H-J; Lederer, H

2014-05-28

Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic structure theory and many other areas of computational science. The computational effort formally scales as O(N(3)) with the size of the investigated problem, N (e.g. the electron count in electronic structure theory), and thus often defines the system size limit that practical calculations cannot overcome. In many cases, more than just a small fraction of the possible eigenvalue/eigenvector pairs is needed, so that iterative solution strategies that focus only on a few eigenvalues become ineffective. Likewise, it is not always desirable or practical to circumvent the eigenvalue solution entirely. We here review some current developments regarding dense eigenvalue solvers and then focus on the Eigenvalue soLvers for Petascale Applications (ELPA) library, which facilitates the efficient algebraic solution of symmetric and Hermitian eigenvalue problems for dense matrices that have real-valued and complex-valued matrix entries, respectively, on parallel computer platforms. ELPA addresses standard as well as generalized eigenvalue problems, relying on the well documented matrix layout of the Scalable Linear Algebra PACKage (ScaLAPACK) library but replacing all actual parallel solution steps with subroutines of its own. For these steps, ELPA significantly outperforms the corresponding ScaLAPACK routines and proprietary libraries that implement the ScaLAPACK interface (e.g. Intel's MKL). The most time-critical step is the reduction of the matrix to tridiagonal form and the corresponding backtransformation of the eigenvectors. ELPA offers both a one-step tridiagonalization (successive Householder transformations) and a two-step transformation that is more efficient especially towards larger matrices and larger numbers of CPU cores. ELPA is based on the MPI standard, with an early hybrid MPI-OpenMPI implementation available as well. Scalability beyond 10,000 CPU cores for problem sizes arising in the field of electronic structure theory is demonstrated for current high-performance computer architectures such as Cray or Intel/Infiniband. For a matrix of dimension 260,000, scalability up to 295,000 CPU cores has been shown on BlueGene/P.

Computer program MCAP-TOSS calculates steady-state fluid dynamics of coolant in parallel channels and temperature distribution in surrounding heat-generating solid

NASA Technical Reports Server (NTRS)

Lee, A. Y.

1967-01-01

Computer program calculates the steady state fluid distribution, temperature rise, and pressure drop of a coolant, the material temperature distribution of a heat generating solid, and the heat flux distributions at the fluid-solid interfaces. It performs the necessary iterations automatically within the computer, in one machine run.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Hixon, Duane; Sankar, L. N.

1993-01-01

During the past two decades, there has been significant progress in the field of numerical simulation of unsteady compressible viscous flows. At present, a variety of solution techniques exist such as the transonic small disturbance analyses (TSD), transonic full potential equation-based methods, unsteady Euler solvers, and unsteady Navier-Stokes solvers. These advances have been made possible by developments in three areas: (1) improved numerical algorithms; (2) automation of body-fitted grid generation schemes; and (3) advanced computer architectures with vector processing and massively parallel processing features. In this work, the GMRES scheme has been considered as a candidate for acceleration of a Newton iteration time marching scheme for unsteady 2-D and 3-D compressible viscous flow calculation; from preliminary calculations, this will provide up to a 65 percent reduction in the computer time requirements over the existing class of explicit and implicit time marching schemes. The proposed method has ben tested on structured grids, but is flexible enough for extension to unstructured grids. The described scheme has been tested only on the current generation of vector processor architecture of the Cray Y/MP class, but should be suitable for adaptation to massively parallel machines.

Effective channel estimation and efficient symbol detection for multi-input multi-output underwater acoustic communications

NASA Astrophysics Data System (ADS)

Ling, Jun

Achieving reliable underwater acoustic communications (UAC) has long been recognized as a challenging problem owing to the scarce bandwidth available and the reverberant spread in both time and frequency domains. To pursue high data rates, we consider a multi-input multi-output (MIMO) UAC system, and our focus is placed on two main issues regarding a MIMO UAC system: (1) channel estimation, which involves the design of the training sequences and the development of a reliable channel estimation algorithm, and (2) symbol detection, which requires interference cancelation schemes due to simultaneous transmission from multiple transducers. To enhance channel estimation performance, we present a cyclic approach for designing training sequences with good auto- and cross-correlation properties, and a channel estimation algorithm called the iterative adaptive approach (IAA). Sparse channel estimates can be obtained by combining IAA with the Bayesian information criterion (BIC). Moreover, we present sparse learning via iterative minimization (SLIM) and demonstrate that SLIM gives similar performance to IAA but at a much lower computational cost. Furthermore, an extension of the SLIM algorithm is introduced to estimate the sparse and frequency modulated acoustic channels. The extended algorithm is referred to as generalization of SLIM (GoSLIM). Regarding symbol detection, a linear minimum mean-squared error based detection scheme, called RELAX-BLAST, which is a combination of vertical Bell Labs layered space-time (V-BLAST) algorithm and the cyclic principle of the RELAX algorithm, is presented and it is shown that RELAX-BLAST outperforms V-BLAST. We show that RELAX-BLAST can be implemented efficiently by making use of the conjugate gradient method and diagonalization properties of circulant matrices. This fast implementation approach requires only simple fast Fourier transform operations and facilitates parallel implementations. The effectiveness of the proposed MIMO schemes is verified by both computer simulations and experimental results obtained by analyzing the measurements acquired in multiple in-water experiments.

Optimizing transformations of stencil operations for parallel cache-based architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bassetti, F.; Davis, K.

This paper describes a new technique for optimizing serial and parallel stencil- and stencil-like operations for cache-based architectures. This technique takes advantage of the semantic knowledge implicity in stencil-like computations. The technique is implemented as a source-to-source program transformation; because of its specificity it could not be expected of a conventional compiler. Empirical results demonstrate a uniform factor of two speedup. The experiments clearly show the benefits of this technique to be a consequence, as intended, of the reduction in cache misses. The test codes are based on a 5-point stencil obtained by the discretization of the Poisson equation andmore » applied to a two-dimensional uniform grid using the Jacobi method as an iterative solver. Results are presented for a 1-D tiling for a single processor, and in parallel using 1-D data partition. For the parallel case both blocking and non-blocking communication are tested. The same scheme of experiments has bee n performed for the 2-D tiling case. However, for the parallel case the 2-D partitioning is not discussed here, so the parallel case handled for 2-D is 2-D tiling with 1-D data partitioning.« less

Streaming parallel GPU acceleration of large-scale filter-based spiking neural networks.

PubMed

Slażyński, Leszek; Bohte, Sander

2012-01-01

The arrival of graphics processing (GPU) cards suitable for massively parallel computing promises affordable large-scale neural network simulation previously only available at supercomputing facilities. While the raw numbers suggest that GPUs may outperform CPUs by at least an order of magnitude, the challenge is to develop fine-grained parallel algorithms to fully exploit the particulars of GPUs. Computation in a neural network is inherently parallel and thus a natural match for GPU architectures: given inputs, the internal state for each neuron can be updated in parallel. We show that for filter-based spiking neurons, like the Spike Response Model, the additive nature of membrane potential dynamics enables additional update parallelism. This also reduces the accumulation of numerical errors when using single precision computation, the native precision of GPUs. We further show that optimizing simulation algorithms and data structures to the GPU's architecture has a large pay-off: for example, matching iterative neural updating to the memory architecture of the GPU speeds up this simulation step by a factor of three to five. With such optimizations, we can simulate in better-than-realtime plausible spiking neural networks of up to 50 000 neurons, processing over 35 million spiking events per second.

Development of a stereo analysis algorithm for generating topographic maps using interactive techniques of the MPP

NASA Technical Reports Server (NTRS)

Strong, James P.

1987-01-01

A local area matching algorithm was developed on the Massively Parallel Processor (MPP). It is an iterative technique that first matches coarse or low resolution areas and at each iteration performs matches of higher resolution. Results so far show that when good matches are possible in the two images, the MPP algorithm matches corresponding areas as well as a human observer. To aid in developing this algorithm, a control or shell program was developed for the MPP that allows interactive experimentation with various parameters and procedures to be used in the matching process. (This would not be possible without the high speed of the MPP). With the system, optimal techniques can be developed for different types of matching problems.

The effect of pre-existing islands on disruption mitigation in MHD simulations of DIII-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Izzo, V. A.

Locked-modes are the most likely cause of disruptions in ITER, so large islands are expected to be common when the ITER disruption mitigation system is deployed. MHD modeling of disruption mitigation by massive gas injection is carried out for DIII-D plasmas with stationary, pre-existing islands. Results show that the magnetic topology at the q=2 surface can affect the parallel spreading of injected impurities, and that, in particular, the break-up of large 2/1 islands into smaller 4/2 islands chains can favorably affect mitigation metrics. The direct imposition of a 4/2 mode is found to have similar results to the case inmore » which the 4/2 harmonic grows spontaneously.« less

The effect of pre-existing islands on disruption mitigation in MHD simulations of DIII-D

DOE PAGES

Izzo, V. A.

