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.

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.

Domain decomposition in time for PDE-constrained optimization

DOE PAGES

Barker, Andrew T.; Stoll, Martin

2015-08-28

Here, PDE-constrained optimization problems have a wide range of applications, but they lead to very large and ill-conditioned linear systems, especially if the problems are time dependent. In this paper we outline an approach for dealing with such problems by decomposing them in time and applying an additive Schwarz preconditioner in time, so that we can take advantage of parallel computers to deal with the very large linear systems. We then illustrate the performance of our method on a variety of problems.

On optimal improvements of classical iterative schemes for Z-matrices

NASA Astrophysics Data System (ADS)

Noutsos, D.; Tzoumas, M.

2006-04-01

Many researchers have considered preconditioners, applied to linear systems, whose matrix coefficient is a Z- or an M-matrix, that make the associated Jacobi and Gauss-Seidel methods converge asymptotically faster than the unpreconditioned ones. Such preconditioners are chosen so that they eliminate the off-diagonal elements of the same column or the elements of the first upper diagonal [Milaszewicz, LAA 93 (1987) 161-170], Gunawardena et al. [LAA 154-156 (1991) 123-143]. In this work we generalize the previous preconditioners to obtain optimal methods. "Good" Jacobi and Gauss-Seidel algorithms are given and preconditioners, that eliminate more than one entry per row, are also proposed and analyzed. Moreover, the behavior of the above preconditioners to the Krylov subspace methods is studied.

A note on the preconditioner Pm=(I+Sm)

NASA Astrophysics Data System (ADS)

Kohno, Toshiyuki; Niki, Hiroshi

2009-03-01

Kotakemori et al. [H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner (I+Smax), Journal of Computational and Applied Mathematics 145 (2002) 373-378] have reported that the convergence rate of the iterative method with a preconditioner Pm=(I+Sm) was superior to one of the modified Gauss-Seidel method under the condition. These authors derived a theorem comparing the Gauss-Seidel method with the proposed method. However, through application of a counter example, Wen Li [Wen Li, A note on the preconditioned GaussSeidel (GS) method for linear systems, Journal of Computational and Applied Mathematics 182 (2005) 81-91] pointed out that there exists a special matrix that does not satisfy this comparison theorem. In this note, we analyze the reason why such a to counter example may be produced, and propose a preconditioner to overcome this problem.

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.

Final Report, DE-FG01-06ER25718 Domain Decomposition and Parallel Computing

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

Widlund, Olof B.

2015-06-09

The goal of this project is to develop and improve domain decomposition algorithms for a variety of partial differential equations such as those of linear elasticity and electro-magnetics.These iterative methods are designed for massively parallel computing systems and allow the fast solution of the very large systems of algebraic equations that arise in large scale and complicated simulations. A special emphasis is placed on problems arising from Maxwell's equation. The approximate solvers, the preconditioners, are combined with the conjugate gradient method and must always include a solver of a coarse model in order to have a performance which is independentmore » of the number of processors used in the computer simulation. A recent development allows for an adaptive construction of this coarse component of the preconditioner.« less

Scalable parallel elastic-plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner

NASA Astrophysics Data System (ADS)

Yusa, Yasunori; Okada, Hiroshi; Yamada, Tomonori; Yoshimura, Shinobu

2018-04-01

A domain decomposition method for large-scale elastic-plastic problems is proposed. The proposed method is based on a quasi-Newton method in conjunction with a balancing domain decomposition preconditioner. The use of a quasi-Newton method overcomes two problems associated with the conventional domain decomposition method based on the Newton-Raphson method: (1) avoidance of a double-loop iteration algorithm, which generally has large computational complexity, and (2) consideration of the local concentration of nonlinear deformation, which is observed in elastic-plastic problems with stress concentration. Moreover, the application of a balancing domain decomposition preconditioner ensures scalability. Using the conventional and proposed domain decomposition methods, several numerical tests, including weak scaling tests, were performed. The convergence performance of the proposed method is comparable to that of the conventional method. In particular, in elastic-plastic analysis, the proposed method exhibits better convergence performance than the conventional method.

Newton-Krylov-Schwarz: An implicit solver for CFD

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Keyes, David E.; Venkatakrishnan, V.

1995-01-01

Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.

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.

Scalable Preconditioners for Structure Preserving Discretizations of Maxwell Equations in First Order Form

DOE PAGES

Phillips, Edward Geoffrey; Shadid, John N.; Cyr, Eric C.

2018-05-01

Here, we report multiple physical time-scales can arise in electromagnetic simulations when dissipative effects are introduced through boundary conditions, when currents follow external time-scales, and when material parameters vary spatially. In such scenarios, the time-scales of interest may be much slower than the fastest time-scales supported by the Maxwell equations, therefore making implicit time integration an efficient approach. The use of implicit temporal discretizations results in linear systems in which fast time-scales, which severely constrain the stability of an explicit method, can manifest as so-called stiff modes. This study proposes a new block preconditioner for structure preserving (also termed physicsmore » compatible) discretizations of the Maxwell equations in first order form. The intent of the preconditioner is to enable the efficient solution of multiple-time-scale Maxwell type systems. An additional benefit of the developed preconditioner is that it requires only a traditional multigrid method for its subsolves and compares well against alternative approaches that rely on specialized edge-based multigrid routines that may not be readily available. Lastly, results demonstrate parallel scalability at large electromagnetic wave CFL numbers on a variety of test problems.« less

Scalable Preconditioners for Structure Preserving Discretizations of Maxwell Equations in First Order Form

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

Phillips, Edward Geoffrey; Shadid, John N.; Cyr, Eric C.

Here, we report multiple physical time-scales can arise in electromagnetic simulations when dissipative effects are introduced through boundary conditions, when currents follow external time-scales, and when material parameters vary spatially. In such scenarios, the time-scales of interest may be much slower than the fastest time-scales supported by the Maxwell equations, therefore making implicit time integration an efficient approach. The use of implicit temporal discretizations results in linear systems in which fast time-scales, which severely constrain the stability of an explicit method, can manifest as so-called stiff modes. This study proposes a new block preconditioner for structure preserving (also termed physicsmore » compatible) discretizations of the Maxwell equations in first order form. The intent of the preconditioner is to enable the efficient solution of multiple-time-scale Maxwell type systems. An additional benefit of the developed preconditioner is that it requires only a traditional multigrid method for its subsolves and compares well against alternative approaches that rely on specialized edge-based multigrid routines that may not be readily available. Lastly, results demonstrate parallel scalability at large electromagnetic wave CFL numbers on a variety of test problems.« less

Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem

NASA Astrophysics Data System (ADS)

Badia, Santiago; Martín, Alberto F.; Planas, Ramon

2014-10-01

The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 × 2 block matrix, and consider an LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknowns, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.

Extending molecular simulation time scales: Parallel in time integrations for high-level quantum chemistry and complex force representations

NASA Astrophysics Data System (ADS)

Bylaska, Eric J.; Weare, Jonathan Q.; Weare, John H.

2013-08-01

Parallel in time simulation algorithms are presented and applied to conventional molecular dynamics (MD) and ab initio molecular dynamics (AIMD) models of realistic complexity. Assuming that a forward time integrator, f (e.g., Verlet algorithm), is available to propagate the system from time ti (trajectory positions and velocities xi = (ri, vi)) to time ti + 1 (xi + 1) by xi + 1 = fi(xi), the dynamics problem spanning an interval from t0…tM can be transformed into a root finding problem, F(X) = [xi - f(x(i - 1)]i = 1, M = 0, for the trajectory variables. The root finding problem is solved using a variety of root finding techniques, including quasi-Newton and preconditioned quasi-Newton schemes that are all unconditionally convergent. The algorithms are parallelized by assigning a processor to each time-step entry in the columns of F(X). The relation of this approach to other recently proposed parallel in time methods is discussed, and the effectiveness of various approaches to solving the root finding problem is tested. We demonstrate that more efficient dynamical models based on simplified interactions or coarsening time-steps provide preconditioners for the root finding problem. However, for MD and AIMD simulations, such preconditioners are not required to obtain reasonable convergence and their cost must be considered in the performance of the algorithm. The parallel in time algorithms developed are tested by applying them to MD and AIMD simulations of size and complexity similar to those encountered in present day applications. These include a 1000 Si atom MD simulation using Stillinger-Weber potentials, and a HCl + 4H2O AIMD simulation at the MP2 level. The maximum speedup (serial execution time/parallel execution time) obtained by parallelizing the Stillinger-Weber MD simulation was nearly 3.0. For the AIMD MP2 simulations, the algorithms achieved speedups of up to 14.3. The parallel in time algorithms can be implemented in a distributed computing environment using very slow transmission control protocol/Internet protocol networks. Scripts written in Python that make calls to a precompiled quantum chemistry package (NWChem) are demonstrated to provide an actual speedup of 8.2 for a 2.5 ps AIMD simulation of HCl + 4H2O at the MP2/6-31G* level. Implemented in this way these algorithms can be used for long time high-level AIMD simulations at a modest cost using machines connected by very slow networks such as WiFi, or in different time zones connected by the Internet. The algorithms can also be used with programs that are already parallel. Using these algorithms, we are able to reduce the cost of a MP2/6-311++G(2d,2p) simulation that had reached its maximum possible speedup in the parallelization of the electronic structure calculation from 32 s/time step to 6.9 s/time step.

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.

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.

3-D modeling of ductile tearing using finite elements: Computational aspects and techniques

NASA Astrophysics Data System (ADS)

Gullerud, Arne Stewart

This research focuses on the development and application of computational tools to perform large-scale, 3-D modeling of ductile tearing in engineering components under quasi-static to mild loading rates. Two standard models for ductile tearing---the computational cell methodology and crack growth controlled by the crack tip opening angle (CTOA)---are described and their 3-D implementations are explored. For the computational cell methodology, quantification of the effects of several numerical issues---computational load step size, procedures for force release after cell deletion, and the porosity for cell deletion---enables construction of computational algorithms to remove the dependence of predicted crack growth on these issues. This work also describes two extensions of the CTOA approach into 3-D: a general 3-D method and a constant front technique. Analyses compare the characteristics of the extensions, and a validation study explores the ability of the constant front extension to predict crack growth in thin aluminum test specimens over a range of specimen geometries, absolutes sizes, and levels of out-of-plane constraint. To provide a computational framework suitable for the solution of these problems, this work also describes the parallel implementation of a nonlinear, implicit finite element code. The implementation employs an explicit message-passing approach using the MPI standard to maintain portability, a domain decomposition of element data to provide parallel execution, and a master-worker organization of the computational processes to enhance future extensibility. A linear preconditioned conjugate gradient (LPCG) solver serves as the core of the solution process. The parallel LPCG solver utilizes an element-by-element (EBE) structure of the computations to permit a dual-level decomposition of the element data: domain decomposition of the mesh provides efficient coarse-grain parallel execution, while decomposition of the domains into blocks of similar elements (same type, constitutive model, etc.) provides fine-grain parallel computation on each processor. A major focus of the LPCG solver is a new implementation of the Hughes-Winget element-by-element (HW) preconditioner. The implementation employs a weighted dependency graph combined with a new coloring algorithm to provide load-balanced scheduling for the preconditioner and overlapped communication/computation. This approach enables efficient parallel application of the HW preconditioner for arbitrary unstructured meshes.

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.

Extending molecular simulation time scales: Parallel in time integrations for high-level quantum chemistry and complex force representations

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

Bylaska, Eric J.; Weare, Jonathan Q.; Weare, John H.

2013-08-21

Parallel in time simulation algorithms are presented and applied to conventional molecular dynamics (MD) and ab initio molecular dynamics (AIMD) models of realistic complexity. Assuming that a forward time integrator, f , (e.g. Verlet algorithm) is available to propagate the system from time ti (trajectory positions and velocities xi = (ri; vi)) to time ti+1 (xi+1) by xi+1 = fi(xi), the dynamics problem spanning an interval from t0 : : : tM can be transformed into a root finding problem, F(X) = [xi - f (x(i-1)]i=1;M = 0, for the trajectory variables. The root finding problem is solved using amore » variety of optimization techniques, including quasi-Newton and preconditioned quasi-Newton optimization schemes that are all unconditionally convergent. The algorithms are parallelized by assigning a processor to each time-step entry in the columns of F(X). The relation of this approach to other recently proposed parallel in time methods is discussed and the effectiveness of various approaches to solving the root finding problem are tested. We demonstrate that more efficient dynamical models based on simplified interactions or coarsening time-steps provide preconditioners for the root finding problem. However, for MD and AIMD simulations such preconditioners are not required to obtain reasonable convergence and their cost must be considered in the performance of the algorithm. The parallel in time algorithms developed are tested by applying them to MD and AIMD simulations of size and complexity similar to those encountered in present day applications. These include a 1000 Si atom MD simulation using Stillinger-Weber potentials, and a HCl+4H2O AIMD simulation at the MP2 level. The maximum speedup obtained by parallelizing the Stillinger-Weber MD simulation was nearly 3.0. For the AIMD MP2 simulations the algorithms achieved speedups of up to 14.3. The parallel in time algorithms can be implemented in a distributed computing environment using very slow TCP/IP networks. Scripts written in Python that make calls to a precompiled quantum chemistry package (NWChem) are demonstrated to provide an actual speedup of 8.2 for a 2.5 ps AIMD simulation of HCl+4H2O at the MP2/6-31G* level. Implemented in this way these algorithms can be used for long time high-level AIMD simulations at a modest cost using machines connected by very slow networks such as WiFi, or in different time zones connected by the Internet. The algorithms can also be used with programs that are already parallel. By using these algorithms we are able to reduce the cost of a MP2/6-311++G(2d,2p) simulation that had reached its maximum possible speedup in the parallelization of the electronic structure calculation from 32 seconds per time step to 6.9 seconds per time step.« less

Extending molecular simulation time scales: Parallel in time integrations for high-level quantum chemistry and complex force representations.

PubMed

Bylaska, Eric J; Weare, Jonathan Q; Weare, John H

2013-08-21

Parallel in time simulation algorithms are presented and applied to conventional molecular dynamics (MD) and ab initio molecular dynamics (AIMD) models of realistic complexity. Assuming that a forward time integrator, f (e.g., Verlet algorithm), is available to propagate the system from time ti (trajectory positions and velocities xi = (ri, vi)) to time ti + 1 (xi + 1) by xi + 1 = fi(xi), the dynamics problem spanning an interval from t0[ellipsis (horizontal)]tM can be transformed into a root finding problem, F(X) = [xi - f(x(i - 1)]i = 1, M = 0, for the trajectory variables. The root finding problem is solved using a variety of root finding techniques, including quasi-Newton and preconditioned quasi-Newton schemes that are all unconditionally convergent. The algorithms are parallelized by assigning a processor to each time-step entry in the columns of F(X). The relation of this approach to other recently proposed parallel in time methods is discussed, and the effectiveness of various approaches to solving the root finding problem is tested. We demonstrate that more efficient dynamical models based on simplified interactions or coarsening time-steps provide preconditioners for the root finding problem. However, for MD and AIMD simulations, such preconditioners are not required to obtain reasonable convergence and their cost must be considered in the performance of the algorithm. The parallel in time algorithms developed are tested by applying them to MD and AIMD simulations of size and complexity similar to those encountered in present day applications. These include a 1000 Si atom MD simulation using Stillinger-Weber potentials, and a HCl + 4H2O AIMD simulation at the MP2 level. The maximum speedup (serial execution/timeparallel execution time) obtained by parallelizing the Stillinger-Weber MD simulation was nearly 3.0. For the AIMD MP2 simulations, the algorithms achieved speedups of up to 14.3. The parallel in time algorithms can be implemented in a distributed computing environment using very slow transmission control protocol/Internet protocol networks. Scripts written in Python that make calls to a precompiled quantum chemistry package (NWChem) are demonstrated to provide an actual speedup of 8.2 for a 2.5 ps AIMD simulation of HCl + 4H2O at the MP2/6-31G* level. Implemented in this way these algorithms can be used for long time high-level AIMD simulations at a modest cost using machines connected by very slow networks such as WiFi, or in different time zones connected by the Internet. The algorithms can also be used with programs that are already parallel. Using these algorithms, we are able to reduce the cost of a MP2/6-311++G(2d,2p) simulation that had reached its maximum possible speedup in the parallelization of the electronic structure calculation from 32 s/time step to 6.9 s/time 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.

A parallel multi-domain solution methodology applied to nonlinear thermal transport problems in nuclear fuel pins

DOE PAGES

Philip, Bobby; Berrill, Mark A.; Allu, Srikanth; ...

2015-01-26

We describe an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors are described. The details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstratingmore » the achieved efficiency of the algorithm are presented. Moreover, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.« less

A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures

PubMed Central

Colli Franzone, Piero; Pavarino, Luca F.; Scacchi, Simone

2018-01-01

We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks. PMID:29674971

Toward an optimal solver for time-spectral fluid-dynamic and aeroelastic solutions on unstructured meshes

NASA Astrophysics Data System (ADS)

Mundis, Nathan L.; Mavriplis, Dimitri J.

2017-09-01

The time-spectral method applied to the Euler and coupled aeroelastic equations theoretically offers significant computational savings for purely periodic problems when compared to standard time-implicit methods. However, attaining superior efficiency with time-spectral methods over traditional time-implicit methods hinges on the ability rapidly to solve the large non-linear system resulting from time-spectral discretizations which become larger and stiffer as more time instances are employed or the period of the flow becomes especially short (i.e. the maximum resolvable wave-number increases). In order to increase the efficiency of these solvers, and to improve robustness, particularly for large numbers of time instances, the Generalized Minimal Residual Method (GMRES) is used to solve the implicit linear system over all coupled time instances. The use of GMRES as the linear solver makes time-spectral methods more robust, allows them to be applied to a far greater subset of time-accurate problems, including those with a broad range of harmonic content, and vastly improves the efficiency of time-spectral methods. In previous work, a wave-number independent preconditioner that mitigates the increased stiffness of the time-spectral method when applied to problems with large resolvable wave numbers has been developed. This preconditioner, however, directly inverts a large matrix whose size increases in proportion to the number of time instances. As a result, the computational time of this method scales as the cube of the number of time instances. In the present work, this preconditioner has been reworked to take advantage of an approximate-factorization approach that effectively decouples the spatial and temporal systems. Once decoupled, the time-spectral matrix can be inverted in frequency space, where it has entries only on the main diagonal and therefore can be inverted quite efficiently. This new GMRES/preconditioner combination is shown to be over an order of magnitude more efficient than the previous wave-number independent preconditioner for problems with large numbers of time instances and/or large reduced frequencies.

Condition number estimation of preconditioned matrices.

PubMed

Kushida, Noriyuki

2015-01-01

The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.

Extending molecular simulation time scales: Parallel in time integrations for high-level quantum chemistry and complex force representations

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

Bylaska, Eric J., E-mail: Eric.Bylaska@pnnl.gov; Weare, Jonathan Q., E-mail: weare@uchicago.edu; Weare, John H., E-mail: jweare@ucsd.edu

2013-08-21

Parallel in time simulation algorithms are presented and applied to conventional molecular dynamics (MD) and ab initio molecular dynamics (AIMD) models of realistic complexity. Assuming that a forward time integrator, f (e.g., Verlet algorithm), is available to propagate the system from time t{sub i} (trajectory positions and velocities x{sub i} = (r{sub i}, v{sub i})) to time t{sub i+1} (x{sub i+1}) by x{sub i+1} = f{sub i}(x{sub i}), the dynamics problem spanning an interval from t{sub 0}…t{sub M} can be transformed into a root finding problem, F(X) = [x{sub i} − f(x{sub (i−1})]{sub i} {sub =1,M} = 0, for themore » trajectory variables. The root finding problem is solved using a variety of root finding techniques, including quasi-Newton and preconditioned quasi-Newton schemes that are all unconditionally convergent. The algorithms are parallelized by assigning a processor to each time-step entry in the columns of F(X). The relation of this approach to other recently proposed parallel in time methods is discussed, and the effectiveness of various approaches to solving the root finding problem is tested. We demonstrate that more efficient dynamical models based on simplified interactions or coarsening time-steps provide preconditioners for the root finding problem. However, for MD and AIMD simulations, such preconditioners are not required to obtain reasonable convergence and their cost must be considered in the performance of the algorithm. The parallel in time algorithms developed are tested by applying them to MD and AIMD simulations of size and complexity similar to those encountered in present day applications. These include a 1000 Si atom MD simulation using Stillinger-Weber potentials, and a HCl + 4H{sub 2}O AIMD simulation at the MP2 level. The maximum speedup ((serial execution time)/(parallel execution time) ) obtained by parallelizing the Stillinger-Weber MD simulation was nearly 3.0. For the AIMD MP2 simulations, the algorithms achieved speedups of up to 14.3. The parallel in time algorithms can be implemented in a distributed computing environment using very slow transmission control protocol/Internet protocol networks. Scripts written in Python that make calls to a precompiled quantum chemistry package (NWChem) are demonstrated to provide an actual speedup of 8.2 for a 2.5 ps AIMD simulation of HCl + 4H{sub 2}O at the MP2/6-31G* level. Implemented in this way these algorithms can be used for long time high-level AIMD simulations at a modest cost using machines connected by very slow networks such as WiFi, or in different time zones connected by the Internet. The algorithms can also be used with programs that are already parallel. Using these algorithms, we are able to reduce the cost of a MP2/6-311++G(2d,2p) simulation that had reached its maximum possible speedup in the parallelization of the electronic structure calculation from 32 s/time step to 6.9 s/time step.« less

A nonrecursive order N preconditioned conjugate gradient: Range space formulation of MDOF dynamics

NASA Technical Reports Server (NTRS)

Kurdila, Andrew J.

1990-01-01

While excellent progress has been made in deriving algorithms that are efficient for certain combinations of system topologies and concurrent multiprocessing hardware, several issues must be resolved to incorporate transient simulation in the control design process for large space structures. Specifically, strategies must be developed that are applicable to systems with numerous degrees of freedom. In addition, the algorithms must have a growth potential in that they must also be amenable to implementation on forthcoming parallel system architectures. For mechanical system simulation, this fact implies that algorithms are required that induce parallelism on a fine scale, suitable for the emerging class of highly parallel processors; and transient simulation methods must be automatically load balancing for a wider collection of system topologies and hardware configurations. These problems are addressed by employing a combination range space/preconditioned conjugate gradient formulation of multi-degree-of-freedom dynamics. The method described has several advantages. In a sequential computing environment, the method has the features that: by employing regular ordering of the system connectivity graph, an extremely efficient preconditioner can be derived from the 'range space metric', as opposed to the system coefficient matrix; because of the effectiveness of the preconditioner, preliminary studies indicate that the method can achieve performance rates that depend linearly upon the number of substructures, hence the title 'Order N'; and the method is non-assembling. Furthermore, the approach is promising as a potential parallel processing algorithm in that the method exhibits a fine parallel granularity suitable for a wide collection of combinations of physical system topologies/computer architectures; and the method is easily load balanced among processors, and does not rely upon system topology to induce parallelism.

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

Analysis of Preconditioning and Relaxation Operators for the Discontinuous Galerkin Method Applied to Diffusion

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Shu, Chi-Wang

2001-01-01

The explicit stability constraint of the discontinuous Galerkin method applied to the diffusion operator decreases dramatically as the order of the method is increased. Block Jacobi and block Gauss-Seidel preconditioner operators are examined for their effectiveness at accelerating convergence. A Fourier analysis for methods of order 2 through 6 reveals that both preconditioner operators bound the eigenvalues of the discrete spatial operator. Additionally, in one dimension, the eigenvalues are grouped into two or three regions that are invariant with order of the method. Local relaxation methods are constructed that rapidly damp high frequencies for arbitrarily large time step.

A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

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

Cortes, Adriano M.; Dalcin, Lisandro; Sarmiento, Adel F.

The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf–sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show howmore » the nesting of “black-box” solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Lastly, besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.« less

A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

DOE PAGES

Cortes, Adriano M.; Dalcin, Lisandro; Sarmiento, Adel F.; ...

2016-10-19

The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf–sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show howmore » the nesting of “black-box” solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Lastly, besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.« less

Efficient Iterative Methods Applied to the Solution of Transonic Flows

NASA Astrophysics Data System (ADS)

Wissink, Andrew M.; Lyrintzis, Anastasios S.; Chronopoulos, Anthony T.

1996-02-01

We investigate the use of an inexact Newton's method to solve the potential equations in the transonic regime. As a test case, we solve the two-dimensional steady transonic small disturbance equation. Approximate factorization/ADI techniques have traditionally been employed for implicit solutions of this nonlinear equation. Instead, we apply Newton's method using an exact analytical determination of the Jacobian with preconditioned conjugate gradient-like iterative solvers for solution of the linear systems in each Newton iteration. Two iterative solvers are tested; a block s-step version of the classical Orthomin(k) algorithm called orthogonal s-step Orthomin (OSOmin) and the well-known GMRES method. The preconditioner is a vectorizable and parallelizable version of incomplete LU (ILU) factorization. Efficiency of the Newton-Iterative method on vector and parallel computer architectures is the main issue addressed. In vectorized tests on a single processor of the Cray C-90, the performance of Newton-OSOmin is superior to Newton-GMRES and a more traditional monotone AF/ADI method (MAF) for a variety of transonic Mach numbers and mesh sizes. Newton-GMRES is superior to MAF for some cases. The parallel performance of the Newton method is also found to be very good on multiple processors of the Cray C-90 and on the massively parallel thinking machine CM-5, where very fast execution rates (up to 9 Gflops) are found for large problems.

Condition Number Estimation of Preconditioned Matrices

PubMed Central

Kushida, Noriyuki

2015-01-01

The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager’s method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei’s matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei’s matrix, and matrices generated with the finite element method. PMID:25816331

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

Chen, Chao; Pouransari, Hadi; Rajamanickam, Sivasankaran

We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by everymore » processor. We also provide various numerical results to demonstrate the versatility and scalability of the parallel algorithm.« less

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

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

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« 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.

Meros Preconditioner Package

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

2004-04-01

Meros uses the compositional, aggregation, and overload operator capabilities of TSF to provide an object-oriented package providing segregated/block preconditioners for linear systems related to fully-coupled Navier-Stokes problems. This class of preconditioners exploits the special properties of these problems to segregate the equations and use multi-level preconditioners (through ML) on the matrix sub-blocks. Several preconditioners are provided, including the Fp and BFB preconditioners of Kay & Loghin and Silvester, Elman, Kay & Wathen. The overall performance and scalability of these preconditioners approaches that of multigrid for certain types of problems. Meros also provides more traditional pressure projection methods including SIMPLE andmore » SIMPLEC.« less

A nonrecursive 'Order N' preconditioned conjugate gradient/range space formulation of MDOF dynamics

NASA Technical Reports Server (NTRS)

Kurdila, A. J.; Menon, R.; Sunkel, John

1991-01-01

This paper addresses the requirements of present-day mechanical system simulations of algorithms that induce parallelism on a fine scale and of transient simulation methods which must be automatically load balancing for a wide collection of system topologies and hardware configurations. To this end, a combination range space/preconditioned conjugage gradient formulation of multidegree-of-freedon dynamics is developed, which, by employing regular ordering of the system connectivity graph, makes it possible to derive an extremely efficient preconditioner from the range space metric (as opposed to the system coefficient matrix). Because of the effectiveness of the preconditioner, the method can achieve performance rates that depend linearly on the number of substructures. The method, termed 'Order N' does not require the assembly of system mass or stiffness matrices, and is therefore amenable to implementation on work stations. Using this method, a 13-substructure model of the Space Station was constructed.

Parallel Performance of Linear Solvers and Preconditioners

DTIC Science & Technology

2014-01-01

are produced by a discrete dislocation dynamics ( DDD ) simulation and change with each timestep of the DDD simulation as the dislocation structure...evolves. However, the coefficient—or stiffness matrix— remains constant during the DDD simulation and some expensive matrix factorizations only occur once...discrete dislocation dynamics ( DDD ) simulations. This can be achieved by coupling a DDD simulator for bulk material (Arsenlis et al., 2007) to a

Improved preconditioned conjugate gradient algorithm and application in 3D inversion of gravity-gradiometry data

NASA Astrophysics Data System (ADS)

Wang, Tai-Han; Huang, Da-Nian; Ma, Guo-Qing; Meng, Zhao-Hai; Li, Ye

2017-06-01

With the continuous development of full tensor gradiometer (FTG) measurement techniques, three-dimensional (3D) inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit (GPU) and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation (SSOR) technique and the incomplete Choleksy decomposition conjugate gradient algorithm (ICCG). Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noisecontaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit (CPU). Real airborne gravity-gradiometry data from Vinton salt dome (southwest Louisiana, USA) are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.

Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling

NASA Technical Reports Server (NTRS)

Fink, P. W.; Wilton, D. R.; Dobbins, J. A.

2002-01-01

In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required to obtain usable convergence from an iterative solver. The authors have examined the use of an Incomplete LU Threshold (ILUT) preconditioner . to solver linear systems stemming from higher order BEM/FEM formulations in 2D scattering problems. Although the resulting preconditioner provided aD excellent approximation to the system inverse, its size in terms of non-zero entries represented only a modest improvement when compared with the fill-in associated with a sparse direct solver. Furthermore, the fill-in of the preconditioner could not be substantially reduced without the occurrence of instabilities. In addition to the results for these 2D problems, the authors will present iterative solution data from the application of the ILUT preconditioner to 3D problems.

Multilevel filtering elliptic preconditioners

NASA Technical Reports Server (NTRS)

Kuo, C. C. Jay; Chan, Tony F.; Tong, Charles

1989-01-01

A class of preconditioners is presented for elliptic problems built on ideas borrowed from the digital filtering theory and implemented on a multilevel grid structure. They are designed to be both rapidly convergent and highly parallelizable. The digital filtering viewpoint allows the use of filter design techniques for constructing elliptic preconditioners and also provides an alternative framework for understanding several other recently proposed multilevel preconditioners. Numerical results are presented to assess the convergence behavior of the new methods and to compare them with other preconditioners of multilevel type, including the usual multigrid method as preconditioner, the hierarchical basis method and a recent method proposed by Bramble-Pasciak-Xu.

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.

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.

Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Pazner, Will; Persson, Per-Olof

2018-02-01

In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Traditional matrix-based preconditioners require O (p2d) storage and O (p3d) computational work, where p is the degree of basis polynomials used, and d is the spatial dimension. Our SVD-based tensor-product preconditioner requires O (p d + 1) storage, O (p d + 1) work in two spatial dimensions, and O (p d + 2) work in three spatial dimensions. Combined with a matrix-free Newton-Krylov solver, these preconditioners allow for the solution of DG systems in linear time in p per degree of freedom in 2D, and reduce the computational complexity from O (p9) to O (p5) in 3D. Numerical results are shown in 2D and 3D for the advection, Euler, and Navier-Stokes equations, using polynomials of degree up to p = 30. For many test cases, the preconditioner results in similar iteration counts when compared with the exact block Jacobi preconditioner, and performance is significantly improved for high polynomial degrees p.

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

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).

Efficient Preconditioning for the p-Version Finite Element Method in Two Dimensions

DTIC Science & Technology

1989-10-01

paper, we study fast parallel preconditioners for systems of equations arising from the p-version finite element method. The p-version finite element...computations and the solution of a relatively small global auxiliary problem. We study two different methods. In the first (Section 3), the global...20], will be studied in the next section. Problem (3.12) is obviously much more easily solved than the original problem ,nd the procedure is highly

Scalable smoothing strategies for a geometric multigrid method for the immersed boundary equations

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

Bhalla, Amneet Pal Singh; Knepley, Matthew G.; Adams, Mark F.