2017-02-27

Locked-modes are the most likely cause of disruptions in ITER, so large islands are expected to be common when the ITER disruption mitigation system is deployed. MHD modeling of disruption mitigation by massive gas injection is carried out for DIII-D plasmas with stationary, pre-existing islands. Results show that the magnetic topology at the q=2 surface can affect the parallel spreading of injected impurities, and that, in particular, the break-up of large 2/1 islands into smaller 4/2 islands chains can favorably affect mitigation metrics. The direct imposition of a 4/2 mode is found to have similar results to the case inmore » which the 4/2 harmonic grows spontaneously.« less

Projection matrix acquisition for cone-beam computed tomography iterative reconstruction

NASA Astrophysics Data System (ADS)

Yang, Fuqiang; Zhang, Dinghua; Huang, Kuidong; Shi, Wenlong; Zhang, Caixin; Gao, Zongzhao

2017-02-01

Projection matrix is an essential and time-consuming part in computed tomography (CT) iterative reconstruction. In this article a novel calculation algorithm of three-dimensional (3D) projection matrix is proposed to quickly acquire the matrix for cone-beam CT (CBCT). The CT data needed to be reconstructed is considered as consisting of the three orthogonal sets of equally spaced and parallel planes, rather than the individual voxels. After getting the intersections the rays with the surfaces of the voxels, the coordinate points and vertex is compared to obtain the index value that the ray traversed. Without considering ray-slope to voxel, it just need comparing the position of two points. Finally, the computer simulation is used to verify the effectiveness of the algorithm.

A conjugate gradient method for solving the non-LTE line radiation transfer problem

NASA Astrophysics Data System (ADS)

Paletou, F.; Anterrieu, E.

2009-12-01

This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently proposed Gauss-Seidel and successive over-relaxation (GS/SOR) schemes. Our study is indeed based on applying a preconditioned bi-conjugate gradient method (BiCG-P). Standard tests, in 1D plane parallel geometry and in the frame of the two-level atom model with monochromatic scattering are discussed. Rates of convergence between the previously mentioned iterative schemes are compared, as are their respective timing properties. The smoothing capability of the BiCG-P method is also demonstrated.

Inner Space Perturbation Theory in Matrix Product States: Replacing Expensive Iterative Diagonalization.

PubMed

Ren, Jiajun; Yi, Yuanping; Shuai, Zhigang

2016-10-11

We propose an inner space perturbation theory (isPT) to replace the expensive iterative diagonalization in the standard density matrix renormalization group theory (DMRG). The retained reduced density matrix eigenstates are partitioned into the active and secondary space. The first-order wave function and the second- and third-order energies are easily computed by using one step Davidson iteration. Our formulation has several advantages including (i) keeping a balance between the efficiency and accuracy, (ii) capturing more entanglement with the same amount of computational time, (iii) recovery of the standard DMRG when all the basis states belong to the active space. Numerical examples for the polyacenes and periacene show that the efficiency gain is considerable and the accuracy loss due to the perturbation treatment is very small, when half of the total basis states belong to the active space. Moreover, the perturbation calculations converge in all our numerical examples.

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

PubMed

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 2¹⁰ times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

A parallelized three-dimensional cellular automaton model for grain growth during additive manufacturing

NASA Astrophysics Data System (ADS)

Lian, Yanping; Lin, Stephen; Yan, Wentao; Liu, Wing Kam; Wagner, Gregory J.

2018-05-01

In this paper, a parallelized 3D cellular automaton computational model is developed to predict grain morphology for solidification of metal during the additive manufacturing process. Solidification phenomena are characterized by highly localized events, such as the nucleation and growth of multiple grains. As a result, parallelization requires careful treatment of load balancing between processors as well as interprocess communication in order to maintain a high parallel efficiency. We give a detailed summary of the formulation of the model, as well as a description of the communication strategies implemented to ensure parallel efficiency. Scaling tests on a representative problem with about half a billion cells demonstrate parallel efficiency of more than 80% on 8 processors and around 50% on 64; loss of efficiency is attributable to load imbalance due to near-surface grain nucleation in this test problem. The model is further demonstrated through an additive manufacturing simulation with resulting grain structures showing reasonable agreement with those observed in experiments.

A parallelized three-dimensional cellular automaton model for grain growth during additive manufacturing

NASA Astrophysics Data System (ADS)

Lian, Yanping; Lin, Stephen; Yan, Wentao; Liu, Wing Kam; Wagner, Gregory J.

2018-01-01

In this paper, a parallelized 3D cellular automaton computational model is developed to predict grain morphology for solidification of metal during the additive manufacturing process. Solidification phenomena are characterized by highly localized events, such as the nucleation and growth of multiple grains. As a result, parallelization requires careful treatment of load balancing between processors as well as interprocess communication in order to maintain a high parallel efficiency. We give a detailed summary of the formulation of the model, as well as a description of the communication strategies implemented to ensure parallel efficiency. Scaling tests on a representative problem with about half a billion cells demonstrate parallel efficiency of more than 80% on 8 processors and around 50% on 64; loss of efficiency is attributable to load imbalance due to near-surface grain nucleation in this test problem. The model is further demonstrated through an additive manufacturing simulation with resulting grain structures showing reasonable agreement with those observed in experiments.

Efficient Parallelization of a Dynamic Unstructured Application on the Tera MTA

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Biswas, Rupak

1999-01-01

The success of parallel computing in solving real-life computationally-intensive problems relies on their efficient mapping and execution on large-scale multiprocessor architectures. Many important applications are both unstructured and dynamic in nature, making their efficient parallel implementation a daunting task. This paper presents the parallelization of a dynamic unstructured mesh adaptation algorithm using three popular programming paradigms on three leading supercomputers. We examine an MPI message-passing implementation on the Cray T3E and the SGI Origin2OOO, a shared-memory implementation using cache coherent nonuniform memory access (CC-NUMA) of the Origin2OOO, and a multi-threaded version on the newly-released Tera Multi-threaded Architecture (MTA). We compare several critical factors of this parallel code development, including runtime, scalability, programmability, and memory overhead. Our overall results demonstrate that multi-threaded systems offer tremendous potential for quickly and efficiently solving some of the most challenging real-life problems on parallel computers.

SU-D-206-03: Segmentation Assisted Fast Iterative Reconstruction Method for Cone-Beam CT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, P; Mao, T; Gong, S

2016-06-15

Purpose: Total Variation (TV) based iterative reconstruction (IR) methods enable accurate CT image reconstruction from low-dose measurements with sparse projection acquisition, due to the sparsifiable feature of most CT images using gradient operator. However, conventional solutions require large amount of iterations to generate a decent reconstructed image. One major reason is that the expected piecewise constant property is not taken into consideration at the optimization starting point. In this work, we propose an iterative reconstruction method for cone-beam CT (CBCT) using image segmentation to guide the optimization path more efficiently on the regularization term at the beginning of the optimizationmore » trajectory. Methods: Our method applies general knowledge that one tissue component in the CT image contains relatively uniform distribution of CT number. This general knowledge is incorporated into the proposed reconstruction using image segmentation technique to generate the piecewise constant template on the first-pass low-quality CT image reconstructed using analytical algorithm. The template image is applied as an initial value into the optimization process. Results: The proposed method is evaluated on the Shepp-Logan phantom of low and high noise levels, and a head patient. The number of iterations is reduced by overall 40%. Moreover, our proposed method tends to generate a smoother reconstructed image with the same TV value. Conclusion: We propose a computationally efficient iterative reconstruction method for CBCT imaging. Our method achieves a better optimization trajectory and a faster convergence behavior. It does not rely on prior information and can be readily incorporated into existing iterative reconstruction framework. Our method is thus practical and attractive as a general solution to CBCT iterative reconstruction. This work is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LR16F010001), National High-tech R&D Program for Young Scientists by the Ministry of Science and Technology of China (Grant No. 2015AA020917).« less

Bayesian block-diagonal variable selection and model averaging

PubMed Central

Papaspiliopoulos, O.; Rossell, D.

2018-01-01

Summary We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general designs. In block-diagonal designs our approach returns the most probable model of any given size without resorting to numerical integration. The algorithm also provides a novel and efficient solution to the frequentist best subset selection problem for block-diagonal designs. Posterior probabilities for any number of models are obtained by evaluating a single one-dimensional integral, and other quantities of interest such as variable inclusion probabilities and model-averaged regression estimates are obtained by an adaptive, deterministic one-dimensional numerical integration. The overall computational cost scales linearly with the number of blocks, which can be processed in parallel, and exponentially with the block size, rendering it most adequate in situations where predictors are organized in many moderately-sized blocks. For general designs, we approximate the Gram matrix by a block-diagonal matrix using spectral clustering and propose an iterative algorithm that capitalizes on the block-diagonal algorithms to explore efficiently the model space. All methods proposed in this paper are implemented in the R library mombf. PMID:29861501

Block-Parallel Data Analysis with DIY2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morozov, Dmitriy; Peterka, Tom

DIY2 is a programming model and runtime for block-parallel analytics on distributed-memory machines. Its main abstraction is block-structured data parallelism: data are decomposed into blocks; blocks are assigned to processing elements (processes or threads); computation is described as iterations over these blocks, and communication between blocks is defined by reusable patterns. By expressing computation in this general form, the DIY2 runtime is free to optimize the movement of blocks between slow and fast memories (disk and flash vs. DRAM) and to concurrently execute blocks residing in memory with multiple threads. This enables the same program to execute in-core, out-of-core, serial,more » parallel, single-threaded, multithreaded, or combinations thereof. This paper describes the implementation of the main features of the DIY2 programming model and optimizations to improve performance. DIY2 is evaluated on benchmark test cases to establish baseline performance for several common patterns and on larger complete analysis codes running on large-scale HPC machines.« less

Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vogiatzis, Konstantinos D.; Ma, Dongxia; Olsen, Jeppe

A new large-scale parallel multiconfigurational self-consistent field (MCSCF) implementation in the open-source NWChem computational chemistry code is presented. The generalized active space approach is used to partition large configuration interaction (CI) vectors and generate a sufficient number of batches that can be distributed to the available cores. Massively parallel CI calculations with large active spaces can be performed. The new parallel MCSCF implementation is tested for the chromium trimer and for an active space of 20 electrons in 20 orbitals, which can now routinely be performed. Unprecedented CI calculations with an active space of 22 electrons in 22 orbitals formore » the pentacene systems were performed and a single CI iteration calculation with an active space of 24 electrons in 24 orbitals for the chromium tetramer was possible. In conclusion, the chromium tetramer corresponds to a CI expansion of one trillion Slater determinants (914 058 513 424) and is the largest conventional CI calculation attempted up to date.« less

Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations

DOE PAGES

Vogiatzis, Konstantinos D.; Ma, Dongxia; Olsen, Jeppe; ...

2017-11-14

A new large-scale parallel multiconfigurational self-consistent field (MCSCF) implementation in the open-source NWChem computational chemistry code is presented. The generalized active space approach is used to partition large configuration interaction (CI) vectors and generate a sufficient number of batches that can be distributed to the available cores. Massively parallel CI calculations with large active spaces can be performed. The new parallel MCSCF implementation is tested for the chromium trimer and for an active space of 20 electrons in 20 orbitals, which can now routinely be performed. Unprecedented CI calculations with an active space of 22 electrons in 22 orbitals formore » the pentacene systems were performed and a single CI iteration calculation with an active space of 24 electrons in 24 orbitals for the chromium tetramer was possible. In conclusion, the chromium tetramer corresponds to a CI expansion of one trillion Slater determinants (914 058 513 424) and is the largest conventional CI calculation attempted up to date.« less

Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations

NASA Astrophysics Data System (ADS)

Vogiatzis, Konstantinos D.; Ma, Dongxia; Olsen, Jeppe; Gagliardi, Laura; de Jong, Wibe A.

2017-11-01

A new large-scale parallel multiconfigurational self-consistent field (MCSCF) implementation in the open-source NWChem computational chemistry code is presented. The generalized active space approach is used to partition large configuration interaction (CI) vectors and generate a sufficient number of batches that can be distributed to the available cores. Massively parallel CI calculations with large active spaces can be performed. The new parallel MCSCF implementation is tested for the chromium trimer and for an active space of 20 electrons in 20 orbitals, which can now routinely be performed. Unprecedented CI calculations with an active space of 22 electrons in 22 orbitals for the pentacene systems were performed and a single CI iteration calculation with an active space of 24 electrons in 24 orbitals for the chromium tetramer was possible. The chromium tetramer corresponds to a CI expansion of one trillion Slater determinants (914 058 513 424) and is the largest conventional CI calculation attempted up to date.

Coupled-Flow Simulation of HP-LP Turbines Has Resulted in Significant Fuel Savings

NASA Technical Reports Server (NTRS)

Veres, Joseph P.

2001-01-01

Our objective was to create a high-fidelity Navier-Stokes computer simulation of the flow through the turbines of a modern high-bypass-ratio turbofan engine. The simulation would have to capture the aerodynamic interactions between closely coupled high- and low-pressure turbines. A computer simulation of the flow in the GE90 turbofan engine's high-pressure (HP) and low-pressure (LP) turbines was created at GE Aircraft Engines under contract with the NASA Glenn Research Center. The three-dimensional steady-state computer simulation was performed using Glenn's average-passage approach named APNASA. The areas upstream and downstream of each blade row mutually interact with each other during engine operation. The embedded blade row operating conditions are modeled since the average passage equations in APNASA actively include the effects of the adjacent blade rows. The turbine airfoils, platforms, and casing are actively cooled by compressor bleed air. Hot gas leaks around the tips of rotors through labyrinth seals. The flow exiting the high work HP turbines is partially transonic and, therefore, has a strong shock system in the transition region. The simulation was done using 121 processors of a Silicon Graphics Origin 2000 (NAS 02K) cluster at the NASA Ames Research Center, with a parallel efficiency of 87 percent in 15 hr. The typical average-passage analysis mesh size per blade row was 280 by 45 by 55, or approx.700,000 grid points. The total number of blade rows was 18 for a combined HP and LP turbine system including the struts in the transition duct and exit guide vane, which contain 12.6 million grid points. Design cycle turnaround time requirements ran typically from 24 to 48 hr of wall clock time. The number of iterations for convergence was 10,000 at 8.03x10(exp -5) sec/iteration/grid point (NAS O2K). Parallel processing by up to 40 processors is required to meet the design cycle time constraints. This is the first-ever flow simulation of an HP and LP turbine. In addition, it includes the struts in the transition duct and exit guide vanes.

Three-dimensional inverse modelling of damped elastic wave propagation in the Fourier domain

NASA Astrophysics Data System (ADS)

Petrov, Petr V.; Newman, Gregory A.

2014-09-01

3-D full waveform inversion (FWI) of seismic wavefields is routinely implemented with explicit time-stepping simulators. A clear advantage of explicit time stepping is the avoidance of solving large-scale implicit linear systems that arise with frequency domain formulations. However, FWI using explicit time stepping may require a very fine time step and (as a consequence) significant computational resources and run times. If the computational challenges of wavefield simulation can be effectively handled, an FWI scheme implemented within the frequency domain utilizing only a few frequencies, offers a cost effective alternative to FWI in the time domain. We have therefore implemented a 3-D FWI scheme for elastic wave propagation in the Fourier domain. To overcome the computational bottleneck in wavefield simulation, we have exploited an efficient Krylov iterative solver for the elastic wave equations approximated with second and fourth order finite differences. The solver does not exploit multilevel preconditioning for wavefield simulation, but is coupled efficiently to the inversion iteration workflow to reduce computational cost. The workflow is best described as a series of sequential inversion experiments, where in the case of seismic reflection acquisition geometries, the data has been laddered such that we first image highly damped data, followed by data where damping is systemically reduced. The key to our modelling approach is its ability to take advantage of solver efficiency when the elastic wavefields are damped. As the inversion experiment progresses, damping is significantly reduced, effectively simulating non-damped wavefields in the Fourier domain. While the cost of the forward simulation increases as damping is reduced, this is counterbalanced by the cost of the outer inversion iteration, which is reduced because of a better starting model obtained from the larger damped wavefield used in the previous inversion experiment. For cross-well data, it is also possible to launch a successful inversion experiment without laddering the damping constants. With this type of acquisition geometry, the solver is still quite effective using a small fixed damping constant. To avoid cycle skipping, we also employ a multiscale imaging approach, in which frequency content of the data is also laddered (with the data now including both reflection and cross-well data acquisition geometries). Thus the inversion process is launched using low frequency data to first recover the long spatial wavelength of the image. With this image as a new starting model, adding higher frequency data refines and enhances the resolution of the image. FWI using laddered frequencies with an efficient damping schemed enables reconstructing elastic attributes of the subsurface at a resolution that approaches half the smallest wavelength utilized to image the subsurface. We show the possibility of effectively carrying out such reconstructions using two to six frequencies, depending upon the application. Using the proposed FWI scheme, massively parallel computing resources are essential for reasonable execution times.

The PRIMA Test Facility: SPIDER and MITICA test-beds for ITER neutral beam injectors

NASA Astrophysics Data System (ADS)

Toigo, V.; Piovan, R.; Dal Bello, S.; Gaio, E.; Luchetta, A.; Pasqualotto, R.; Zaccaria, P.; Bigi, M.; Chitarin, G.; Marcuzzi, D.; Pomaro, N.; Serianni, G.; Agostinetti, P.; Agostini, M.; Antoni, V.; Aprile, D.; Baltador, C.; Barbisan, M.; Battistella, M.; Boldrin, M.; Brombin, M.; Dalla Palma, M.; De Lorenzi, A.; Delogu, R.; De Muri, M.; Fellin, F.; Ferro, A.; Fiorentin, A.; Gambetta, G.; Gnesotto, F.; Grando, L.; Jain, P.; Maistrello, A.; Manduchi, G.; Marconato, N.; Moresco, M.; Ocello, E.; Pavei, M.; Peruzzo, S.; Pilan, N.; Pimazzoni, A.; Recchia, M.; Rizzolo, A.; Rostagni, G.; Sartori, E.; Siragusa, M.; Sonato, P.; Sottocornola, A.; Spada, E.; Spagnolo, S.; Spolaore, M.; Taliercio, C.; Valente, M.; Veltri, P.; Zamengo, A.; Zaniol, B.; Zanotto, L.; Zaupa, M.; Boilson, D.; Graceffa, J.; Svensson, L.; Schunke, B.; Decamps, H.; Urbani, M.; Kushwah, M.; Chareyre, J.; Singh, M.; Bonicelli, T.; Agarici, G.; Garbuglia, A.; Masiello, A.; Paolucci, F.; Simon, M.; Bailly-Maitre, L.; Bragulat, E.; Gomez, G.; Gutierrez, D.; Mico, G.; Moreno, J.-F.; Pilard, V.; Kashiwagi, M.; Hanada, M.; Tobari, H.; Watanabe, K.; Maejima, T.; Kojima, A.; Umeda, N.; Yamanaka, H.; Chakraborty, A.; Baruah, U.; Rotti, C.; Patel, H.; Nagaraju, M. V.; Singh, N. P.; Patel, A.; Dhola, H.; Raval, B.; Fantz, U.; Heinemann, B.; Kraus, W.; Hanke, S.; Hauer, V.; Ochoa, S.; Blatchford, P.; Chuilon, B.; Xue, Y.; De Esch, H. P. L.; Hemsworth, R.; Croci, G.; Gorini, G.; Rebai, M.; Muraro, A.; Tardocchi, M.; Cavenago, M.; D'Arienzo, M.; Sandri, S.; Tonti, A.

2017-08-01

The ITER Neutral Beam Test Facility (NBTF), called PRIMA (Padova Research on ITER Megavolt Accelerator), is hosted in Padova, Italy and includes two experiments: MITICA, the full-scale prototype of the ITER heating neutral beam injector, and SPIDER, the full-size radio frequency negative-ions source. The NBTF realization and the exploitation of SPIDER and MITICA have been recognized as necessary to make the future operation of the ITER heating neutral beam injectors efficient and reliable, fundamental to the achievement of thermonuclear-relevant plasma parameters in ITER. This paper reports on design and R&D carried out to construct PRIMA, SPIDER and MITICA, and highlights the huge progress made in just a few years, from the signature of the agreement for the NBTF realization in 2011, up to now—when the buildings and relevant infrastructures have been completed, SPIDER is entering the integrated commissioning phase and the procurements of several MITICA components are at a well advanced stage.

S-HARP: A parallel dynamic spectral partitioner

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sohn, A.; Simon, H.

1998-01-01

Computational science problems with adaptive meshes involve dynamic load balancing when implemented on parallel machines. This dynamic load balancing requires fast partitioning of computational meshes at run time. The authors present in this report a fast parallel dynamic partitioner, called S-HARP. The underlying principles of S-HARP are the fast feature of inertial partitioning and the quality feature of spectral partitioning. S-HARP partitions a graph from scratch, requiring no partition information from previous iterations. Two types of parallelism have been exploited in S-HARP, fine grain loop level parallelism and coarse grain recursive parallelism. The parallel partitioner has been implemented in Messagemore » Passing Interface on Cray T3E and IBM SP2 for portability. Experimental results indicate that S-HARP can partition a mesh of over 100,000 vertices into 256 partitions in 0.2 seconds on a 64 processor Cray T3E. S-HARP is much more scalable than other dynamic partitioners, giving over 15 fold speedup on 64 processors while ParaMeTiS1.0 gives a few fold speedup. Experimental results demonstrate that S-HARP is three to 10 times faster than the dynamic partitioners ParaMeTiS and Jostle on six computational meshes of size over 100,000 vertices.« less

A high-speed linear algebra library with automatic parallelism

NASA Technical Reports Server (NTRS)

Boucher, Michael L.

1994-01-01

Parallel or distributed processing is key to getting highest performance workstations. However, designing and implementing efficient parallel algorithms is difficult and error-prone. It is even more difficult to write code that is both portable to and efficient on many different computers. Finally, it is harder still to satisfy the above requirements and include the reliability and ease of use required of commercial software intended for use in a production environment. As a result, the application of parallel processing technology to commercial software has been extremely small even though there are numerous computationally demanding programs that would significantly benefit from application of parallel processing. This paper describes DSSLIB, which is a library of subroutines that perform many of the time-consuming computations in engineering and scientific software. DSSLIB combines the high efficiency and speed of parallel computation with a serial programming model that eliminates many undesirable side-effects of typical parallel code. The result is a simple way to incorporate the power of parallel processing into commercial software without compromising maintainability, reliability, or ease of use. This gives significant advantages over less powerful non-parallel entries in the market.

Multiple Revolution Solutions for the Perturbed Lambert Problem using the Method of Particular Solutions and Picard Iteration

NASA Astrophysics Data System (ADS)

Woollands, Robyn M.; Read, Julie L.; Probe, Austin B.; Junkins, John L.

2017-12-01

We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not required, and instead it makes use of a reference trajectory and a set of n particular solutions. Any numerical integrator can be used for solving two-point boundary problems with the method of particular solutions, however we show that using modified Chebyshev-Picard iteration affords an avenue for increased efficiency that is not available with other step-by-step integrators. We take advantage of the path approximation nature of modified Chebyshev-Picard iteration (nodes iteratively converge to fixed points in space) and utilize a variable fidelity force model for propagating the reference trajectory. Remarkably, we demonstrate that computing the particular solutions with only low fidelity function evaluations greatly increases the efficiency of the algorithm while maintaining machine precision accuracy. Our study reveals that solving the perturbed Lambert's problem using the method of particular solutions with modified Chebyshev-Picard iteration is about an order of magnitude faster compared with the classical shooting method and a tenth-twelfth order Runge-Kutta integrator. It is well known that the solution to Lambert's problem over multiple revolutions is not unique and to ensure that all possible solutions are considered we make use of a reliable preexisting Keplerian Lambert solver to warm start our perturbed algorithm.

Characterization of onset of parametric decay instability of lower hybrid waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baek, S. G.; Bonoli, P. T.; Parker, R. R.

2014-02-12

The goal of the lower hybrid current drive (LHCD) program on Alcator C-Mod is to develop and optimize ITER-relevant steady-state plasmas by controlling the current density profile. Using a 4×16 waveguide array, over 1 MW of LH power at 4.6 GHz has been successfully coupled to the plasmas. However, current drive efficiency precipitously drops as the line averaged density (nÐœ„{sub e}) increases above 10{sup 20}m{sup −3}. Previous numerical work shows that the observed loss of current drive efficiency in high density plasmas stems from the interactions of LH waves with edge/scrape-off layer (SOL) plasmas [Wallace et al., Physics of Plasmasmore » 19, 062505 (2012)]. Recent observations of parametric decay instability (PDI) suggest that non-linear effects should be also taken into account to fully characterize the parasitic loss mechanisms [Baek et al., Plasma Phys. Control Fusion 55, 052001 (2013)]. In particular, magnetic configuration dependent ion cyclotron PDIs are observed using the probes near nÐœ„{sub e}≈1.2×10{sup 20}m{sup −3}. In upper single null plasmas, ion cyclotron PDI is excited near the low field side separatrix with no apparent indications of pump depletion. The observed ion cyclotron PDI becomes weaker in inner wall limited plasmas, which exhibit enhanced current drive effects. In lower single null plasmas, the dominant ion cyclotron PDI is excited near the high field side (HFS) separatrix. In this case, the onset of PDI is correlated with the decrease in pump power, indicating that pump wave power propagates to the HFS and is absorbed locally near the HFS separatrix. Comparing the observed spectra with the homogeneous growth rate calculation indicates that the observed ion cyclotron instability is excited near the plasma periphery. The incident pump power density is high enough to overcome the collisional homogeneous threshold. For C-Mod plasma parameters, the growth rate of ion sound quasi-modes is found to be typically smaller by an order of magnitude than that of ion cyclotron quasi-modes. When considering the convective threshold near the plasma edge, convective growth due to parallel coupling rather than perpendicular coupling is likely to be responsible for the observed strength of the sidebands. To demonstrate the improved LHCD efficiency in high density plasmas, an additional launcher has been designed. In conjunction with the existing launcher, this new launcher will allow access to an ITER-like high single pass absorption regime, replicating the J{sub LH}(r) expected in ITER. The predictions from the time domain discharge scenarios, in which the two launchers are used, will be also presented.« less

A class of parallel algorithms for computation of the manipulator inertia matrix

NASA Technical Reports Server (NTRS)

Fijany, Amir; Bejczy, Antal K.

1989-01-01

Parallel and parallel/pipeline algorithms for computation of the manipulator inertia matrix are presented. An algorithm based on composite rigid-body spatial inertia method, which provides better features for parallelization, is used for the computation of the inertia matrix. Two parallel algorithms are developed which achieve the time lower bound in computation. Also described is the mapping of these algorithms with topological variation on a two-dimensional processor array, with nearest-neighbor connection, and with cardinality variation on a linear processor array. An efficient parallel/pipeline algorithm for the linear array was also developed, but at significantly higher efficiency.