2016-12-20

The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular because of their simplicity and generality. In prior work (Guy et al., Adv Comput Math, 2015), some of us developed a geometric multigrid preconditioner for a stable semi-implicit IB method under Stokes flow conditions; however, this solver methodology used a Vanka-type smoother that presented limited opportunities for parallelization. This work extends this Stokes-IB solver methodology by developing smoothing techniques that are suitable for parallel implementation. Specifically,more » we demonstrate that an additive version of the Vanka smoother can yield an effective multigrid preconditioner for the Stokes-IB equations, and we introduce an efficient Schur complement-based smoother that is also shown to be effective for the Stokes-IB equations. We investigate the performance of these solvers for a broad range of material stiffnesses, both for Stokes flows and flows at nonzero Reynolds numbers, and for thick and thin structural models. We show here that linear solver performance degrades with increasing Reynolds number and material stiffness, especially for thin interface cases. Nonetheless, the proposed approaches promise to yield effective solution algorithms, especially at lower Reynolds numbers and at modest-to-high elastic stiffnesses.« less

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.

The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1984-01-01

The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner.

An extended GS method for dense linear systems

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi

2009-09-01

Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.

On the scalability of the Albany/FELIX first-order Stokes approximation ice sheet solver for large-scale simulations of the Greenland and Antarctic ice sheets

DOE PAGES

Tezaur, Irina K.; Tuminaro, Raymond S.; Perego, Mauro; ...

2015-01-01

We examine the scalability of the recently developed Albany/FELIX finite-element based code for the first-order Stokes momentum balance equations for ice flow. We focus our analysis on the performance of two possible preconditioners for the iterative solution of the sparse linear systems that arise from the discretization of the governing equations: (1) a preconditioner based on the incomplete LU (ILU) factorization, and (2) a recently-developed algebraic multigrid (AMG) preconditioner, constructed using the idea of semi-coarsening. A strong scalability study on a realistic, high resolution Greenland ice sheet problem reveals that, for a given number of processor cores, the AMG preconditionermore » results in faster linear solve times but the ILU preconditioner exhibits better scalability. In addition, a weak scalability study is performed on a realistic, moderate resolution Antarctic ice sheet problem, a substantial fraction of which contains floating ice shelves, making it fundamentally different from the Greenland ice sheet problem. We show that as the problem size increases, the performance of the ILU preconditioner deteriorates whereas the AMG preconditioner maintains scalability. This is because the linear systems are extremely ill-conditioned in the presence of floating ice shelves, and the ill-conditioning has a greater negative effect on the ILU preconditioner than on the AMG preconditioner.« less

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

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

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

Effective matrix-free preconditioning for the augmented immersed interface method

NASA Astrophysics Data System (ADS)

Xia, Jianlin; Li, Zhilin; Ye, Xin

2015-12-01

We present effective and efficient matrix-free preconditioning techniques for the augmented immersed interface method (AIIM). AIIM has been developed recently and is shown to be very effective for interface problems and problems on irregular domains. GMRES is often used to solve for the augmented variable(s) associated with a Schur complement A in AIIM that is defined along the interface or the irregular boundary. The efficiency of AIIM relies on how quickly the system for A can be solved. For some applications, there are substantial difficulties involved, such as the slow convergence of GMRES (particularly for free boundary and moving interface problems), and the inconvenience in finding a preconditioner (due to the situation that only the products of A and vectors are available). Here, we propose matrix-free structured preconditioning techniques for AIIM via adaptive randomized sampling, using only the products of A and vectors to construct a hierarchically semiseparable matrix approximation to A. Several improvements over existing schemes are shown so as to enhance the efficiency and also avoid potential instability. The significance of the preconditioners includes: (1) they do not require the entries of A or the multiplication of AT with vectors; (2) constructing the preconditioners needs only O (log ⁡ N) matrix-vector products and O (N) storage, where N is the size of A; (3) applying the preconditioners needs only O (N) flops; (4) they are very flexible and do not require any a priori knowledge of the structure of A. The preconditioners are observed to significantly accelerate the convergence of GMRES, with heuristical justifications of the effectiveness. Comprehensive tests on several important applications are provided, such as Navier-Stokes equations on irregular domains with traction boundary conditions, interface problems in incompressible flows, mixed boundary problems, and free boundary problems. The preconditioning techniques are also useful for several other problems and methods.

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.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

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

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-06-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner formore » scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.« less

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

Coupled Modeling of Hydrodynamics and Sound in Coastal Ocean for Renewable Ocean Energy Development

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

Long, Wen; Jung, Ki Won; Yang, Zhaoqing

An underwater sound model was developed to simulate sound propagation from marine and hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite difference methods were developed to solve the 3D Helmholtz equation for sound propagation in the coastal environment. A 3D sparse matrix solver with complex coefficients was formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method was applied to solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model was then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generatedmore » by human activities, such as construction of OSW turbines or tidal stream turbine operations, in a range-dependent setting. As a proof of concept, initial validation of the solver is presented for two coastal wedge problems. This sound model can be useful for evaluating impacts on marine mammals due to deployment of MHK devices and OSW energy platforms.« 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.

Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction.

PubMed

Fessler, J A; Booth, S D

1999-01-01

Gradient-based iterative methods often converge slowly for tomographic image reconstruction and image restoration problems, but can be accelerated by suitable preconditioners. Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian matrices in imaging problems. Circulant preconditioners can provide remarkable acceleration for inverse problems that are approximately shift-invariant, i.e., for those with approximately block-Toeplitz or block-circulant Hessians. However, in applications with nonuniform noise variance, such as arises from Poisson statistics in emission tomography and in quantum-limited optical imaging, the Hessian of the weighted least-squares objective function is quite shift-variant, and circulant preconditioners perform poorly. Additional shift-variance is caused by edge-preserving regularization methods based on nonquadratic penalty functions. This paper describes new preconditioners that approximate more accurately the Hessian matrices of shift-variant imaging problems. Compared to diagonal or circulant preconditioning, the new preconditioners lead to significantly faster convergence rates for the unconstrained conjugate-gradient (CG) iteration. We also propose a new efficient method for the line-search step required by CG methods. Applications to positron emission tomography (PET) illustrate the method.

Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics

NASA Astrophysics Data System (ADS)

Gilles, Luc; Ellerbroek, Brent L.; Vogel, Curtis R.

2003-09-01

Multiconjugate adaptive optics (MCAO) systems with 104-105 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wave-front control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 104 actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10-2 Hz, i.e., 4-5 orders of magnitude lower than the typical 103 Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.

Two new modified Gauss-Seidel methods for linear system with M-matrices

NASA Astrophysics Data System (ADS)

Zheng, Bing; Miao, Shu-Xin

2009-12-01

In 2002, H. Kotakemori et al. proposed the modified Gauss-Seidel (MGS) method for solving the linear system with the preconditioner [H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner () J. Comput. Appl. Math. 145 (2002) 373-378]. Since this preconditioner is constructed by only the largest element on each row of the upper triangular part of the coefficient matrix, the preconditioning effect is not observed on the nth row. In the present paper, to deal with this drawback, we propose two new preconditioners. The convergence and comparison theorems of the modified Gauss-Seidel methods with these two preconditioners for solving the linear system are established. The convergence rates of the new proposed preconditioned methods are compared. In addition, numerical experiments are used to show the effectiveness of the new MGS methods.

Teko: A block preconditioning capability with concrete example applications in Navier--Stokes and MHD

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

Cyr, Eric C.; Shadid, John N.; Tuminaro, Raymond S.

This study describes the design of Teko, an object-oriented C++ library for implementing advanced block preconditioners. Mathematical design criteria that elucidate the needs of block preconditioning libraries and techniques are explained and shown to motivate the structure of Teko. For instance, a principal design choice was for Teko to strongly reflect the mathematical statement of the preconditioners to reduce development burden and permit focus on the numerics. Additional mechanisms are explained that provide a pathway to developing an optimized production capable block preconditioning capability with Teko. Finally, Teko is demonstrated on fluid flow and magnetohydrodynamics applications. In addition to highlightingmore » the features of the Teko library, these new results illustrate the effectiveness of recent preconditioning developments applied to advanced discretization approaches.« less

The preconditioned Gauss-Seidel method faster than the SOR method

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Kohno, Toshiyuki; Morimoto, Munenori

2008-09-01

In recent years, a number of preconditioners have been applied to linear systems [A.D. Gunawardena, S.K. Jain, L. Snyder, Modified iterative methods for consistent linear systems, Linear Algebra Appl. 154-156 (1991) 123-143; T. Kohno, H. Kotakemori, H. Niki, M. Usui, Improving modified Gauss-Seidel method for Z-matrices, Linear Algebra Appl. 267 (1997) 113-123; H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner (I+Smax), J. Comput. Appl. Math. 145 (2002) 373-378; H. Kotakemori, H. Niki, N. Okamoto, Accelerated iteration method for Z-matrices, J. Comput. Appl. Math. 75 (1996) 87-97; M. Usui, H. Niki, T.Kohno, Adaptive Gauss-Seidel method for linear systems, Internat. J. Comput. Math. 51(1994)119-125 [10

Teko: A block preconditioning capability with concrete example applications in Navier--Stokes and MHD

DOE PAGES

Cyr, Eric C.; Shadid, John N.; Tuminaro, Raymond S.

2016-10-27

This study describes the design of Teko, an object-oriented C++ library for implementing advanced block preconditioners. Mathematical design criteria that elucidate the needs of block preconditioning libraries and techniques are explained and shown to motivate the structure of Teko. For instance, a principal design choice was for Teko to strongly reflect the mathematical statement of the preconditioners to reduce development burden and permit focus on the numerics. Additional mechanisms are explained that provide a pathway to developing an optimized production capable block preconditioning capability with Teko. Finally, Teko is demonstrated on fluid flow and magnetohydrodynamics applications. In addition to highlightingmore » the features of the Teko library, these new results illustrate the effectiveness of recent preconditioning developments applied to advanced discretization approaches.« less

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

NASA Astrophysics Data System (ADS)

Kong, Fande; Cai, Xiao-Chuan

2017-07-01

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here "geometry" includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

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

Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD

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

Lin, P. T.; Shadid, J. N.; Hu, J. J.

Here, we explore the current performance and scaling of a fully-implicit stabilized unstructured finite element (FE) variational multiscale (VMS) capability for large-scale simulations of 3D incompressible resistive magnetohydrodynamics (MHD). The large-scale linear systems that are generated by a Newton nonlinear solver approach are iteratively solved by preconditioned Krylov subspace methods. The efficiency of this approach is critically dependent on the scalability and performance of the algebraic multigrid preconditioner. Our study considers the performance of the numerical methods as recently implemented in the second-generation Trilinos implementation that is 64-bit compliant and is not limited by the 32-bit global identifiers of themore » original Epetra-based Trilinos. The study presents representative results for a Poisson problem on 1.6 million cores of an IBM Blue Gene/Q platform to demonstrate very large-scale parallel execution. Additionally, results for a more challenging steady-state MHD generator and a transient solution of a benchmark MHD turbulence calculation for the full resistive MHD system are also presented. These results are obtained on up to 131,000 cores of a Cray XC40 and one million cores of a BG/Q system.« less

Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD

DOE PAGES

Lin, P. T.; Shadid, J. N.; Hu, J. J.; ...

2017-11-06

Here, we explore the current performance and scaling of a fully-implicit stabilized unstructured finite element (FE) variational multiscale (VMS) capability for large-scale simulations of 3D incompressible resistive magnetohydrodynamics (MHD). The large-scale linear systems that are generated by a Newton nonlinear solver approach are iteratively solved by preconditioned Krylov subspace methods. The efficiency of this approach is critically dependent on the scalability and performance of the algebraic multigrid preconditioner. Our study considers the performance of the numerical methods as recently implemented in the second-generation Trilinos implementation that is 64-bit compliant and is not limited by the 32-bit global identifiers of themore » original Epetra-based Trilinos. The study presents representative results for a Poisson problem on 1.6 million cores of an IBM Blue Gene/Q platform to demonstrate very large-scale parallel execution. Additionally, results for a more challenging steady-state MHD generator and a transient solution of a benchmark MHD turbulence calculation for the full resistive MHD system are also presented. These results are obtained on up to 131,000 cores of a Cray XC40 and one million cores of a BG/Q system.« less

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

DOE PAGES

Kong, Fande; Cai, Xiao-Chuan

2017-03-24

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexactmore » Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.« less

Physics-Based Preconditioning of a Compressible Flow Solver for Large-Scale Simulations of Additive Manufacturing Processes

NASA Astrophysics Data System (ADS)

Weston, Brian; Nourgaliev, Robert; Delplanque, Jean-Pierre

2017-11-01

We present a new block-based Schur complement preconditioner for simulating all-speed compressible flow with phase change. The conservation equations are discretized with a reconstructed Discontinuous Galerkin method and integrated in time with fully implicit time discretization schemes. The resulting set of non-linear equations is converged using a robust Newton-Krylov framework. Due to the stiffness of the underlying physics associated with stiff acoustic waves and viscous material strength effects, we solve for the primitive-variables (pressure, velocity, and temperature). To enable convergence of the highly ill-conditioned linearized systems, we develop a physics-based preconditioner, utilizing approximate block factorization techniques to reduce the fully-coupled 3×3 system to a pair of reduced 2×2 systems. We demonstrate that our preconditioned Newton-Krylov framework converges on very stiff multi-physics problems, corresponding to large CFL and Fourier numbers, with excellent algorithmic and parallel scalability. Results are shown for the classic lid-driven cavity flow problem as well as for 3D laser-induced phase change. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics.

PubMed

Gilles, Luc; Ellerbroek, Brent L; Vogel, Curtis R

2003-09-10

Multiconjugate adaptive optics (MCAO) systems with 10(4)-10(5) degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 10(4) actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10(-2) Hz, i.e., 4-5 orders of magnitude lower than the typical 10(3) Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.

On polynomial preconditioning for indefinite Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1989-01-01

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.

PubMed

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.

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.

Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations

PubMed Central

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids. PMID:24235888

Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems

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

Zheng, Bin; Chen, Luoping; Hu, Xiaozhe

2016-03-05

In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show that these preconditioners only need to be solved inexactly by optimal multigrid algorithms. Our numerical examples indicate that the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients. We also investigatemore » the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems.« less

The role of grape seed extract in the remineralization of demineralized dentine: micromorphological and physical analyses.

PubMed

Tang, Cheng-fang; Fang, Ming; Liu, Rui-rui; Dou, Qi; Chai, Zhi-guo; Xiao, Yu-hong; Chen, Ji-hua

2013-12-01

Grape seed extract (GSE) is known to have a positive effect on the demineralization and/or remineralization of artificial root caries lesions. The present study aimed to investigate whether biomodification of caries-like acid-etched demineralized dentine, using proanthocyanidins-rich GSE, would promote its remineralization potential. Dentine specimens were acid-etched for 30s, then biomodified using proanthocyanidin-based preconditioners (at different concentrations and pH values) for 2min, followed by a 15-day artificial remineralization regimen. They were subsequently subjected to microhardness measurements, micromorphological evaluation and X-ray diffraction analyses. Stability of the preconditioners was also analyzed, spectrophotometrically. A concentration-dependent increase was observed in the microhardness of the specimens that were biomodified using GSE preconditioners, without pH adjustment. Field emission scanning electron microscopy revealed greater mineral deposition on their surfaces, which was further identified mainly as hydroxylapatite. The absorbances of preconditioner dilutions at pH 7.4 and pH 10.0 decreased at the two typical polyphenol bands. Transient GSE biomodification promoted remineralization on the surface of demineralized dentine, and this process was influenced by the concentration and pH value of the preconditioner. GSE preconditioner at a concentration of 15%, without pH adjustment, presented with the best results, and this may be attributed to its high polyphenolic content. Copyright © 2013 Elsevier Ltd. All rights reserved.

Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes

NASA Astrophysics Data System (ADS)

Austin, Travis M.; Brezina, Marian; Jamroz, Ben; Jhurani, Chetan; Manteuffel, Thomas A.; Ruge, John

2012-05-01

High-order finite elements often have a higher accuracy per degree of freedom than the classical low-order finite elements. However, in the context of implicit time-stepping methods, high-order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element matrix. There are many cases where simulations are limited by the memory required to store the matrix and/or the algorithmic components of the linear solver. We are particularly interested in preconditioned Krylov methods for linear systems generated by discretization of elliptic partial differential equations with high-order finite elements. Using a preconditioner like Algebraic Multigrid can be costly in terms of memory due to the need to store matrix information at the various levels. We present a novel method for defining a preconditioner for systems generated by high-order finite elements that is based on a much sparser system than the original high-order finite element system. We investigate the performance for non-uniform meshes on a cube and a cubed sphere mesh, showing that the sparser preconditioner is more efficient and uses significantly less memory. Finally, we explore new methods to construct the sparse preconditioner and examine their effectiveness for non-uniform meshes. We compare results to a direct use of Algebraic Multigrid as a preconditioner and to a two-level additive Schwarz method.

A universal preconditioner for simulating condensed phase materials.

PubMed

Packwood, David; Kermode, James; Mones, Letif; Bernstein, Noam; Woolley, John; Gould, Nicholas; Ortner, Christoph; Csányi, Gábor

2016-04-28

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.

A universal preconditioner for simulating condensed phase materials

NASA Astrophysics Data System (ADS)

Packwood, David; Kermode, James; Mones, Letif; Bernstein, Noam; Woolley, John; Gould, Nicholas; Ortner, Christoph; Csányi, Gábor

2016-04-01

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.

Novel numerical techniques for magma dynamics

NASA Astrophysics Data System (ADS)

Rhebergen, S.; Katz, R. F.; Wathen, A.; Alisic, L.; Rudge, J. F.; Wells, G.

2013-12-01

We discuss the development of finite element techniques and solvers for magma dynamics computations. These are implemented within the FEniCS framework. This approach allows for user-friendly, expressive, high-level code development, but also provides access to powerful, scalable numerical solvers and a large family of finite element discretisations. With the recent addition of dolfin-adjoint, FeniCS supports automated adjoint and tangent-linear models, enabling the rapid development of Generalised Stability Analysis. The ability to easily scale codes to three dimensions with large meshes, and/or to apply intricate adjoint calculations means that efficiency of the numerical algorithms is vital. We therefore describe our development and analysis of preconditioners designed specifically for finite element discretizations of equations governing magma dynamics. The preconditioners are based on Elman-Silvester-Wathen methods for the Stokes equation, and we extend these to flows with compaction. Our simulations are validated by comparison of results with laboratory experiments on partially molten aggregates.

Preconditioner-free Wiener filtering with a dense noise matrix

NASA Astrophysics Data System (ADS)

Huffenberger, Kevin M.

2018-05-01

This work extends the Elsner & Wandelt (2013) iterative method for efficient, preconditioner-free Wiener filtering to cases in which the noise covariance matrix is dense, but can be decomposed into a sum whose parts are sparse in convenient bases. The new method, which uses multiple messenger fields, reproduces Wiener-filter solutions for test problems, and we apply it to a case beyond the reach of the Elsner & Wandelt (2013) method. We compute the Wiener-filter solution for a simulated Cosmic Microwave Background (CMB) map that contains spatially varying, uncorrelated noise, isotropic 1/f noise, and large-scale horizontal stripes (like those caused by atmospheric noise). We discuss simple extensions that can filter contaminated modes or inverse-noise-filter the data. These techniques help to address complications in the noise properties of maps from current and future generations of ground-based Microwave Background experiments, like Advanced ACTPol, Simons Observatory, and CMB-S4.

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

DOE PAGES

Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong

2015-08-23

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

Incomplete Gröbner basis as a preconditioner for polynomial systems

NASA Astrophysics Data System (ADS)

Sun, Yang; Tao, Yu-Hui; Bai, Feng-Shan

2009-04-01

Precondition plays a critical role in the numerical methods for large and sparse linear systems. It is also true for nonlinear algebraic systems. In this paper incomplete Gröbner basis (IGB) is proposed as a preconditioner of homotopy methods for polynomial systems of equations, which transforms a deficient system into a system with the same finite solutions, but smaller degree. The reduced system can thus be solved faster. Numerical results show the efficiency of the preconditioner.

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.

Sub-domain decomposition methods and computational controls for multibody dynamical systems. [of spacecraft structures

NASA Technical Reports Server (NTRS)

Menon, R. G.; Kurdila, A. J.

1992-01-01

This paper presents a concurrent methodology to simulate the dynamics of flexible multibody systems with a large number of degrees of freedom. A general class of open-loop structures is treated and a redundant coordinate formulation is adopted. A range space method is used in which the constraint forces are calculated using a preconditioned conjugate gradient method. By using a preconditioner motivated by the regular ordering of the directed graph of the structures, it is shown that the method is order N in the total number of coordinates of the system. The overall formulation has the advantage that it permits fine parallelization and does not rely on system topology to induce concurrency. It can be efficiently implemented on the present generation of parallel computers with a large number of processors. Validation of the method is presented via numerical simulations of space structures incorporating large number of flexible degrees of freedom.

A universal preconditioner for simulating condensed phase materials

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

Packwood, David; Ortner, Christoph, E-mail: c.ortner@warwick.ac.uk; Kermode, James, E-mail: j.r.kermode@warwick.ac.uk

2016-04-28

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor ofmore » two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.« less

Performance of an MPI-only semiconductor device simulator on a quad socket/quad core InfiniBand platform.

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

Shadid, John Nicolas; Lin, Paul Tinphone

2009-01-01

This preliminary study considers the scaling and performance of a finite element (FE) semiconductor device simulator on a capacity cluster with 272 compute nodes based on a homogeneous multicore node architecture utilizing 16 cores. The inter-node communication backbone for this Tri-Lab Linux Capacity Cluster (TLCC) machine is comprised of an InfiniBand interconnect. The nonuniform memory access (NUMA) nodes consist of 2.2 GHz quad socket/quad core AMD Opteron processors. The performance results for this study are obtained with a FE semiconductor device simulation code (Charon) that is based on a fully-coupled Newton-Krylov solver with domain decomposition and multilevel preconditioners. Scaling andmore » multicore performance results are presented for large-scale problems of 100+ million unknowns on up to 4096 cores. A parallel scaling comparison is also presented with the Cray XT3/4 Red Storm capability platform. The results indicate that an MPI-only programming model for utilizing the multicore nodes is reasonably efficient on all 16 cores per compute node. However, the results also indicated that the multilevel preconditioner, which is critical for large-scale capability type simulations, scales better on the Red Storm machine than the TLCC machine.« less

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

Collins, Benjamin S.

The Futility package contains the following: 1) Definition of the size of integers and real numbers; 2) A generic Unit test harness; 3) Definitions for some basic extensions to the Fortran language: arbitrary length strings, a parameter list construct, exception handlers, command line processor, timers; 4) Geometry definitions: point, line, plane, box, cylinder, polyhedron; 5) File wrapper functions: standard Fortran input/output files, Fortran binary files, HDF5 files; 6) Parallel wrapper functions: MPI, and Open MP abstraction layers, partitioning algorithms; 7) Math utilities: BLAS, Matrix and Vector definitions, Linear Solver methods and wrappers for other TPLs (PETSC, MKL, etc), preconditioner classes;more » 8) Misc: random number generator, water saturation properties, sorting algorithms.« less

Graph Embedding Techniques for Bounding Condition Numbers of Incomplete Factor Preconditioning

NASA Technical Reports Server (NTRS)

Guattery, Stephen

1997-01-01

We extend graph embedding techniques for bounding the spectral condition number of preconditioned systems involving symmetric, irreducibly diagonally dominant M-matrices to systems where the preconditioner is not diagonally dominant. In particular, this allows us to bound the spectral condition number when the preconditioner is based on an incomplete factorization. We provide a review of previous techniques, describe our extension, and give examples both of a bound for a model problem, and of ways in which our techniques give intuitive way of looking at incomplete factor preconditioners.

PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code.

NASA Astrophysics Data System (ADS)

Chacon, L.; Knoll, D. A.

2004-11-01

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended primitive-variable MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field, non-dissipative, and stable in the absence of physical dissipation.(L. Chacón , phComput. Phys. Comm.) submitted (2004) PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, first and second-order implicit schemes are available, although higher-order temporal implicit schemes can be effortlessly implemented within the Newton-Krylov framework. A successful, scalable, MG physics-based preconditioning strategy, similar in concept to previous 2D MHD efforts,(L. Chacón et al., phJ. Comput. Phys). 178 (1), 15- 36 (2002); phJ. Comput. Phys., 188 (2), 573-592 (2003) has been developed. We are currently in the process of parallelizing the code using the PETSc library, and a Newton-Krylov-Schwarz approach for the parallel treatment of the preconditioner. In this poster, we will report on both the serial and parallel performance of PIXIE3D, focusing primarily on scalability and CPU speedup vs. an explicit approach.

Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE

DOE PAGES

Lott, P. Aaron; Woodward, Carol S.; Evans, Katherine J.

2014-10-19

Performing accurate and efficient numerical simulation of global atmospheric climate models is challenging due to the disparate length and time scales over which physical processes interact. Implicit solvers enable the physical system to be integrated with a time step commensurate with processes being studied. The dominant cost of an implicit time step is the ancillary linear system solves, so we have developed a preconditioner aimed at improving the efficiency of these linear system solves. Our preconditioner is based on an approximate block factorization of the linearized shallow-water equations and has been implemented within the spectral element dynamical core within themore » Community Atmospheric Model (CAM-SE). Furthermore, in this paper we discuss the development and scalability of the preconditioner for a suite of test cases with the implicit shallow-water solver within CAM-SE.« less

Solving Graph Laplacian Systems Through Recursive Bisections and Two-Grid Preconditioning

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

Ponce, Colin; Vassilevski, Panayot S.

2016-02-18

We present a parallelizable direct method for computing the solution to graph Laplacian-based linear systems derived from graphs that can be hierarchically bipartitioned with small edge cuts. For a graph of size n with constant-size edge cuts, our method decomposes a graph Laplacian in time O(n log n), and then uses that decomposition to perform a linear solve in time O(n log n). We then use the developed technique to design a preconditioner for graph Laplacians that do not have this property. Finally, we augment this preconditioner with a two-grid method that accounts for much of the preconditioner's weaknesses. Wemore » present an analysis of this method, as well as a general theorem for the condition number of a general class of two-grid support graph-based preconditioners. Numerical experiments illustrate the performance of the studied methods.« less

Local multiplicative Schwarz algorithms for convection-diffusion equations

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Sarkis, Marcus

1995-01-01

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

Efficiency and flexibility using implicit methods within atmosphere dycores

NASA Astrophysics Data System (ADS)

Evans, K. J.; Archibald, R.; Norman, M. R.; Gardner, D. J.; Woodward, C. S.; Worley, P.; Taylor, M.

2016-12-01

A suite of explicit and implicit methods are evaluated for a range of configurations of the shallow water dynamical core within the spectral-element Community Atmosphere Model (CAM-SE) to explore their relative computational performance. The configurations are designed to explore the attributes of each method under different but relevant model usage scenarios including varied spectral order within an element, static regional refinement, and scaling to large problem sizes. The limitations and benefits of using explicit versus implicit, with different discretizations and parameters, are discussed in light of trade-offs such as MPI communication, memory, and inherent efficiency bottlenecks. For the regionally refined shallow water configurations, the implicit BDF2 method is about the same efficiency as an explicit Runge-Kutta method, without including a preconditioner. Performance of the implicit methods with the residual function executed on a GPU is also presented; there is speed up for the residual relative to a CPU, but overwhelming transfer costs motivate moving more of the solver to the device. Given the performance behavior of implicit methods within the shallow water dynamical core, the recommendation for future work using implicit solvers is conditional based on scale separation and the stiffness of the problem. The strong growth of linear iterations with increasing resolution or time step size is the main bottleneck to computational efficiency. Within the hydrostatic dynamical core, of CAM-SE, we present results utilizing approximate block factorization preconditioners implemented using the Trilinos library of solvers. They reduce the cost of linear system solves and improve parallel scalability. We provide a summary of the remaining efficiency considerations within the preconditioner and utilization of the GPU, as well as a discussion about the benefits of a time stepping method that provides converged and stable solutions for a much wider range of time step sizes. As more complex model components, for example new physics and aerosols, are connected in the model, having flexibility in the time stepping will enable more options for combining and resolving multiple scales of behavior.

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.

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

Distributed Memory Parallel Computing with SEAWAT

NASA Astrophysics Data System (ADS)

Verkaik, J.; Huizer, S.; van Engelen, J.; Oude Essink, G.; Ram, R.; Vuik, K.

2017-12-01

Fresh groundwater reserves in coastal aquifers are threatened by sea-level rise, extreme weather conditions, increasing urbanization and associated groundwater extraction rates. To counteract these threats, accurate high-resolution numerical models are required to optimize the management of these precious reserves. The major model drawbacks are long run times and large memory requirements, limiting the predictive power of these models. Distributed memory parallel computing is an efficient technique for reducing run times and memory requirements, where the problem is divided over multiple processor cores. A new Parallel Krylov Solver (PKS) for SEAWAT is presented. PKS has recently been applied to MODFLOW and includes Conjugate Gradient (CG) and Biconjugate Gradient Stabilized (BiCGSTAB) linear accelerators. Both accelerators are preconditioned by an overlapping additive Schwarz preconditioner in a way that: a) subdomains are partitioned using Recursive Coordinate Bisection (RCB) load balancing, b) each subdomain uses local memory only and communicates with other subdomains by Message Passing Interface (MPI) within the linear accelerator, c) it is fully integrated in SEAWAT. Within SEAWAT, the PKS-CG solver replaces the Preconditioned Conjugate Gradient (PCG) solver for solving the variable-density groundwater flow equation and the PKS-BiCGSTAB solver replaces the Generalized Conjugate Gradient (GCG) solver for solving the advection-diffusion equation. PKS supports the third-order Total Variation Diminishing (TVD) scheme for computing advection. Benchmarks were performed on the Dutch national supercomputer (https://userinfo.surfsara.nl/systems/cartesius) using up to 128 cores, for a synthetic 3D Henry model (100 million cells) and the real-life Sand Engine model ( 10 million cells). The Sand Engine model was used to investigate the potential effect of the long-term morphological evolution of a large sand replenishment and climate change on fresh groundwater resources. Speed-ups up to 40 were obtained with the new PKS solver.

Un-collided-flux preconditioning for the first order transport equation

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

Rigley, M.; Koebbe, J.; Drumm, C.