On the Optimality of Serial and Parallel Processing in the Psychological Refractory Period Paradigm: Effects of the Distribution of Stimulus Onset Asynchronies

ERIC Educational Resources Information Center

Miller, Jeff; Ulrich, Rolf; Rolke, Bettina

2009-01-01

Within the context of the psychological refractory period (PRP) paradigm, we developed a general theoretical framework for deciding when it is more efficient to process two tasks in serial and when it is more efficient to process them in parallel. This analysis suggests that a serial mode is more efficient than a parallel mode under a wide variety…

Parallelization of interpolation, solar radiation and water flow simulation modules in GRASS GIS using OpenMP

NASA Astrophysics Data System (ADS)

Hofierka, Jaroslav; Lacko, Michal; Zubal, Stanislav

2017-10-01

In this paper, we describe the parallelization of three complex and computationally intensive modules of GRASS GIS using the OpenMP application programming interface for multi-core computers. These include the v.surf.rst module for spatial interpolation, the r.sun module for solar radiation modeling and the r.sim.water module for water flow simulation. We briefly describe the functionality of the modules and parallelization approaches used in the modules. Our approach includes the analysis of the module's functionality, identification of source code segments suitable for parallelization and proper application of OpenMP parallelization code to create efficient threads processing the subtasks. We document the efficiency of the solutions using the airborne laser scanning data representing land surface in the test area and derived high-resolution digital terrain model grids. We discuss the performance speed-up and parallelization efficiency depending on the number of processor threads. The study showed a substantial increase in computation speeds on a standard multi-core computer while maintaining the accuracy of results in comparison to the output from original modules. The presented parallelization approach showed the simplicity and efficiency of the parallelization of open-source GRASS GIS modules using OpenMP, leading to an increased performance of this geospatial software on standard multi-core computers.

A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Jameson, Antony

1986-01-01

A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.

Iterative Nonlinear Tikhonov Algorithm with Constraints for Electromagnetic Tomography

NASA Technical Reports Server (NTRS)

Xu, Feng; Deshpande, Manohar

2012-01-01

Low frequency electromagnetic tomography such as the capacitance tomography (ECT) has been proposed for monitoring and mass-gauging of gas-liquid two-phase system under microgravity condition in NASA's future long-term space missions. Due to the ill-posed inverse problem of ECT, images reconstructed using conventional linear algorithms often suffer from limitations such as low resolution and blurred edges. Hence, new efficient high resolution nonlinear imaging algorithms are needed for accurate two-phase imaging. The proposed Iterative Nonlinear Tikhonov Regularized Algorithm with Constraints (INTAC) is based on an efficient finite element method (FEM) forward model of quasi-static electromagnetic problem. It iteratively minimizes the discrepancy between FEM simulated and actual measured capacitances by adjusting the reconstructed image using the Tikhonov regularized method. More importantly, it enforces the known permittivity of two phases to the unknown pixels which exceed the reasonable range of permittivity in each iteration. This strategy does not only stabilize the converging process, but also produces sharper images. Simulations show that resolution improvement of over 2 times can be achieved by INTAC with respect to conventional approaches. Strategies to further improve spatial imaging resolution are suggested, as well as techniques to accelerate nonlinear forward model and thus increase the temporal resolution.

On efficiency of fire simulation realization: parallelization with greater number of computational meshes

NASA Astrophysics Data System (ADS)

Valasek, Lukas; Glasa, Jan

2017-12-01

Current fire simulation systems are capable to utilize advantages of high-performance computer (HPC) platforms available and to model fires efficiently in parallel. In this paper, efficiency of a corridor fire simulation on a HPC computer cluster is discussed. The parallel MPI version of Fire Dynamics Simulator is used for testing efficiency of selected strategies of allocation of computational resources of the cluster using a greater number of computational cores. Simulation results indicate that if the number of cores used is not equal to a multiple of the total number of cluster node cores there are allocation strategies which provide more efficient calculations.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi; Hixon, Duane

1993-01-01

The work done under this project was documented in detail as the Ph. D. dissertation of Dr. Duane Hixon. The objectives of the research project were evaluation of the generalized minimum residual method (GMRES) as a tool for accelerating 2-D and 3-D unsteady flows and evaluation of the suitability of the GMRES algorithm for unsteady flows, computed on parallel computer architectures.

Methods for design and evaluation of integrated hardware-software systems for concurrent computation

NASA Technical Reports Server (NTRS)

Pratt, T. W.

1985-01-01

Research activities and publications are briefly summarized. The major tasks reviewed are: (1) VAX implementation of the PISCES parallel programming environment; (2) Apollo workstation network implementation of the PISCES environment; (3) FLEX implementation of the PISCES environment; (4) sparse matrix iterative solver in PSICES Fortran; (5) image processing application of PISCES; and (6) a formal model of concurrent computation being developed.

Efficiency of parallel direct optimization

NASA Technical Reports Server (NTRS)

Janies, D. A.; Wheeler, W. C.

2001-01-01

Tremendous progress has been made at the level of sequential computation in phylogenetics. However, little attention has been paid to parallel computation. Parallel computing is particularly suited to phylogenetics because of the many ways large computational problems can be broken into parts that can be analyzed concurrently. In this paper, we investigate the scaling factors and efficiency of random addition and tree refinement strategies using the direct optimization software, POY, on a small (10 slave processors) and a large (256 slave processors) cluster of networked PCs running LINUX. These algorithms were tested on several data sets composed of DNA and morphology ranging from 40 to 500 taxa. Various algorithms in POY show fundamentally different properties within and between clusters. All algorithms are efficient on the small cluster for the 40-taxon data set. On the large cluster, multibuilding exhibits excellent parallel efficiency, whereas parallel building is inefficient. These results are independent of data set size. Branch swapping in parallel shows excellent speed-up for 16 slave processors on the large cluster. However, there is no appreciable speed-up for branch swapping with the further addition of slave processors (>16). This result is independent of data set size. Ratcheting in parallel is efficient with the addition of up to 32 processors in the large cluster. This result is independent of data set size. c2001 The Willi Hennig Society.

Burning plasma regime for Fussion-Fission Research Facility

NASA Astrophysics Data System (ADS)

Zakharov, Leonid E.

2010-11-01

The basic aspects of burning plasma regimes of Fusion-Fission Research Facility (FFRF, R/a=4/1 m/m, Ipl=5 MA, Btor=4-6 T, P^DT=50-100 MW, P^fission=80-4000 MW, 1 m thick blanket), which is suggested as the next step device for Chinese fusion program, are presented. The mission of FFRF is to advance magnetic fusion to the level of a stationary neutron source and to create a technical, scientific, and technology basis for the utilization of high-energy fusion neutrons for the needs of nuclear energy and technology. FFRF will rely as much as possible on ITER design. Thus, the magnetic system, especially TFC, will take advantage of ITER experience. TFC will use the same superconductor as ITER. The plasma regimes will represent an extension of the stationary plasma regimes on HT-7 and EAST tokamaks at ASIPP. Both inductive discharges and stationary non-inductive Lower Hybrid Current Drive (LHCD) will be possible. FFRF strongly relies on new, Lithium Wall Fusion (LiWF) plasma regimes, the development of which will be done on NSTX, HT-7, EAST in parallel with the design work. This regime will eliminate a number of uncertainties, still remaining unresolved in the ITER project. Well controlled, hours long inductive current drive operation at P^DT=50-100 MW is predicted.

Functional materials for breeding blankets—status and developments

NASA Astrophysics Data System (ADS)

Konishi, S.; Enoeda, M.; Nakamichi, M.; Hoshino, T.; Ying, A.; Sharafat, S.; Smolentsev, S.

2017-09-01

The development of tritium breeder, neutron multiplier and flow channel insert materials for the breeding blanket of the DEMO reactor is reviewed. Present emphasis is on the ITER test blanket module (TBM); lithium metatitanate (Li2TiO3) and lithium orthosilicate (Li4SiO4) pebbles have been developed by leading TBM parties. Beryllium pebbles have been selected as the neutron multiplier. Good progress has been made in their fabrication; however, verification of the design by experiments is in the planning stage. Irradiation data are also limited, but the decrease in thermal conductivity of beryllium due to irradiation followed by swelling is a concern. Tests at ITER are regarded as a major milestone. For the DEMO reactor, improvement of the breeder has been attempted to obtain a higher lithium content, and Be12Ti and other beryllide intermetallic compounds that have superior chemical stability have been studied. LiPb eutectic has been considered as a DEMO blanket in the liquid breeder option and is used as a coolant to achieve a higher outlet temperature; a SiC flow channel insert is used to prevent magnetohydrodynamic pressure drop and corrosion. A significant technical gap between ITER TBM and DEMO is recognized, and the world fusion community is working on ITER TBM and DEMO blanket development in parallel.

External heating and current drive source requirements towards steady-state operation in ITER

NASA Astrophysics Data System (ADS)

Poli, F. M.; Kessel, C. E.; Bonoli, P. T.; Batchelor, D. B.; Harvey, R. W.; Snyder, P. B.