2013-07-01

Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods. These codes include a least squares finite element method and a discontinuous finite element method. The performance of each code is shown on problems in one and two dimensions. The un-collided-flux preconditioner shows good speedup on each of the given methods. The un-collided-flux preconditioner has been used on the second-order equation, and here we extend those results to the first order equation. (authors)

An iterative solver for the 3D Helmholtz equation

NASA Astrophysics Data System (ADS)

Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

2017-09-01

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

Multigrid solvers and multigrid preconditioners for the solution of variational data assimilation problems

NASA Astrophysics Data System (ADS)

Debreu, Laurent; Neveu, Emilie; Simon, Ehouarn; Le Dimet, Francois Xavier; Vidard, Arthur

2014-05-01

In order to lower the computational cost of the variational data assimilation process, we investigate the use of multigrid methods to solve the associated optimal control system. On a linear advection equation, we study the impact of the regularization term on the optimal control and the impact of discretization errors on the efficiency of the coarse grid correction step. We show that even if the optimal control problem leads to the solution of an elliptic system, numerical errors introduced by the discretization can alter the success of the multigrid methods. The view of the multigrid iteration as a preconditioner for a Krylov optimization method leads to a more robust algorithm. A scale dependent weighting of the multigrid preconditioner and the usual background error covariance matrix based preconditioner is proposed and brings significant improvements. [1] Laurent Debreu, Emilie Neveu, Ehouarn Simon, François-Xavier Le Dimet and Arthur Vidard, 2014: Multigrid solvers and multigrid preconditioners for the solution of variational data assimilation problems, submitted to QJRMS, http://hal.inria.fr/hal-00874643 [2] Emilie Neveu, Laurent Debreu and François-Xavier Le Dimet, 2011: Multigrid methods and data assimilation - Convergence study and first experiments on non-linear equations, ARIMA, 14, 63-80, http://intranet.inria.fr/international/arima/014/014005.html

Cosmic Microwave Background Mapmaking with a Messenger Field

NASA Astrophysics Data System (ADS)

Huffenberger, Kevin M.; Næss, Sigurd K.

2018-01-01

We apply a messenger field method to solve the linear minimum-variance mapmaking equation in the context of Cosmic Microwave Background (CMB) observations. In simulations, the method produces sky maps that converge significantly faster than those from a conjugate gradient descent algorithm with a diagonal preconditioner, even though the computational cost per iteration is similar. The messenger method recovers large scales in the map better than conjugate gradient descent, and yields a lower overall χ2. In the single, pencil beam approximation, each iteration of the messenger mapmaking procedure produces an unbiased map, and the iterations become more optimal as they proceed. A variant of the method can handle differential data or perform deconvolution mapmaking. The messenger method requires no preconditioner, but a high-quality solution needs a cooling parameter to control the convergence. We study the convergence properties of this new method and discuss how the algorithm is feasible for the large data sets of current and future CMB experiments.

Repeated Red-Black ordering

NASA Astrophysics Data System (ADS)

Ciarlet, P.

1994-09-01

Hereafter, we describe and analyze, from both a theoretical and a numerical point of view, an iterative method for efficiently solving symmetric elliptic problems with possibly discontinuous coefficients. In the following, we use the Preconditioned Conjugate Gradient method to solve the symmetric positive definite linear systems which arise from the finite element discretization of the problems. We focus our interest on sparse and efficient preconditioners. In order to define the preconditioners, we perform two steps: first we reorder the unknowns and then we carry out a (modified) incomplete factorization of the original matrix. We study numerically and theoretically two preconditioners, the second preconditioner corresponding to the one investigated by Brand and Heinemann [2]. We prove convergence results about the Poisson equation with either Dirichlet or periodic boundary conditions. For a meshsizeh, Brand proved that the condition number of the preconditioned system is bounded byO(h-1/2) for Dirichlet boundary conditions. By slightly modifying the preconditioning process, we prove that the condition number is bounded byO(h-1/3).

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.

Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

NASA Astrophysics Data System (ADS)

Kaporin, I. E.

2012-02-01

In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

Large Scale, High Resolution, Mantle Dynamics Modeling

NASA Astrophysics Data System (ADS)

Geenen, T.; Berg, A. V.; Spakman, W.

2007-12-01

To model the geodynamic evolution of plate convergence, subduction and collision and to allow for a connection to various types of observational data, geophysical, geodetical and geological, we developed a 4D (space-time) numerical mantle convection code. The model is based on a spherical 3D Eulerian fem model, with quadratic elements, on top of which we constructed a 3D Lagrangian particle in cell(PIC) method. We use the PIC method to transport material properties and to incorporate a viscoelastic rheology. Since capturing small scale processes associated with localization phenomena require a high resolution, we spend a considerable effort on implementing solvers suitable to solve for models with over 100 million degrees of freedom. We implemented Additive Schwartz type ILU based methods in combination with a Krylov solver, GMRES. However we found that for problems with over 500 thousend degrees of freedom the convergence of the solver degraded severely. This observation is known from the literature [Saad, 2003] and results from the local character of the ILU preconditioner resulting in a poor approximation of the inverse of A for large A. The size of A for which ILU is no longer usable depends on the condition of A and on the amount of fill in allowed for the ILU preconditioner. We found that for our problems with over 5×105 degrees of freedom convergence became to slow to solve the system within an acceptable amount of walltime, one minute, even when allowing for considerable amount of fill in. We also implemented MUMPS and found good scaling results for problems up to 107 degrees of freedom for up to 32 CPU¡¯s. For problems with over 100 million degrees of freedom we implemented Algebraic Multigrid type methods (AMG) from the ML library [Sala, 2006]. Since multigrid methods are most effective for single parameter problems, we rebuild our model to use the SIMPLE method in the Stokes solver [Patankar, 1980]. We present scaling results from these solvers for 3D spherical models. We also applied the above mentioned method to a high resolution (~ 1 km) 2D mantle convection model with temperature, pressure and phase dependent rheology including several phase transitions. We focus on a model of a subducting lithospheric slab which is subject to strong folding at the bottom of the mantle's D" region which includes the postperovskite phase boundary. For a detailed description of this model we refer to poster [Mantel convection models of the D" region, U17] [Saad, 2003] Saad, Y. (2003). Iterative methods for sparse linear systems. [Sala, 2006] Sala. M (2006) An Object-Oriented Framework for the Development of Scalable Parallel Multilevel Preconditioners. ACM Transactions on Mathematical Software, 32 (3), 2006 [Patankar, 1980] Patankar, S. V.(1980) Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington.

Efficient solvers for coupled models in respiratory mechanics.

PubMed

Verdugo, Francesc; Roth, Christian J; Yoshihara, Lena; Wall, Wolfgang A

2017-02-01

We present efficient preconditioners for one of the most physiologically relevant pulmonary models currently available. Our underlying motivation is to enable the efficient simulation of such a lung model on high-performance computing platforms in order to assess mechanical ventilation strategies and contributing to design more protective patient-specific ventilation treatments. The system of linear equations to be solved using the proposed preconditioners is essentially the monolithic system arising in fluid-structure interaction (FSI) extended by additional algebraic constraints. The introduction of these constraints leads to a saddle point problem that cannot be solved with usual FSI preconditioners available in the literature. The key ingredient in this work is to use the idea of the semi-implicit method for pressure-linked equations (SIMPLE) for getting rid of the saddle point structure, resulting in a standard FSI problem that can be treated with available techniques. The numerical examples show that the resulting preconditioners approach the optimal performance of multigrid methods, even though the lung model is a complex multiphysics problem. Moreover, the preconditioners are robust enough to deal with physiologically relevant simulations involving complex real-world patient-specific lung geometries. The same approach is applicable to other challenging biomedical applications where coupling between flow and tissue deformations is modeled with additional algebraic constraints. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

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

Parallel Computation of Flow in Heterogeneous Media Modelled by Mixed Finite Elements

NASA Astrophysics Data System (ADS)

Cliffe, K. A.; Graham, I. G.; Scheichl, R.; Stals, L.

2000-11-01

In this paper we describe a fast parallel method for solving highly ill-conditioned saddle-point systems arising from mixed finite element simulations of stochastic partial differential equations (PDEs) modelling flow in heterogeneous media. Each realisation of these stochastic PDEs requires the solution of the linear first-order velocity-pressure system comprising Darcy's law coupled with an incompressibility constraint. The chief difficulty is that the permeability may be highly variable, especially when the statistical model has a large variance and a small correlation length. For reasonable accuracy, the discretisation has to be extremely fine. We solve these problems by first reducing the saddle-point formulation to a symmetric positive definite (SPD) problem using a suitable basis for the space of divergence-free velocities. The reduced problem is solved using parallel conjugate gradients preconditioned with an algebraically determined additive Schwarz domain decomposition preconditioner. The result is a solver which exhibits a good degree of robustness with respect to the mesh size as well as to the variance and to physically relevant values of the correlation length of the underlying permeability field. Numerical experiments exhibit almost optimal levels of parallel efficiency. The domain decomposition solver (DOUG, http://www.maths.bath.ac.uk/~parsoft) used here not only is applicable to this problem but can be used to solve general unstructured finite element systems on a wide range of parallel architectures.

An Implicit Solver on A Parallel Block-Structured Adaptive Mesh Grid for FLASH

NASA Astrophysics Data System (ADS)

Lee, D.; Gopal, S.; Mohapatra, P.

2012-07-01

We introduce a fully implicit solver for FLASH based on a Jacobian-Free Newton-Krylov (JFNK) approach with an appropriate preconditioner. The main goal of developing this JFNK-type implicit solver is to provide efficient high-order numerical algorithms and methodology for simulating stiff systems of differential equations on large-scale parallel computer architectures. A large number of natural problems in nonlinear physics involve a wide range of spatial and time scales of interest. A system that encompasses such a wide magnitude of scales is described as "stiff." A stiff system can arise in many different fields of physics, including fluid dynamics/aerodynamics, laboratory/space plasma physics, low Mach number flows, reactive flows, radiation hydrodynamics, and geophysical flows. One of the big challenges in solving such a stiff system using current-day computational resources lies in resolving time and length scales varying by several orders of magnitude. We introduce FLASH's preliminary implementation of a time-accurate JFNK-based implicit solver in the framework of FLASH's unsplit hydro solver.

Solving coupled groundwater flow systems using a Jacobian Free Newton Krylov method

NASA Astrophysics Data System (ADS)

Mehl, S.

2012-12-01

Jacobian Free Newton Kyrlov (JFNK) methods can have several advantages for simulating coupled groundwater flow processes versus conventional methods. Conventional methods are defined here as those based on an iterative coupling (rather than a direct coupling) and/or that use Picard iteration rather than Newton iteration. In an iterative coupling, the systems are solved separately, coupling information is updated and exchanged between the systems, and the systems are re-solved, etc., until convergence is achieved. Trusted simulators, such as Modflow, are based on these conventional methods of coupling and work well in many cases. An advantage of the JFNK method is that it only requires calculation of the residual vector of the system of equations and thus can make use of existing simulators regardless of how the equations are formulated. This opens the possibility of coupling different process models via augmentation of a residual vector by each separate process, which often requires substantially fewer changes to the existing source code than if the processes were directly coupled. However, appropriate perturbation sizes need to be determined for accurate approximations of the Frechet derivative, which is not always straightforward. Furthermore, preconditioning is necessary for reasonable convergence of the linear solution required at each Kyrlov iteration. Existing preconditioners can be used and applied separately to each process which maximizes use of existing code and robust preconditioners. In this work, iteratively coupled parent-child local grid refinement models of groundwater flow and groundwater flow models with nonlinear exchanges to streams are used to demonstrate the utility of the JFNK approach for Modflow models. Use of incomplete Cholesky preconditioners with various levels of fill are examined on a suite of nonlinear and linear models to analyze the effect of the preconditioner. Comparisons of convergence and computer simulation time are made using conventional iteratively coupled methods and those based on Picard iteration to those formulated with JFNK to gain insights on the types of nonlinearities and system features that make one approach advantageous. Results indicate that nonlinearities associated with stream/aquifer exchanges are more problematic than those resulting from unconfined flow.

A parallel electrostatic Particle-in-Cell method on unstructured tetrahedral grids for large-scale bounded collisionless plasma simulations

NASA Astrophysics Data System (ADS)

Averkin, Sergey N.; Gatsonis, Nikolaos A.

2018-06-01

An unstructured electrostatic Particle-In-Cell (EUPIC) method is developed on arbitrary tetrahedral grids for simulation of plasmas bounded by arbitrary geometries. The electric potential in EUPIC is obtained on cell vertices from a finite volume Multi-Point Flux Approximation of Gauss' law using the indirect dual cell with Dirichlet, Neumann and external circuit boundary conditions. The resulting matrix equation for the nodal potential is solved with a restarted generalized minimal residual method (GMRES) and an ILU(0) preconditioner algorithm, parallelized using a combination of node coloring and level scheduling approaches. The electric field on vertices is obtained using the gradient theorem applied to the indirect dual cell. The algorithms for injection, particle loading, particle motion, and particle tracking are parallelized for unstructured tetrahedral grids. The algorithms for the potential solver, electric field evaluation, loading, scatter-gather algorithms are verified using analytic solutions for test cases subject to Laplace and Poisson equations. Grid sensitivity analysis examines the L2 and L∞ norms of the relative error in potential, field, and charge density as a function of edge-averaged and volume-averaged cell size. Analysis shows second order of convergence for the potential and first order of convergence for the electric field and charge density. Temporal sensitivity analysis is performed and the momentum and energy conservation properties of the particle integrators in EUPIC are examined. The effects of cell size and timestep on heating, slowing-down and the deflection times are quantified. The heating, slowing-down and the deflection times are found to be almost linearly dependent on number of particles per cell. EUPIC simulations of current collection by cylindrical Langmuir probes in collisionless plasmas show good comparison with previous experimentally validated numerical results. These simulations were also used in a parallelization efficiency investigation. Results show that the EUPIC has efficiency of more than 80% when the simulation is performed on a single CPU from a non-uniform memory access node and the efficiency is decreasing as the number of threads further increases. The EUPIC is applied to the simulation of the multi-species plasma flow over a geometrically complex CubeSat in Low Earth Orbit. The EUPIC potential and flowfield distribution around the CubeSat exhibit features that are consistent with previous simulations over simpler geometrical bodies.

Assessment of Preconditioner for a USM3D Hierarchical Adaptive Nonlinear Method (HANIM) (Invited)

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2016-01-01

Enhancements to the previously reported mixed-element USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM) framework have been made to further improve robustness, efficiency, and accuracy of computational fluid dynamic simulations. The key enhancements include a multi-color line-implicit preconditioner, a discretely consistent symmetry boundary condition, and a line-mapping method for the turbulence source term discretization. The USM3D iterative convergence for the turbulent flows is assessed on four configurations. The configurations include a two-dimensional (2D) bump-in-channel, the 2D NACA 0012 airfoil, a three-dimensional (3D) bump-in-channel, and a 3D hemisphere cylinder. The Reynolds Averaged Navier Stokes (RANS) solutions have been obtained using a Spalart-Allmaras turbulence model and families of uniformly refined nested grids. Two types of HANIM solutions using line- and point-implicit preconditioners have been computed. Additional solutions using the point-implicit preconditioner alone (PA) method that broadly represents the baseline solver technology have also been computed. The line-implicit HANIM shows superior iterative convergence in most cases with progressively increasing benefits on finer grids.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE PAGES

Desai, Ajit; Khalil, Mohammad; Pettit, Chris; ...

2017-09-21

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

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

Desai, Ajit; Khalil, Mohammad; Pettit, Chris

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD

NASA Technical Reports Server (NTRS)

Gropp, W. D.; Keyes, D. E.; McInnes, L. C.; Tidriri, M. D.

1998-01-01

Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, "routine" parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (Psi-NKS) algorithmic framework is presented as an answer. We show that, for the classical problem of three-dimensional transonic Euler flow about an M6 wing, Psi-NKS can simultaneously deliver: globalized, asymptotically rapid convergence through adaptive pseudo- transient continuation and Newton's method-, reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per- processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of Psi-NKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. We therefore distill several recommendations from our experience and from our reading of the literature on various algorithmic components of Psi-NKS, and we describe a freely available, MPI-based portable parallel software implementation of the solver employed here.