2014-07-01

Steady state scenarios envisaged for ITER aim at optimizing the bootstrap current, while maintaining sufficient confinement and stability to provide the necessary fusion yield. Non-inductive scenarios will need to operate with internal transport barriers (ITBs) in order to reach adequate fusion gain at typical currents of 9 MA. However, the large pressure gradients associated with ITBs in regions of weak or negative magnetic shear can be conducive to ideal MHD instabilities, reducing the no-wall limit. The E × B flow shear from toroidal plasma rotation is expected to be low in ITER, with a major role in the ITB dynamics being played by magnetic geometry. Combinations of heating and current drive (H/CD) sources that sustain reversed magnetic shear profiles throughout the discharge are the focus of this work. Time-dependent transport simulations indicate that a combination of electron cyclotron (EC) and lower hybrid (LH) waves is a promising route towards steady state operation in ITER. The LH forms and sustains expanded barriers and the EC deposition at mid-radius freezes the bootstrap current profile stabilizing the barrier and leading to confinement levels 50% higher than typical H-mode energy confinement times. Using LH spectra with spectrum centred on parallel refractive index of 1.75-1.85, the performance of these plasma scenarios is close to the ITER target of 9 MA non-inductive current, global confinement gain H98 = 1.6 and fusion gain Q = 5.

Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

NASA Astrophysics Data System (ADS)

Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

2017-10-01

This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

Optimized iterative decoding method for TPC coded CPM

NASA Astrophysics Data System (ADS)

Ma, Yanmin; Lai, Penghui; Wang, Shilian; Xie, Shunqin; Zhang, Wei

2018-05-01

Turbo Product Code (TPC) coded Continuous Phase Modulation (CPM) system (TPC-CPM) has been widely used in aeronautical telemetry and satellite communication. This paper mainly investigates the improvement and optimization on the TPC-CPM system. We first add the interleaver and deinterleaver to the TPC-CPM system, and then establish an iterative system to iteratively decode. However, the improved system has a poor convergence ability. To overcome this issue, we use the Extrinsic Information Transfer (EXIT) analysis to find the optimal factors for the system. The experiments show our method is efficient to improve the convergence performance.

Optimization under uncertainty of parallel nonlinear energy sinks

NASA Astrophysics Data System (ADS)

Boroson, Ethan; Missoum, Samy; Mattei, Pierre-Olivier; Vergez, Christophe

2017-04-01

Nonlinear Energy Sinks (NESs) are a promising technique for passively reducing the amplitude of vibrations. Through nonlinear stiffness properties, a NES is able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NESs do not require a specific tuning and absorb energy over a wider range of frequencies. Nevertheless, they are still only efficient over a limited range of excitations. In order to mitigate this limitation and maximize the efficiency range, this work investigates the optimization of multiple NESs configured in parallel. It is well known that the efficiency of a NES is extremely sensitive to small perturbations in loading conditions or design parameters. In fact, the efficiency of a NES has been shown to be nearly discontinuous in the neighborhood of its activation threshold. For this reason, uncertainties must be taken into account in the design optimization of NESs. In addition, the discontinuities require a specific treatment during the optimization process. In this work, the objective of the optimization is to maximize the expected value of the efficiency of NESs in parallel. The optimization algorithm is able to tackle design variables with uncertainty (e.g., nonlinear stiffness coefficients) as well as aleatory variables such as the initial velocity of the main system. The optimal design of several parallel NES configurations for maximum mean efficiency is investigated. Specifically, NES nonlinear stiffness properties, considered random design variables, are optimized for cases with 1, 2, 3, 4, 5, and 10 NESs in parallel. The distributions of efficiency for the optimal parallel configurations are compared to distributions of efficiencies of non-optimized NESs. It is observed that the optimization enables a sharp increase in the mean value of efficiency while reducing the corresponding variance, thus leading to more robust NES designs.

The source of dual-task limitations: Serial or parallel processing of multiple response selections?

PubMed Central

Marois, René

2014-01-01

Although it is generally recognized that the concurrent performance of two tasks incurs costs, the sources of these dual-task costs remain controversial. The serial bottleneck model suggests that serial postponement of task performance in dual-task conditions results from a central stage of response selection that can only process one task at a time. Cognitive-control models, by contrast, propose that multiple response selections can proceed in parallel, but that serial processing of task performance is predominantly adopted because its processing efficiency is higher than that of parallel processing. In the present study, we empirically tested this proposition by examining whether parallel processing would occur when it was more efficient and financially rewarded. The results indicated that even when parallel processing was more efficient and was incentivized by financial reward, participants still failed to process tasks in parallel. We conclude that central information processing is limited by a serial bottleneck. PMID:23864266

Basic features of boron isotope separation by SILARC method in the two-step iterative static model

NASA Astrophysics Data System (ADS)

Lyakhov, K. A.; Lee, H. J.

2013-05-01

In this paper we develop a new static model for boron isotope separation by the laser assisted retardation of condensation method (SILARC) on the basis of model proposed by Jeff Eerkens. Our model is thought to be adequate to so-called two-step iterative scheme for isotope separation. This rather simple model helps to understand combined action on boron separation by SILARC method of all important parameters and relations between them. These parameters include carrier gas, molar fraction of BCl3 molecules in carrier gas, laser pulse intensity, gas pulse duration, gas pressure and temperature in reservoir and irradiation cells, optimal irradiation cell and skimmer chamber volumes, and optimal nozzle throughput. A method for finding optimal values of these parameters based on some objective function global minimum search was suggested. It turns out that minimum of this objective function is directly related to the minimum of total energy consumed, and total setup volume. Relations between nozzle throat area, IC volume, laser intensity, number of nozzles, number of vacuum pumps, and required isotope production rate were derived. Two types of industrial scale irradiation cells are compared. The first one has one large throughput slit nozzle, while the second one has numerous small nozzles arranged in parallel arrays for better overlap with laser beam. It is shown that the last one outperforms the former one significantly. It is argued that NO2 is the best carrier gas for boron isotope separation from the point of view of energy efficiency and Ar from the point of view of setup compactness.

Sequential and parallel image restoration: neural network implementations.

PubMed

Figueiredo, M T; Leitao, J N

1994-01-01

Sequential and parallel image restoration algorithms and their implementations on neural networks are proposed. For images degraded by linear blur and contaminated by additive white Gaussian noise, maximum a posteriori (MAP) estimation and regularization theory lead to the same high dimension convex optimization problem. The commonly adopted strategy (in using neural networks for image restoration) is to map the objective function of the optimization problem into the energy of a predefined network, taking advantage of its energy minimization properties. Departing from this approach, we propose neural implementations of iterative minimization algorithms which are first proved to converge. The developed schemes are based on modified Hopfield (1985) networks of graded elements, with both sequential and parallel updating schedules. An algorithm supported on a fully standard Hopfield network (binary elements and zero autoconnections) is also considered. Robustness with respect to finite numerical precision is studied, and examples with real images are presented.

Reducing neural network training time with parallel processing

NASA Technical Reports Server (NTRS)

Rogers, James L., Jr.; Lamarsh, William J., II

1995-01-01

Obtaining optimal solutions for engineering design problems is often expensive because the process typically requires numerous iterations involving analysis and optimization programs. Previous research has shown that a near optimum solution can be obtained in less time by simulating a slow, expensive analysis with a fast, inexpensive neural network. A new approach has been developed to further reduce this time. This approach decomposes a large neural network into many smaller neural networks that can be trained in parallel. Guidelines are developed to avoid some of the pitfalls when training smaller neural networks in parallel. These guidelines allow the engineer: to determine the number of nodes on the hidden layer of the smaller neural networks; to choose the initial training weights; and to select a network configuration that will capture the interactions among the smaller neural networks. This paper presents results describing how these guidelines are developed.

An efficient numerical algorithm for transverse impact problems

NASA Technical Reports Server (NTRS)

Sankar, B. V.; Sun, C. T.

1985-01-01

Transverse impact problems in which the elastic and plastic indentation effects are considered, involve a nonlinear integral equation for the contact force, which, in practice, is usually solved by an iterative scheme with small increments in time. In this paper, a numerical method is proposed wherein the iterations of the nonlinear problem are separated from the structural response computations. This makes the numerical procedures much simpler and also efficient. The proposed method is applied to some impact problems for which solutions are available, and they are found to be in good agreement. The effect of the magnitude of time increment on the results is also discussed.

Energy-Efficient Cognitive Radio Sensor Networks: Parametric and Convex Transformations

PubMed Central

Naeem, Muhammad; Illanko, Kandasamy; Karmokar, Ashok; Anpalagan, Alagan; Jaseemuddin, Muhammad

2013-01-01

Designing energy-efficient cognitive radio sensor networks is important to intelligently use battery energy and to maximize the sensor network life. In this paper, the problem of determining the power allocation that maximizes the energy-efficiency of cognitive radio-based wireless sensor networks is formed as a constrained optimization problem, where the objective function is the ratio of network throughput and the network power. The proposed constrained optimization problem belongs to a class of nonlinear fractional programming problems. Charnes-Cooper Transformation is used to transform the nonlinear fractional problem into an equivalent concave optimization problem. The structure of the power allocation policy for the transformed concave problem is found to be of a water-filling type. The problem is also transformed into a parametric form for which a ε-optimal iterative solution exists. The convergence of the iterative algorithms is proven, and numerical solutions are presented. The iterative solutions are compared with the optimal solution obtained from the transformed concave problem, and the effects of different system parameters (interference threshold level, the number of primary users and secondary sensor nodes) on the performance of the proposed algorithms are investigated. PMID:23966194

Physics and technology in the ion-cyclotron range of frequency on Tore Supra and TITAN test facility: implication for ITER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Litaudon, X; Bernard, J. M.; Colas, L.