Final Report for "Implimentation and Evaluation of Multigrid Linear Solvers into Extended Magnetohydrodynamic Codes for Petascale Computing"

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

Srinath Vadlamani; Scott Kruger; Travis Austin

Extended magnetohydrodynamic (MHD) codes are used to model the large, slow-growing instabilities that are projected to limit the performance of International Thermonuclear Experimental Reactor (ITER). The multiscale nature of the extended MHD equations requires an implicit approach. The current linear solvers needed for the implicit algorithm scale poorly because the resultant matrices are so ill-conditioned. A new solver is needed, especially one that scales to the petascale. The most successful scalable parallel processor solvers to date are multigrid solvers. Applying multigrid techniques to a set of equations whose fundamental modes are dispersive waves is a promising solution to CEMM problems.more » For the Phase 1, we implemented multigrid preconditioners from the HYPRE project of the Center for Applied Scientific Computing at LLNL via PETSc of the DOE SciDAC TOPS for the real matrix systems of the extended MHD code NIMROD which is a one of the primary modeling codes of the OFES-funded Center for Extended Magnetohydrodynamic Modeling (CEMM) SciDAC. We implemented the multigrid solvers on the fusion test problem that allows for real matrix systems with success, and in the process learned about the details of NIMROD data structures and the difficulties of inverting NIMROD operators. The further success of this project will allow for efficient usage of future petascale computers at the National Leadership Facilities: Oak Ridge National Laboratory, Argonne National Laboratory, and National Energy Research Scientific Computing Center. The project will be a collaborative effort between computational plasma physicists and applied mathematicians at Tech-X Corporation, applied mathematicians Front Range Scientific Computations, Inc. (who are collaborators on the HYPRE project), and other computational plasma physicists involved with the CEMM project.« less

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

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

Lin, Paul T.; Shadid, John N.; Tsuji, Paul H.

Here, this study explores the performance and scaling of a GMRES Krylov method employed as a smoother for an algebraic multigrid (AMG) preconditioned Newton- Krylov solution approach applied to a fully-implicit variational multiscale (VMS) nite element (FE) resistive magnetohydrodynamics (MHD) formulation. In this context a Newton iteration is used for the nonlinear system and a Krylov (GMRES) method is employed for the linear subsystems. The efficiency of this approach is critically dependent on the scalability and performance of the AMG preconditioner for the linear solutions and the performance of the smoothers play a critical role. Krylov smoothers are considered inmore » an attempt to reduce the time and memory requirements of existing robust smoothers based on additive Schwarz domain decomposition (DD) with incomplete LU factorization solves on each subdomain. Three time dependent resistive MHD test cases are considered to evaluate the method. The results demonstrate that the GMRES smoother can be faster due to a decrease in the preconditioner setup time and a reduction in outer GMRESR solver iterations, and requires less memory (typically 35% less memory for global GMRES smoother) than the DD ILU smoother.« less

Keeping it Together: Advanced algorithms and software for magma dynamics (and other coupled multi-physics problems)

NASA Astrophysics Data System (ADS)

Spiegelman, M.; Wilson, C. R.

2011-12-01

A quantitative theory of magma production and transport is essential for understanding the dynamics of magmatic plate boundaries, intra-plate volcanism and the geochemical evolution of the planet. It also provides one of the most challenging computational problems in solid Earth science, as it requires consistent coupling of fluid and solid mechanics together with the thermodynamics of melting and reactive flows. Considerable work on these problems over the past two decades shows that small changes in assumptions of coupling (e.g. the relationship between melt fraction and solid rheology), can have profound changes on the behavior of these systems which in turn affects critical computational choices such as discretizations, solvers and preconditioners. To make progress in exploring and understanding this physically rich system requires a computational framework that allows more flexible, high-level description of multi-physics problems as well as increased flexibility in composing efficient algorithms for solution of the full non-linear coupled system. Fortunately, recent advances in available computational libraries and algorithms provide a platform for implementing such a framework. We present results from a new model building system that leverages functionality from both the FEniCS project (www.fenicsproject.org) and PETSc libraries (www.mcs.anl.gov/petsc) along with a model independent options system and gui, Spud (amcg.ese.ic.ac.uk/Spud). Key features from FEniCS include fully unstructured FEM with a wide range of elements; a high-level language (ufl) and code generation compiler (FFC) for describing the weak forms of residuals and automatic differentiation for calculation of exact and approximate jacobians. The overall strategy is to monitor/calculate residuals and jacobians for the entire non-linear system of equations within a global non-linear solve based on PETSc's SNES routines. PETSc already provides a wide range of solvers and preconditioners, from parallel sparse direct to algebraic multigrid, that can be chosen at runtime. In particular, we make extensive use of PETSc's FieldSplit block preconditioners that allow us to use optimal solvers for subproblems (such as Stokes, or advection/diffusion of temperature) as preconditioners for the full problem. Thus these routines let us reuse effective solving recipes/splittings from previous experience while monitoring the convergence of the global problem. These techniques often yield quadratic (Newton like) convergence for the work of standard Picard schemes. We will illustrate this new framework with examples from the Magma Dynamic Demonstration suite (MADDs) of well understood magma dynamics benchmark problems including stokes flow in ridge geometries, magmatic solitary waves and shear-driven melt bands. While development of this system has been driven by magma dynamics, this framework is much more general and can be used for a wide range of PDE based multi-physics models.

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.

Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes

DOE PAGES

Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

2016-08-18

In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used tomore » project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.« less

Preconditioner and convergence study for the Quantum Computer Aided Design (QCAD) nonlinear poisson problem posed on the Ottawa Flat 270 design geometry.

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

Kalashnikova, Irina

2012-05-01

A numerical study aimed to evaluate different preconditioners within the Trilinos Ifpack and ML packages for the Quantum Computer Aided Design (QCAD) non-linear Poisson problem implemented within the Albany code base and posed on the Ottawa Flat 270 design geometry is performed. This study led to some new development of Albany that allows the user to select an ML preconditioner with Zoltan repartitioning based on nodal coordinates, which is summarized. Convergence of the numerical solutions computed within the QCAD computational suite with successive mesh refinement is examined in two metrics, the mean value of the solution (an L{sup 1} norm)more » and the field integral of the solution (L{sup 2} norm).« less

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

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

Lott, P. Aaron; Woodward, Carol S.; Evans, Katherine J.

Performing accurate and efficient numerical simulation of global atmospheric climate models is challenging due to the disparate length and time scales over which physical processes interact. Implicit solvers enable the physical system to be integrated with a time step commensurate with processes being studied. The dominant cost of an implicit time step is the ancillary linear system solves, so we have developed a preconditioner aimed at improving the efficiency of these linear system solves. Our preconditioner is based on an approximate block factorization of the linearized shallow-water equations and has been implemented within the spectral element dynamical core within themore » Community Atmospheric Model (CAM-SE). Furthermore, in this paper we discuss the development and scalability of the preconditioner for a suite of test cases with the implicit shallow-water solver within CAM-SE.« less

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Parallel Simulation of Three-Dimensional Free Surface Fluid Flow Problems

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

BAER,THOMAS A.; SACKINGER,PHILIP A.; SUBIA,SAMUEL R.

1999-10-14

Simulation of viscous three-dimensional fluid flow typically involves a large number of unknowns. When free surfaces are included, the number of unknowns increases dramatically. Consequently, this class of problem is an obvious application of parallel high performance computing. We describe parallel computation of viscous, incompressible, free surface, Newtonian fluid flow problems that include dynamic contact fines. The Galerkin finite element method was used to discretize the fully-coupled governing conservation equations and a ''pseudo-solid'' mesh mapping approach was used to determine the shape of the free surface. In this approach, the finite element mesh is allowed to deform to satisfy quasi-staticmore » solid mechanics equations subject to geometric or kinematic constraints on the boundaries. As a result, nodal displacements must be included in the set of unknowns. Other issues discussed are the proper constraints appearing along the dynamic contact line in three dimensions. Issues affecting efficient parallel simulations include problem decomposition to equally distribute computational work among a SPMD computer and determination of robust, scalable preconditioners for the distributed matrix systems that must be solved. Solution continuation strategies important for serial simulations have an enhanced relevance in a parallel coquting environment due to the difficulty of solving large scale systems. Parallel computations will be demonstrated on an example taken from the coating flow industry: flow in the vicinity of a slot coater edge. This is a three dimensional free surface problem possessing a contact line that advances at the web speed in one region but transitions to static behavior in another region. As such, a significant fraction of the computational time is devoted to processing boundary data. Discussion focuses on parallel speed ups for fixed problem size, a class of problems of immediate practical importance.« less

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

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

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3Dmore » sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.« less

A hierarchical preconditioner for the electric field integral equation on unstructured meshes based on primal and dual Haar bases

NASA Astrophysics Data System (ADS)

Adrian, S. B.; Andriulli, F. P.; Eibert, T. F.

2017-02-01

A new hierarchical basis preconditioner for the electric field integral equation (EFIE) operator is introduced. In contrast to existing hierarchical basis preconditioners, it works on arbitrary meshes and preconditions both the vector and the scalar potential within the EFIE operator. This is obtained by taking into account that the vector and the scalar potential discretized with loop-star basis functions are related to the hypersingular and the single layer operator (i.e., the well known integral operators from acoustics). For the single layer operator discretized with piecewise constant functions, a hierarchical preconditioner can easily be constructed. Thus the strategy we propose in this work for preconditioning the EFIE is the transformation of the scalar and the vector potential into operators equivalent to the single layer operator and to its inverse. More specifically, when the scalar potential is discretized with star functions as source and testing functions, the resulting matrix is a single layer operator discretized with piecewise constant functions and multiplied left and right with two additional graph Laplacian matrices. By inverting these graph Laplacian matrices, the discretized single layer operator is obtained, which can be preconditioned with the hierarchical basis. Dually, when the vector potential is discretized with loop functions, the resulting matrix can be interpreted as a hypersingular operator discretized with piecewise linear functions. By leveraging on a scalar Calderón identity, we can interpret this operator as spectrally equivalent to the inverse single layer operator. Then we use a linear-in-complexity, closed-form inverse of the dual hierarchical basis to precondition the hypersingular operator. The numerical results show the effectiveness of the proposed preconditioner and the practical impact of theoretical developments in real case scenarios.

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.

Three dimensional modelling of earthquake rupture cycles on frictional faults

NASA Astrophysics Data System (ADS)

Simpson, Guy; May, Dave

2017-04-01

We are developing an efficient MPI-parallel numerical method to simulate earthquake sequences on preexisting faults embedding within a three dimensional viscoelastic half-space. We solve the velocity form of the elasto(visco)dynamic equations using a continuous Galerkin Finite Element Method on an unstructured pentahedral mesh, which thus permits local spatial refinement in the vicinity of the fault. Friction sliding is coupled to the viscoelastic solid via rate- and state-dependent friction laws using the split-node technique. Our coupled formulation employs a picard-type non-linear solver with a fully implicit, first order accurate time integrator that utilises an adaptive time step that efficiently evolves the system through multiple seismic cycles. The implementation leverages advanced parallel solvers, preconditioners and linear algebra from the Portable Extensible Toolkit for Scientific Computing (PETSc) library. The model can treat heterogeneous frictional properties and stress states on the fault and surrounding solid as well as non-planar fault geometries. Preliminary tests show that the model successfully reproduces dynamic rupture on a vertical strike-slip fault in a half-space governed by rate-state friction with the ageing law.

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.

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

Jing Yanfei, E-mail: yanfeijing@uestc.edu.c; Huang Tingzhu, E-mail: tzhuang@uestc.edu.c; Duan Yong, E-mail: duanyong@yahoo.c

This study is mainly focused on iterative solutions with simple diagonal preconditioning to two complex-valued nonsymmetric systems of linear equations arising from a computational chemistry model problem proposed by Sherry Li of NERSC. Numerical experiments show the feasibility of iterative methods to some extent when applied to the problems and reveal the competitiveness of our recently proposed Lanczos biconjugate A-orthonormalization methods to other classic and popular iterative methods. By the way, experiment results also indicate that application specific preconditioners may be mandatory and required for accelerating convergence.

Weighted graph based ordering techniques for preconditioned conjugate gradient methods

NASA Technical Reports Server (NTRS)

Clift, Simon S.; Tang, Wei-Pai

1994-01-01

We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.

Udzawa-type iterative method with parareal preconditioner for a parabolic optimal control problem

NASA Astrophysics Data System (ADS)

Lapin, A.; Romanenko, A.

2016-11-01

The article deals with the optimal control problem with the parabolic equation as state problem. There are point-wise constraints on the state and control functions. The objective functional involves the observation given in the domain at each moment. The conditions for convergence Udzawa's type iterative method are given. The parareal method to inverse preconditioner is given. The results of calculations are presented.

Tensor-product preconditioners for a space-time discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2014-10-01

A space-time discontinuous Galerkin spectral element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is presented. A diagonalized alternating direction implicit preconditioner is extended to a space-time formulation using entropy variables. The effectiveness of this technique is demonstrated for the direct numerical simulation of turbulent flow in a channel.

Incompressible SPH (ISPH) with fast Poisson solver on a GPU

NASA Astrophysics Data System (ADS)

Chow, Alex D.; Rogers, Benedict D.; Lind, Steven J.; Stansby, Peter K.

2018-05-01

This paper presents a fast incompressible SPH (ISPH) solver implemented to run entirely on a graphics processing unit (GPU) capable of simulating several millions of particles in three dimensions on a single GPU. The ISPH algorithm is implemented by converting the highly optimised open-source weakly-compressible SPH (WCSPH) code DualSPHysics to run ISPH on the GPU, combining it with the open-source linear algebra library ViennaCL for fast solutions of the pressure Poisson equation (PPE). Several challenges are addressed with this research: constructing a PPE matrix every timestep on the GPU for moving particles, optimising the limited GPU memory, and exploiting fast matrix solvers. The ISPH pressure projection algorithm is implemented as 4 separate stages, each with a particle sweep, including an algorithm for the population of the PPE matrix suitable for the GPU, and mixed precision storage methods. An accurate and robust ISPH boundary condition ideal for parallel processing is also established by adapting an existing WCSPH boundary condition for ISPH. A variety of validation cases are presented: an impulsively started plate, incompressible flow around a moving square in a box, and dambreaks (2-D and 3-D) which demonstrate the accuracy, flexibility, and speed of the methodology. Fragmentation of the free surface is shown to influence the performance of matrix preconditioners and therefore the PPE matrix solution time. The Jacobi preconditioner demonstrates robustness and reliability in the presence of fragmented flows. For a dambreak simulation, GPU speed ups demonstrate up to 10-18 times and 1.1-4.5 times compared to single-threaded and 16-threaded CPU run times respectively.

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Preconditioning strategies for nonlinear conjugate gradient methods, based on quasi-Newton updates

NASA Astrophysics Data System (ADS)

Andrea, Caliciotti; Giovanni, Fasano; Massimo, Roma

2016-10-01

This paper reports two proposals of possible preconditioners for the Nonlinear Conjugate Gradient (NCG) method, in large scale unconstrained optimization. On one hand, the common idea of our preconditioners is inspired to L-BFGS quasi-Newton updates, on the other hand we aim at explicitly approximating in some sense the inverse of the Hessian matrix. Since we deal with large scale optimization problems, we propose matrix-free approaches where the preconditioners are built using symmetric low-rank updating formulae. Our distinctive new contributions rely on using information on the objective function collected as by-product of the NCG, at previous iterations. Broadly speaking, our first approach exploits the secant equation, in order to impose interpolation conditions on the objective function. In the second proposal we adopt and ad hoc modified-secant approach, in order to possibly guarantee some additional theoretical properties.

Real-time simulation of contact and cutting of heterogeneous soft-tissues.