2013-01-01

To support the design of an ITER ion-cyclotron range of frequency heating (ICRH) system and to mitigate risks of operation in ITER, CEA has initiated an ambitious Research & Development program accompanied by experiments on Tore Supra or test-bed facility together with a significant modelling effort. The paper summarizes the recent results in the following areas: Comprehensive characterization (experiments and modelling) of a new Faraday screen concept tested on the Tore Supra antenna. A new model is developed for calculating the ICRH sheath rectification at the antenna vicinity. The model is applied to calculate the local heat flux on Toremore » Supra and ITER ICRH antennas. Full-wave modelling of ITER ICRH heating and current drive scenarios with the EVE code. With 20 MW of power, a current of 400 kA could be driven on axis in the DT scenario. Comparison between DT and DT(3He) scenario is given for heating and current drive efficiencies. First operation of CW test-bed facility, TITAN, designed for ITER ICRH components testing and could host up to a quarter of an ITER antenna. R&D of high permittivity materials to improve load of test facilities to better simulate ITER plasma antenna loading conditions.« less

String-averaging incremental subgradients for constrained convex optimization with applications to reconstruction of tomographic images

NASA Astrophysics Data System (ADS)

Massambone de Oliveira, Rafael; Salomão Helou, Elias; Fontoura Costa, Eduardo

2016-11-01

We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed independently along each string, possibly in parallel, by an incremental subgradient method (ISM). The end-points of all strings are averaged to form the next iterate. The method is useful to solve sparse and large-scale non-smooth convex optimization problems, such as those arising in tomographic imaging. A convergence analysis is provided under realistic, standard conditions. Numerical tests are performed in a tomographic image reconstruction application, showing good performance for the convergence speed when measured as the decrease ratio of the objective function, in comparison to classical ISM.

3D unstructured-mesh radiation transport codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morel, J.

1997-12-31

Three unstructured-mesh radiation transport codes are currently being developed at Los Alamos National Laboratory. The first code is ATTILA, which uses an unstructured tetrahedral mesh in conjunction with standard Sn (discrete-ordinates) angular discretization, standard multigroup energy discretization, and linear-discontinuous spatial differencing. ATTILA solves the standard first-order form of the transport equation using source iteration in conjunction with diffusion-synthetic acceleration of the within-group source iterations. DANTE is designed to run primarily on workstations. The second code is DANTE, which uses a hybrid finite-element mesh consisting of arbitrary combinations of hexahedra, wedges, pyramids, and tetrahedra. DANTE solves several second-order self-adjoint forms of the transport equation including the even-parity equation, the odd-parity equation, and a new equation called the self-adjoint angular flux equation. DANTE also offers three angular discretization options:more » $$S{_}n$$ (discrete-ordinates), $$P{_}n$$ (spherical harmonics), and $$SP{_}n$$ (simplified spherical harmonics). DANTE is designed to run primarily on massively parallel message-passing machines, such as the ASCI-Blue machines at LANL and LLNL. The third code is PERICLES, which uses the same hybrid finite-element mesh as DANTE, but solves the standard first-order form of the transport equation rather than a second-order self-adjoint form. DANTE uses a standard $$S{_}n$$ discretization in angle in conjunction with trilinear-discontinuous spatial differencing, and diffusion-synthetic acceleration of the within-group source iterations. PERICLES was initially designed to run on workstations, but a version for massively parallel message-passing machines will be built. The three codes will be described in detail and computational results will be presented.« less

A fresh look at electron cyclotron current drive power requirements for stabilization of tearing modes in ITER

DOE Office of Scientific and Technical Information (OSTI.GOV)

La Haye, R. J., E-mail: lahaye@fusion.gat.com

2015-12-10

ITER is an international project to design and build an experimental fusion reactor based on the “tokamak” concept. ITER relies upon localized electron cyclotron current drive (ECCD) at the rational safety factor q=2 to suppress or stabilize the expected poloidal mode m=2, toroidal mode n=1 neoclassical tearing mode (NTM) islands. Such islands if unmitigated degrade energy confinement, lock to the resistive wall (stop rotating), cause loss of “H-mode” and induce disruption. The International Tokamak Physics Activity (ITPA) on MHD, Disruptions and Magnetic Control joint experiment group MDC-8 on Current Drive Prevention/Stabilization of Neoclassical Tearing Modes started in 2005, after whichmore » assessments were made for the requirements for ECCD needed in ITER, particularly that of rf power and alignment on q=2 [1]. Narrow well-aligned rf current parallel to and of order of one percent of the total plasma current is needed to replace the “missing” current in the island O-points and heal or preempt (avoid destabilization by applying ECCD on q=2 in absence of the mode) the island [2-4]. This paper updates the advances in ECCD stabilization on NTMs learned in DIII-D experiments and modeling during the last 5 to 10 years as applies to stabilization by localized ECCD of tearing modes in ITER. This includes the ECCD (inside the q=1 radius) stabilization of the NTM “seeding” instability known as sawteeth (m/n=1/1) [5]. Recent measurements in DIII-D show that the ITER-similar current profile is classically unstable, curvature stabilization must not be neglected, and the small island width stabilization effect from helical ion polarization currents is stronger than was previously thought [6]. The consequences of updated assumptions in ITER modeling of the minimum well-aligned ECCD power needed are all-in-all favorable (and well-within the ITER 24 gyrotron capability) when all effects are included. However, a “wild card” may be broadening of the localized ECCD by the presence of the island; various theories predict broadening could occur and there is experimental evidence for broadening in DIII-D. Wider than now expected ECCD in ITER would make alignment easier to do but weaken the stabilization and thus require more rf power. In addition to updated modeling for ITER, advances in the ITER-relevant DIII-D ECCD gyrotron launch mirror control system hardware and real-time plasma control system have been made [7] and there are plans for application in DIII-D ITER demonstration discharges.« less

A fresh look at electron cyclotron current drive power requirements for stabilization of tearing modes in ITER

NASA Astrophysics Data System (ADS)

La Haye, R. J.

2015-12-01

ITER is an international project to design and build an experimental fusion reactor based on the "tokamak" concept. ITER relies upon localized electron cyclotron current drive (ECCD) at the rational safety factor q=2 to suppress or stabilize the expected poloidal mode m=2, toroidal mode n=1 neoclassical tearing mode (NTM) islands. Such islands if unmitigated degrade energy confinement, lock to the resistive wall (stop rotating), cause loss of "H-mode" and induce disruption. The International Tokamak Physics Activity (ITPA) on MHD, Disruptions and Magnetic Control joint experiment group MDC-8 on Current Drive Prevention/Stabilization of Neoclassical Tearing Modes started in 2005, after which assessments were made for the requirements for ECCD needed in ITER, particularly that of rf power and alignment on q=2 [1]. Narrow well-aligned rf current parallel to and of order of one percent of the total plasma current is needed to replace the "missing" current in the island O-points and heal or preempt (avoid destabilization by applying ECCD on q=2 in absence of the mode) the island [2-4]. This paper updates the advances in ECCD stabilization on NTMs learned in DIII-D experiments and modeling during the last 5 to 10 years as applies to stabilization by localized ECCD of tearing modes in ITER. This includes the ECCD (inside the q=1 radius) stabilization of the NTM "seeding" instability known as sawteeth (m/n=1/1) [5]. Recent measurements in DIII-D show that the ITER-similar current profile is classically unstable, curvature stabilization must not be neglected, and the small island width stabilization effect from helical ion polarization currents is stronger than was previously thought [6]. The consequences of updated assumptions in ITER modeling of the minimum well-aligned ECCD power needed are all-in-all favorable (and well-within the ITER 24 gyrotron capability) when all effects are included. However, a "wild card" may be broadening of the localized ECCD by the presence of the island; various theories predict broadening could occur and there is experimental evidence for broadening in DIII-D. Wider than now expected ECCD in ITER would make alignment easier to do but weaken the stabilization and thus require more rf power. In addition to updated modeling for ITER, advances in the ITER-relevant DIII-D ECCD gyrotron launch mirror control system hardware and real-time plasma control system have been made [7] and there are plans for application in DIII-D ITER demonstration discharges.

Controlled iterative cross-coupling: on the way to the automation of organic synthesis.

PubMed

Wang, Congyang; Glorius, Frank

2009-01-01

Repetition does not hurt! New strategies for the modulation of the reactivity of difunctional building blocks are discussed, allowing the palladium-catalyzed controlled iterative cross-coupling and, thus, the efficient formation of complex molecules of defined size and structure (see scheme). As in peptide synthesis, this development will enable the automation of these reactions. M(PG)=protected metal, M(act)=metal.

Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes.

PubMed

Hudson, H M; Ma, J; Green, P

1994-01-01

Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

MPI_XSTAR: MPI-based Parallelization of the XSTAR Photoionization Program

NASA Astrophysics Data System (ADS)

Danehkar, Ashkbiz; Nowak, Michael A.; Lee, Julia C.; Smith, Randall K.