PubMed

Courtecuisse, Hadrien; Allard, Jérémie; Kerfriden, Pierre; Bordas, Stéphane P A; Cotin, Stéphane; Duriez, Christian

2014-02-01

This paper presents a numerical method for interactive (real-time) simulations, which considerably improves the accuracy of the response of heterogeneous soft-tissue models undergoing contact, cutting and other topological changes. We provide an integrated methodology able to deal both with the ill-conditioning issues associated with material heterogeneities, contact boundary conditions which are one of the main sources of inaccuracies, and cutting which is one of the most challenging issues in interactive simulations. Our approach is based on an implicit time integration of a non-linear finite element model. To enable real-time computations, we propose a new preconditioning technique, based on an asynchronous update at low frequency. The preconditioner is not only used to improve the computation of the deformation of the tissues, but also to simulate the contact response of homogeneous and heterogeneous bodies with the same accuracy. We also address the problem of cutting the heterogeneous structures and propose a method to update the preconditioner according to the topological modifications. Finally, we apply our approach to three challenging demonstrators: (i) a simulation of cataract surgery (ii) a simulation of laparoscopic hepatectomy (iii) a brain tumor surgery. Copyright © 2013 Elsevier B.V. All rights reserved.

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

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

Feng, Wenqiang, E-mail: wfeng1@vols.utk.edu; Salgado, Abner J., E-mail: asalgad1@utk.edu; Wang, Cheng, E-mail: cwang1@umassd.edu

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a generalmore » framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.« less

A Tensor-Train accelerated solver for integral equations in complex geometries

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Rahimian, Abtin; Zorin, Denis

2017-04-01

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O (log ⁡ N) and once the inverse is computed, it can be applied in O (Nlog ⁡ N) . We analyze the QTT ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as FMM and HSS. We prove that the QTT ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the QTT decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the QTT-based solver when applied to both translation and non-translation invariant volume integrals in 3D. For boundary integral equations, we demonstrate that using a QTT decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the QTT preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries.

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Salgado, Abner J.; Wang, Cheng; Wise, Steven M.

2017-04-01

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems - including thin film epitaxy with slope selection and the square phase field crystal model - are carried out to verify the efficiency of the scheme.

High performance computation of radiative transfer equation using the finite element method

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Favennec, Y.

2018-05-01

This article deals with an efficient strategy for numerically simulating radiative transfer phenomena using distributed computing. The finite element method alongside the discrete ordinate method is used for spatio-angular discretization of the monochromatic steady-state radiative transfer equation in an anisotropically scattering media. Two very different methods of parallelization, angular and spatial decomposition methods, are presented. To do so, the finite element method is used in a vectorial way. A detailed comparison of scalability, performance, and efficiency on thousands of processors is established for two- and three-dimensional heterogeneous test cases. Timings show that both algorithms scale well when using proper preconditioners. It is also observed that our angular decomposition scheme outperforms our domain decomposition method. Overall, we perform numerical simulations at scales that were previously unattainable by standard radiative transfer equation solvers.

Improved L-BFGS diagonal preconditioners for a large-scale 4D-Var inversion system: application to CO2 flux constraints and analysis error calculation

NASA Astrophysics Data System (ADS)

Bousserez, Nicolas; Henze, Daven; Bowman, Kevin; Liu, Junjie; Jones, Dylan; Keller, Martin; Deng, Feng

2013-04-01

This work presents improved analysis error estimates for 4D-Var systems. From operational NWP models to top-down constraints on trace gas emissions, many of today's data assimilation and inversion systems in atmospheric science rely on variational approaches. This success is due to both the mathematical clarity of these formulations and the availability of computationally efficient minimization algorithms. However, unlike Kalman Filter-based algorithms, these methods do not provide an estimate of the analysis or forecast error covariance matrices, these error statistics being propagated only implicitly by the system. From both a practical (cycling assimilation) and scientific perspective, assessing uncertainties in the solution of the variational problem is critical. For large-scale linear systems, deterministic or randomization approaches can be considered based on the equivalence between the inverse Hessian of the cost function and the covariance matrix of analysis error. For perfectly quadratic systems, like incremental 4D-Var, Lanczos/Conjugate-Gradient algorithms have proven to be most efficient in generating low-rank approximations of the Hessian matrix during the minimization. For weakly non-linear systems though, the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), a quasi-Newton descent algorithm, is usually considered the best method for the minimization. Suitable for large-scale optimization, this method allows one to generate an approximation to the inverse Hessian using the latest m vector/gradient pairs generated during the minimization, m depending upon the available core memory. At each iteration, an initial low-rank approximation to the inverse Hessian has to be provided, which is called preconditioning. The ability of the preconditioner to retain useful information from previous iterations largely determines the efficiency of the algorithm. Here we assess the performance of different preconditioners to estimate the inverse Hessian of a large-scale 4D-Var system. The impact of using the diagonal preconditioners proposed by Gilbert and Le Maréchal (1989) instead of the usual Oren-Spedicato scalar will be first presented. We will also introduce new hybrid methods that combine randomization estimates of the analysis error variance with L-BFGS diagonal updates to improve the inverse Hessian approximation. Results from these new algorithms will be evaluated against standard large ensemble Monte-Carlo simulations. The methods explored here are applied to the problem of inferring global atmospheric CO2 fluxes using remote sensing observations, and are intended to be integrated with the future NASA Carbon Monitoring 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

Computational simulations of supersonic magnetohydrodynamic flow control, power and propulsion systems

NASA Astrophysics Data System (ADS)

Wan, Tian

This work is motivated by the lack of fully coupled computational tool that solves successfully the turbulent chemically reacting Navier-Stokes equation, the electron energy conservation equation and the electric current Poisson equation. In the present work, the abovementioned equations are solved in a fully coupled manner using fully implicit parallel GMRES methods. The system of Navier-Stokes equations are solved using a GMRES method with combined Schwarz and ILU(0) preconditioners. The electron energy equation and the electric current Poisson equation are solved using a GMRES method with combined SOR and Jacobi preconditioners. The fully coupled method has also been implemented successfully in an unstructured solver, US3D, and convergence test results were presented. This new method is shown two to five times faster than the original DPLR method. The Poisson solver is validated with analytic test problems. Then, four problems are selected; two of them are computed to explore the possibility of onboard MHD control and power generation, and the other two are simulation of experiments. First, the possibility of onboard reentry shock control by a magnetic field is explored. As part of a previous project, MHD power generation onboard a re-entry vehicle is also simulated. Then, the MHD acceleration experiments conducted at NASA Ames research center are simulated. Lastly, the MHD power generation experiments known as the HVEPS project are simulated. For code validation, the scramjet experiments at University of Queensland are simulated first. The generator section of the HVEPS test facility is computed then. The main conclusion is that the computational tool is accurate for different types of problems and flow conditions, and its accuracy and efficiency are necessary when the flow complexity increases.

Angular Multigrid Preconditioner for Krylov-Based Solution Techniques Applied to the Sn Equations with Highly Forward-Peaked Scattering

NASA Astrophysics Data System (ADS)

Turcksin, Bruno; Ragusa, Jean C.; Morel, Jim E.

2012-01-01

It is well known that the diffusion synthetic acceleration (DSA) methods for the Sn equations become ineffective in the Fokker-Planck forward-peaked scattering limit. In response to this deficiency, Morel and Manteuffel (1991) developed an angular multigrid method for the 1-D Sn equations. This method is very effective, costing roughly twice as much as DSA per source iteration, and yielding a maximum spectral radius of approximately 0.6 in the Fokker-Planck limit. Pautz, Adams, and Morel (PAM) (1999) later generalized the angular multigrid to 2-D, but it was found that the method was unstable with sufficiently forward-peaked mappings between the angular grids. The method was stabilized via a filtering technique based on diffusion operators, but this filtering also degraded the effectiveness of the overall scheme. The spectral radius was not bounded away from unity in the Fokker-Planck limit, although the method remained more effective than DSA. The purpose of this article is to recast the multidimensional PAM angular multigrid method without the filtering as an Sn preconditioner and use it in conjunction with the Generalized Minimal RESidual (GMRES) Krylov method. The approach ensures stability and our computational results demonstrate that it is also significantly more efficient than an analogous DSA-preconditioned Krylov method.

Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Swanson, Roy C., Jr.; Turkel, Eli; Rossow, C.-C.

2007-01-01

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.

Layout optimization with algebraic multigrid methods

NASA Technical Reports Server (NTRS)

Regler, Hans; Ruede, Ulrich

1993-01-01

Finding the optimal position for the individual cells (also called functional modules) on the chip surface is an important and difficult step in the design of integrated circuits. This paper deals with the problem of relative placement, that is the minimization of a quadratic functional with a large, sparse, positive definite system matrix. The basic optimization problem must be augmented by constraints to inhibit solutions where cells overlap. Besides classical iterative methods, based on conjugate gradients (CG), we show that algebraic multigrid methods (AMG) provide an interesting alternative. For moderately sized examples with about 10000 cells, AMG is already competitive with CG and is expected to be superior for larger problems. Besides the classical 'multiplicative' AMG algorithm where the levels are visited sequentially, we propose an 'additive' variant of AMG where levels may be treated in parallel and that is suitable as a preconditioner in the CG algorithm.

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.

Electrical Resistivity Tomography using a finite element based BFGS algorithm with algebraic multigrid preconditioning

NASA Astrophysics Data System (ADS)

Codd, A. L.; Gross, L.

2018-03-01

We present a new inversion method for Electrical Resistivity Tomography which, in contrast to established approaches, minimizes the cost function prior to finite element discretization for the unknown electric conductivity and electric potential. Minimization is performed with the Broyden-Fletcher-Goldfarb-Shanno method (BFGS) in an appropriate function space. BFGS is self-preconditioning and avoids construction of the dense Hessian which is the major obstacle to solving large 3-D problems using parallel computers. In addition to the forward problem predicting the measurement from the injected current, the so-called adjoint problem also needs to be solved. For this problem a virtual current is injected through the measurement electrodes and an adjoint electric potential is obtained. The magnitude of the injected virtual current is equal to the misfit at the measurement electrodes. This new approach has the advantage that the solution process of the optimization problem remains independent to the meshes used for discretization and allows for mesh adaptation during inversion. Computation time is reduced by using superposition of pole loads for the forward and adjoint problems. A smoothed aggregation algebraic multigrid (AMG) preconditioned conjugate gradient is applied to construct the potentials for a given electric conductivity estimate and for constructing a first level BFGS preconditioner. Through the additional reuse of AMG operators and coarse grid solvers inversion time for large 3-D problems can be reduced further. We apply our new inversion method to synthetic survey data created by the resistivity profile representing the characteristics of subsurface fluid injection. We further test it on data obtained from a 2-D surface electrode survey on Heron Island, a small tropical island off the east coast of central Queensland, Australia.

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

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

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

A Polynomial-Based Nonlinear Least Squares Optimized Preconditioner for Continuous and Discontinuous Element-Based Discretizations of the Euler Equations

DTIC Science & Technology

2014-01-01

system (here using left- preconditioning ) (KÃ)x = Kb̃, (3.1) where K is a low-order polynomial in à given by K = s(Ã) = m∑ i=0 kià i, (3.2) and has a... system with a complex spectrum, region E in the complex plane must be some convex form (e.g., an ellipse or polygon) that approximately encloses the...preconditioners with p = 2 and p = 20 on the spectrum of the preconditioned system matrices Kà and KH̃ for both CG Schur-complement form and DG form cases

Development of the PARVMEC Code for Rapid Analysis of 3D MHD Equilibrium

NASA Astrophysics Data System (ADS)

Seal, Sudip; Hirshman, Steven; Cianciosa, Mark; Wingen, Andreas; Unterberg, Ezekiel; Wilcox, Robert; ORNL Collaboration

2015-11-01

The VMEC three-dimensional (3D) MHD equilibrium has been used extensively for designing stellarator experiments and analyzing experimental data in such strongly 3D systems. Recent applications of VMEC include 2D systems such as tokamaks (in particular, the D3D experiment), where application of very small (delB/B ~ 10-3) 3D resonant magnetic field perturbations render the underlying assumption of axisymmetry invalid. In order to facilitate the rapid analysis of such equilibria (for example, for reconstruction purposes), we have undertaken the task of parallelizing the VMEC code (PARVMEC) to produce a scalable and temporally rapidly convergent equilibrium code for use on parallel distributed memory platforms. The parallelization task naturally splits into three distinct parts 1) radial surfaces in the fixed-boundary part of the calculation; 2) two 2D angular meshes needed to compute the Green's function integrals over the plasma boundary for the free-boundary part of the code; and 3) block tridiagonal matrix needed to compute the full (3D) pre-conditioner near the final equilibrium state. Preliminary results show that scalability is achieved for tasks 1 and 3, with task 2 still nearing completion. The impact of this work on the rapid reconstruction of D3D plasmas using PARVMEC in the V3FIT code will be discussed. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

First Applications of the New Parallel Krylov Solver for MODFLOW on a National and Global Scale

NASA Astrophysics Data System (ADS)

Verkaik, J.; Hughes, J. D.; Sutanudjaja, E.; van Walsum, P.

2016-12-01

Integrated high-resolution hydrologic models are increasingly being used for evaluating water management measures at field scale. Their drawbacks are large memory requirements and long run times. Examples of such models are The Netherlands Hydrological Instrument (NHI) model and the PCRaster Global Water Balance (PCR-GLOBWB) model. Typical simulation periods are 30-100 years with daily timesteps. The NHI model predicts water demands in periods of drought, supporting operational and long-term water-supply decisions. The NHI is a state-of-the-art coupling of several models: a 7-layer MODFLOW groundwater model ( 6.5M 250m cells), a MetaSWAP model for the unsaturated zone (Richards emulator of 0.5M cells), and a surface water model (MOZART-DM). The PCR-GLOBWB model provides a grid-based representation of global terrestrial hydrology and this work uses the version that includes a 2-layer MODFLOW groundwater model ( 4.5M 10km cells). The Parallel Krylov Solver (PKS) speeds up computation by both distributed memory parallelization (Message Passing Interface) and shared memory parallelization (Open Multi-Processing). PKS includes conjugate gradient, bi-conjugate gradient stabilized, and generalized minimal residual linear accelerators that use an overlapping additive Schwarz domain decomposition preconditioner. PKS can be used for both structured and unstructured grids and has been fully integrated in MODFLOW-USG using METIS partitioning and in iMODFLOW using RCB partitioning. iMODFLOW is an accelerated version of MODFLOW-2005 that is implicitly and online coupled to MetaSWAP. Results for benchmarks carried out on the Cartesius Dutch supercomputer (https://userinfo.surfsara.nl/systems/cartesius) for the PCRGLOB-WB model and on a 2x16 core Windows machine for the NHI model show speedups up to 10-20 and 5-10, respectively.

Two variants of minimum discarded fill ordering

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

D'Azevedo, E.F.; Forsyth, P.A.; Tang, Wei-Pai

1991-01-01

It is well known that the ordering of the unknowns can have a significant effect on the convergence of Preconditioned Conjugate Gradient (PCG) methods. There has been considerable experimental work on the effects of ordering for regular finite difference problems. In many cases, good results have been obtained with preconditioners based on diagonal, spiral or natural row orderings. However, for finite element problems having unstructured grids or grids generated by a local refinement approach, it is difficult to define many of the orderings for more regular problems. A recently proposed Minimum Discarded Fill (MDF) ordering technique is effective in findingmore » high quality Incomplete LU (ILU) preconditioners, especially for problems arising from unstructured finite element grids. Testing indicates this algorithm can identify a rather complicated physical structure in an anisotropic problem and orders the unknowns in the preferred'' direction. The MDF technique may be viewed as the numerical analogue of the minimum deficiency algorithm in sparse matrix technology. At any stage of the partial elimination, the MDF technique chooses the next pivot node so as to minimize the amount of discarded fill. In this work, two efficient variants of the MDF technique are explored to produce cost-effective high-order ILU preconditioners. The Threshold MDF orderings combine MDF ideas with drop tolerance techniques to identify the sparsity pattern in the ILU preconditioners. These techniques identify an ordering that encourages fast decay of the entries in the ILU factorization. The Minimum Update Matrix (MUM) ordering technique is a simplification of the MDF ordering and is closely related to the minimum degree algorithm. The MUM ordering is especially for large problems arising from Navier-Stokes problems. Some interesting pictures of the orderings are presented using a visualization tool. 22 refs., 4 figs., 7 tabs.« less

Iterative methods for mixed finite element equations

NASA Technical Reports Server (NTRS)

Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.