2018-02-01

We describe a program for the parallel implementation of multiple runs of XSTAR, a photoionization code that is used to predict the physical properties of an ionized gas from its emission and/or absorption lines. The parallelization program, called MPI_XSTAR, has been developed and implemented in the C++ language by using the Message Passing Interface (MPI) protocol, a conventional standard of parallel computing. We have benchmarked parallel multiprocessing executions of XSTAR, using MPI_XSTAR, against a serial execution of XSTAR, in terms of the parallelization speedup and the computing resource efficiency. Our experience indicates that the parallel execution runs significantly faster than the serial execution, however, the efficiency in terms of the computing resource usage decreases with increasing the number of processors used in the parallel computing.

Parallel Simulation of Subsonic Fluid Dynamics on a Cluster of Workstations.

DTIC Science & Technology

1994-11-01

inside wind musical instruments. Typical simulations achieve $80\\%$ parallel efficiency (speedup/processors) using 20 HP-Apollo workstations. Detailed...TERMS AI, MIT, Artificial Intelligence, Distributed Computing, Workstation Cluster, Network, Fluid Dynamics, Musical Instruments 17. SECURITY...for example, the flow of air inside wind musical instruments. Typical simulations achieve 80% parallel efficiency (speedup/processors) using 20 HP

A fast method to emulate an iterative POCS image reconstruction algorithm.

PubMed

Zeng, Gengsheng L

2017-10-01

Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection. This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge-preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. A windowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge-enhancement denoising. Each segment performs nonlinear filtering. The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low-dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge-enhancing noise-smoothing filter. The patient studies results demonstrate its effectiveness in processing low-dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms. © 2017 American Association of Physicists in Medicine.

PISCES: An environment for parallel scientific computation

NASA Technical Reports Server (NTRS)

Pratt, T. W.

1985-01-01

The parallel implementation of scientific computing environment (PISCES) is a project to provide high-level programming environments for parallel MIMD computers. Pisces 1, the first of these environments, is a FORTRAN 77 based environment which runs under the UNIX operating system. The Pisces 1 user programs in Pisces FORTRAN, an extension of FORTRAN 77 for parallel processing. The major emphasis in the Pisces 1 design is in providing a carefully specified virtual machine that defines the run-time environment within which Pisces FORTRAN programs are executed. Each implementation then provides the same virtual machine, regardless of differences in the underlying architecture. The design is intended to be portable to a variety of architectures. Currently Pisces 1 is implemented on a network of Apollo workstations and on a DEC VAX uniprocessor via simulation of the task level parallelism. An implementation for the Flexible Computing Corp. FLEX/32 is under construction. An introduction to the Pisces 1 virtual computer and the FORTRAN 77 extensions is presented. An example of an algorithm for the iterative solution of a system of equations is given. The most notable features of the design are the provision for several granularities of parallelism in programs and the provision of a window mechanism for distributed access to large arrays of data.

Symmetry Breaking by Parallel Flow Shear

NASA Astrophysics Data System (ADS)

Li, Jiacong; Diamond, Patrick

2015-11-01

Plasma rotation is important in reducing turbulent transport, suppressing MHD instabilities, and is beneficial to confinement. Intrinsic rotation without an external momentum input is of interest for its plausible application on ITER. k∥ spectrum asymmetry is required for residual Reynolds stress that drives the intrinsic rotation. Parallel flows are reported in linear devices without magnetic shear. In CSDX, parallel flows are mostly peaked in the core [Thakur et al., 2014]; more robust flows and reversed profiles are seen in PANTA [Oldenburger, et al. 2012]. A novel mechanism for symmetry breaking in momentum transport is proposed. Magnetic shear or mean flow profile are not required. A seed parallel flow shear (PFS) sets the sign of residual stress by selecting certain modes to grow faster. The resulted spectrum imbalance leads to a nonzero residual stress, which further drives a parallel flow with ∇n as the free energy source, adding to the shear until saturated by diffusion. Balanced flow gradient is set by Π∥Res /χϕ . Residual stress is calculated for ITG turbulence and collisional drift wave turbulence where electron-ion and electron-neutral collisions are discussed and compared. Numerical simulation is proposed for testing the effect of PFS.

Plasma cleaning of ITER edge Thomson scattering mock-up mirror in the EAST tokamak

NASA Astrophysics Data System (ADS)

Yan, Rong; Moser, Lucas; Wang, Baoguo; Peng, Jiao; Vorpahl, Christian; Leipold, Frank; Reichle, Roger; Ding, Rui; Chen, Junling; Mu, Lei; Steiner, Roland; Meyer, Ernst; Zhao, Mingzhong; Wu, Jinhua; Marot, Laurent

2018-02-01

First mirrors are the key element of all optical and laser diagnostics in ITER. Facing the plasma directly, the surface of the first mirrors could be sputtered by energetic particles or deposited with contaminants eroded from the first wall (tungsten and beryllium), which would result in the degradation of the reflectivity. The impurity deposits emphasize the necessity of the first mirror in situ cleaning for ITER. The mock-up first mirror system for ITER edge Thomson scattering diagnostics has been cleaned in EAST for the first time in a tokamak using radio frequency capacitively coupled plasma. The cleaning properties, namely the removal of contaminants and homogeneity of cleaning were investigated with molybdenum mirror insets (25 mm diameter) located at five positions over the mock-up plate (center to edge) on which 10 nm of aluminum oxide, used as beryllium proxy, were deposited. The cleaning efficiency was evaluated using energy dispersive x-ray spectroscopy, reflectivity measurements and x-ray photoelectron spectroscopy. Using argon or neon plasma without magnetic field in the laboratory and with a 1.7 T magnetic field in the EAST tokamak, the aluminum oxide films were homogeneously removed. The full recovery of the mirrors’ reflectivity was attained after cleaning in EAST with the magnetic field, and the cleaning efficiency was about 40 times higher than that without the magnetic field. All these results are promising for the plasma cleaning baseline scenario of ITER.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

A Performance Comparison of the Parallel Preconditioners for Iterative Methods for Large Sparse Linear Systems Arising from Partial Differential Equations on Structured Grids

NASA Astrophysics Data System (ADS)

Ma, Sangback

In this paper we compare various parallel preconditioners such as Point-SSOR (Symmetric Successive OverRelaxation), ILU(0) (Incomplete LU) in the Wavefront ordering, ILU(0) in the Multi-color ordering, Multi-Color Block SOR (Successive OverRelaxation), SPAI (SParse Approximate Inverse) and pARMS (Parallel Algebraic Recursive Multilevel Solver) for solving large sparse linear systems arising from two-dimensional PDE (Partial Differential Equation)s on structured grids. Point-SSOR is well-known, and ILU(0) is one of the most popular preconditioner, but it is inherently serial. ILU(0) in the Wavefront ordering maximizes the parallelism in the natural order, but the lengths of the wave-fronts are often nonuniform. ILU(0) in the Multi-color ordering is a simple way of achieving a parallelism of the order N, where N is the order of the matrix, but its convergence rate often deteriorates as compared to that of natural ordering. We have chosen the Multi-Color Block SOR preconditioner combined with direct sparse matrix solver, since for the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with the Multi-Color ordering. By using block version we expect to minimize the interprocessor communications. SPAI computes the sparse approximate inverse directly by least squares method. Finally, ARMS is a preconditioner recursively exploiting the concept of independent sets and pARMS is the parallel version of ARMS. Experiments were conducted for the Finite Difference and Finite Element discretizations of five two-dimensional PDEs with large meshsizes up to a million on an IBM p595 machine with distributed memory. Our matrices are real positive, i. e., their real parts of the eigenvalues are positive. We have used GMRES(m) as our outer iterative method, so that the convergence of GMRES(m) for our test matrices are mathematically guaranteed. Interprocessor communications were done using MPI (Message Passing Interface) primitives. The results show that in general ILU(0) in the Multi-Color ordering ahd ILU(0) in the Wavefront ordering outperform the other methods but for symmetric and nearly symmetric 5-point matrices Multi-Color Block SOR gives the best performance, except for a few cases with a small number of processors.

Conceptual design of the DEMO neutral beam injectors: main developments and R&D achievements

NASA Astrophysics Data System (ADS)

Sonato, P.; Agostinetti, P.; Bolzonella, T.; Cismondi, F.; Fantz, U.; Fassina, A.; Franke, T.; Furno, I.; Hopf, C.; Jenkins, I.; Sartori, E.; Tran, M. Q.; Varje, J.; Vincenzi, P.; Zanotto, L.

2017-05-01

The objectives of the nuclear fusion power plant DEMO, to be built after the ITER experimental reactor, are usually understood to lie somewhere between those of ITER and a ‘first of a kind’ commercial plant. Hence, in DEMO the issues related to efficiency and RAMI (reliability, availability, maintainability and inspectability) are among the most important drivers for the design, as the cost of the electricity produced by this power plant will strongly depend on these aspects. In the framework of the EUROfusion Work Package Heating and Current Drive within the Power Plant Physics and Development activities, a conceptual design of the neutral beam injector (NBI) for the DEMO fusion reactor has been developed by Consorzio RFX in collaboration with other European research institutes. In order to improve efficiency and RAMI aspects, several innovative solutions have been introduced in comparison to the ITER NBI, mainly regarding the beam source, neutralizer and vacuum pumping systems.