1985-01-01

Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

NASA Astrophysics Data System (ADS)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

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.

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.

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%.

Application of Conjugate Gradient methods to tidal simulation

USGS Publications Warehouse

Barragy, E.; Carey, G.F.; Walters, R.A.

1993-01-01

A harmonic decomposition technique is applied to the shallow water equations to yield a complex, nonsymmetric, nonlinear, Helmholtz type problem for the sea surface and an accompanying complex, nonlinear diagonal problem for the velocities. The equation for the sea surface is linearized using successive approximation and then discretized with linear, triangular finite elements. The study focuses on applying iterative methods to solve the resulting complex linear systems. The comparative evaluation includes both standard iterative methods for the real subsystems and complex versions of the well known Bi-Conjugate Gradient and Bi-Conjugate Gradient Squared methods. Several Incomplete LU type preconditioners are discussed, and the effects of node ordering, rejection strategy, domain geometry and Coriolis parameter (affecting asymmetry) are investigated. Implementation details for the complex case are discussed. Performance studies are presented and comparisons made with a frontal solver. ?? 1993.

Solving groundwater flow problems by conjugate-gradient methods and the strongly implicit procedure

USGS Publications Warehouse

Hill, Mary C.

1990-01-01

The performance of the preconditioned conjugate-gradient method with three preconditioners is compared with the strongly implicit procedure (SIP) using a scalar computer. The preconditioners considered are the incomplete Cholesky (ICCG) and the modified incomplete Cholesky (MICCG), which require the same computer storage as SIP as programmed for a problem with a symmetric matrix, and a polynomial preconditioner (POLCG), which requires less computer storage than SIP. Although POLCG is usually used on vector computers, it is included here because of its small storage requirements. In this paper, published comparisons of the solvers are evaluated, all four solvers are compared for the first time, and new test cases are presented to provide a more complete basis by which the solvers can be judged for typical groundwater flow problems. Based on nine test cases, the following conclusions are reached: (1) SIP is actually as efficient as ICCG for some of the published, linear, two-dimensional test cases that were reportedly solved much more efficiently by ICCG; (2) SIP is more efficient than other published comparisons would indicate when common convergence criteria are used; and (3) for problems that are three-dimensional, nonlinear, or both, and for which common convergence criteria are used, SIP is often more efficient than ICCG, and is sometimes more efficient than MICCG.

A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Biros, George

2017-01-01

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.

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.)

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

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

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

A fast, preconditioned conjugate gradient Toeplitz solver

NASA Technical Reports Server (NTRS)

Pan, Victor; Schrieber, Robert

1989-01-01

A simple factorization is given of an arbitrary hermitian, positive definite matrix in which the factors are well-conditioned, hermitian, and positive definite. In fact, given knowledge of the extreme eigenvalues of the original matrix A, an optimal improvement can be achieved, making the condition numbers of each of the two factors equal to the square root of the condition number of A. This technique is to applied to the solution of hermitian, positive definite Toeplitz systems. Large linear systems with hermitian, positive definite Toeplitz matrices arise in some signal processing applications. A stable fast algorithm is given for solving these systems that is based on the preconditioned conjugate gradient method. The algorithm exploits Toeplitz structure to reduce the cost of an iteration to O(n log n) by applying the fast Fourier Transform to compute matrix-vector products. Matrix factorization is used as a preconditioner.

Some Remarks on GMRES for Transport Theory

NASA Technical Reports Server (NTRS)

Patton, Bruce W.; Holloway, James Paul

2003-01-01

We review some work on the application of GMRES to the solution of the discrete ordinates transport equation in one-dimension. We note that GMRES can be applied directly to the angular flux vector, or it can be applied to only a vector of flux moments as needed to compute the scattering operator of the transport equation. In the former case we illustrate both the delights and defects of ILU right-preconditioners for problems with anisotropic scatter and for problems with upscatter. When working with flux moments we note that GMRES can be used as an accelerator for any existing transport code whose solver is based on a stationary fixed-point iteration, including transport sweeps and DSA transport sweeps. We also provide some numerical illustrations of this idea. We finally show how space can be traded for speed by taking multiple transport sweeps per GMRES iteration. Key Words: transport equation, GMRES, Krylov subspace

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner

NASA Astrophysics Data System (ADS)

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner.

PubMed

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

Composite solvers for linear saddle point problems arising from the incompressible Stokes equations with highly heterogeneous viscosity structure

NASA Astrophysics Data System (ADS)

Sanan, P.; Schnepp, S. M.; May, D.; Schenk, O.

2014-12-01

Geophysical applications require efficient forward models for non-linear Stokes flow on high resolution spatio-temporal domains. The bottleneck in applying the forward model is solving the linearized, discretized Stokes problem which takes the form of a large, indefinite (saddle point) linear system. Due to the heterogeniety of the effective viscosity in the elliptic operator, devising effective preconditioners for saddle point problems has proven challenging and highly problem-dependent. Nevertheless, at least three approaches show promise for preconditioning these difficult systems in an algorithmically scalable way using multigrid and/or domain decomposition techniques. The first is to work with a hierarchy of coarser or smaller saddle point problems. The second is to use the Schur complement method to decouple and sequentially solve for the pressure and velocity. The third is to use the Schur decomposition to devise preconditioners for the full operator. These involve sub-solves resembling inexact versions of the sequential solve. The choice of approach and sub-methods depends crucially on the motivating physics, the discretization, and available computational resources. Here we examine the performance trade-offs for preconditioning strategies applied to idealized models of mantle convection and lithospheric dynamics, characterized by large viscosity gradients. Due to the arbitrary topological structure of the viscosity field in geodynamical simulations, we utilize low order, inf-sup stable mixed finite element spatial discretizations which are suitable when sharp viscosity variations occur in element interiors. Particular attention is paid to possibilities within the decoupled and approximate Schur complement factorization-based monolithic approaches to leverage recently-developed flexible, communication-avoiding, and communication-hiding Krylov subspace methods in combination with `heavy' smoothers, which require solutions of large per-node sub-problems, well-suited to solution on hybrid computational clusters. To manage the combinatorial explosion of solver options (which include hybridizations of all the approaches mentioned above), we leverage the modularity of the PETSc library.

Preconditioned conjugate gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1994-01-01

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

Scalable algorithms for three-field mixed finite element coupled poromechanics

NASA Astrophysics Data System (ADS)

Castelletto, Nicola; White, Joshua A.; Ferronato, Massimiliano

2016-12-01

We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 × 3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. The performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions

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

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switchingmore » technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.« less

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions

DOE PAGES

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-02-06

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switchingmore » technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.« less

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

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

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

Chacon, Luis; Stanier, Adam John

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« 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

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Yang, Haijian; Sun, Shuyu; Yang, Chao

2017-03-01

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

AztecOO user guide.

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

Heroux, Michael Allen

2004-07-01

The Trilinos{trademark} Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries. AztecOO{trademark} is a package within Trilinos that enables the use of the Aztec solver library [19] with Epetra{trademark} [13] objects. AztecOO provides access to Aztec preconditioners and solvers by implementing the Aztec 'matrix-free' interface using Epetra. While Aztec is written in C and procedure-oriented, AztecOO is written in C++ and is object-oriented. In addition to providing access to Aztec capabilities, AztecOO also provides some signficant new functionality. In particular it provides an extensible status testing capability that allows expression of sophisticatedmore » stopping criteria as is needed in production use of iterative solvers. AztecOO also provides mechanisms for using Ifpack [2], ML [20] and AztecOO itself as preconditioners.« less

On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland W.

1992-01-01

The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed, which aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, we investigate the use of Bernstein-Szego weights.

Applicability of Kerker preconditioning scheme to the self-consistent density functional theory calculations of inhomogeneous systems

NASA Astrophysics Data System (ADS)

Zhou, Yuzhi; Wang, Han; Liu, Yu; Gao, Xingyu; Song, Haifeng

2018-03-01

The Kerker preconditioner, based on the dielectric function of homogeneous electron gas, is designed to accelerate the self-consistent field (SCF) iteration in the density functional theory calculations. However, a question still remains regarding its applicability to the inhomogeneous systems. We develop a modified Kerker preconditioning scheme which captures the long-range screening behavior of inhomogeneous systems and thus improves the SCF convergence. The effectiveness and efficiency is shown by the tests on long-z slabs of metals, insulators, and metal-insulator contacts. For situations without a priori knowledge of the system, we design the a posteriori indicator to monitor if the preconditioner has suppressed charge sloshing during the iterations. Based on the a posteriori indicator, we demonstrate two schemes of the self-adaptive configuration for the SCF iteration.

A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic Problems

NASA Technical Reports Server (NTRS)

Maliassov, Serguei

1996-01-01

In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.

Optimal preconditioning of lattice Boltzmann methods

NASA Astrophysics Data System (ADS)

Izquierdo, Salvador; Fueyo, Norberto

2009-09-01

A preconditioning technique to accelerate the simulation of steady-state problems using the single-relaxation-time (SRT) lattice Boltzmann (LB) method was first proposed by Guo et al. [Z. Guo, T. Zhao, Y. Shi, Preconditioned lattice-Boltzmann method for steady flows, Phys. Rev. E 70 (2004) 066706-1]. The key idea in this preconditioner is to modify the equilibrium distribution function in such a way that, by means of a Chapman-Enskog expansion, a time-derivative preconditioner of the Navier-Stokes (NS) equations is obtained. In the present contribution, the optimal values for the free parameter γ of this preconditioner are searched both numerically and theoretically; the later with the aid of linear-stability analysis and with the condition number of the system of NS equations. The influence of the collision operator, single- versus multiple-relaxation-times (MRT), is also studied. Three steady-state laminar test cases are used for validation, namely: the two-dimensional lid-driven cavity, a two-dimensional microchannel and the three-dimensional backward-facing step. Finally, guidelines are suggested for an a priori definition of optimal preconditioning parameters as a function of the Reynolds and Mach numbers. The new optimally preconditioned MRT method derived is shown to improve, simultaneously, the rate of convergence, the stability and the accuracy of the lattice Boltzmann simulations, when compared to the non-preconditioned methods and to the optimally preconditioned SRT one. Additionally, direct time-derivative preconditioning of the LB equation is also studied.

Preconditioned conjugate-gradient methods for low-speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations is integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the Lower-Upper Successive Symmetric Over-Relaxation iterative scheme is more efficient than a preconditioner based on Incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional Line Gauss-Seidel Relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Preconditioned Conjugate Gradient methods for low speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Application of PDSLin to the magnetic reconnection problem

NASA Astrophysics Data System (ADS)

Yuan, Xuefei; Li, Xiaoye S.; Yamazaki, Ichitaro; Jardin, Stephen C.; Koniges, Alice E.; Keyes, David E.

2013-01-01

Magnetic reconnection is a fundamental process in a magnetized plasma at both low and high magnetic Lundquist numbers (the ratio of the resistive diffusion time to the Alfvén wave transit time), which occurs in a wide variety of laboratory and space plasmas, e.g. magnetic fusion experiments, the solar corona and the Earth's magnetotail. An implicit time advance for the two-fluid magnetic reconnection problem is known to be difficult because of the large condition number of the associated matrix. This is especially troublesome when the collisionless ion skin depth is large so that the Whistler waves, which cause the fast reconnection, dominate the physics (Yuan et al 2012 J. Comput. Phys. 231 5822-53). For small system sizes, a direct solver such as SuperLU can be employed to obtain an accurate solution as long as the condition number is bounded by the reciprocal of the floating-point machine precision. However, SuperLU scales effectively only to hundreds of processors or less. For larger system sizes, it has been shown that physics-based (Chacón and Knoll 2003 J. Comput. Phys. 188 573-92) or other preconditioners can be applied to provide adequate solver performance. In recent years, we have been developing a new algebraic hybrid linear solver, PDSLin (Parallel Domain decomposition Schur complement-based Linear solver) (Yamazaki and Li 2010 Proc. VECPAR pp 421-34 and Yamazaki et al 2011 Technical Report). In this work, we compare numerical results from a direct solver and the proposed hybrid solver for the magnetic reconnection problem and demonstrate that the new hybrid solver is scalable to thousands of processors while maintaining the same robustness as a direct solver.

Layer-oriented multigrid wavefront reconstruction algorithms for multi-conjugate adaptive optics

NASA Astrophysics Data System (ADS)

Gilles, Luc; Ellerbroek, Brent L.; Vogel, Curtis R.

2003-02-01

Multi-conjugate adaptive optics (MCAO) systems with 104-105 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of AO degrees of freedom. In this paper, we develop an iterative sparse matrix implementation of minimum variance wavefront reconstruction for telescope diameters up to 32m with more than 104 actuators. The basic approach is the preconditioned conjugate gradient method, using a multigrid preconditioner incorporating a layer-oriented (block) symmetric Gauss-Seidel iterative smoothing operator. We present open-loop numerical simulation results to illustrate algorithm convergence.

Numerical Technology for Large-Scale Computational Electromagnetics

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

Sharpe, R; Champagne, N; White, D

The key bottleneck of implicit computational electromagnetics tools for large complex geometries is the solution of the resulting linear system of equations. The goal of this effort was to research and develop critical numerical technology that alleviates this bottleneck for large-scale computational electromagnetics (CEM). The mathematical operators and numerical formulations used in this arena of CEM yield linear equations that are complex valued, unstructured, and indefinite. Also, simultaneously applying multiple mathematical modeling formulations to different portions of a complex problem (hybrid formulations) results in a mixed structure linear system, further increasing the computational difficulty. Typically, these hybrid linear systems aremore » solved using a direct solution method, which was acceptable for Cray-class machines but does not scale adequately for ASCI-class machines. Additionally, LLNL's previously existing linear solvers were not well suited for the linear systems that are created by hybrid implicit CEM codes. Hence, a new approach was required to make effective use of ASCI-class computing platforms and to enable the next generation design capabilities. Multiple approaches were investigated, including the latest sparse-direct methods developed by our ASCI collaborators. In addition, approaches that combine domain decomposition (or matrix partitioning) with general-purpose iterative methods and special purpose pre-conditioners were investigated. Special-purpose pre-conditioners that take advantage of the structure of the matrix were adapted and developed based on intimate knowledge of the matrix properties. Finally, new operator formulations were developed that radically improve the conditioning of the resulting linear systems thus greatly reducing solution time. The goal was to enable the solution of CEM problems that are 10 to 100 times larger than our previous capability.« less

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.

A Robust Locally Preconditioned Semi-Coarsening Multigrid Algorithm for the 2-D Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Cain, Michael D.

1999-01-01

The goal of this thesis is to develop an efficient and robust locally preconditioned semi-coarsening multigrid algorithm for the two-dimensional Navier-Stokes equations. This thesis examines the performance of the multigrid algorithm with local preconditioning for an upwind-discretization of the Navier-Stokes equations. A block Jacobi iterative scheme is used because of its high frequency error mode damping ability. At low Mach numbers, the performance of a flux preconditioner is investigated. The flux preconditioner utilizes a new limiting technique based on local information that was developed by Siu. Full-coarsening and-semi-coarsening are examined as well as the multigrid V-cycle and full multigrid. The numerical tests were performed on a NACA 0012 airfoil at a range of Mach numbers. The tests show that semi-coarsening with flux preconditioning is the most efficient and robust combination of coarsening strategy, and iterative scheme - especially at low Mach numbers.

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2016-01-01

Several improvements to the mixed-element USM3D discretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Improved Convergence and Robustness of USM3D Solutions on Mixed-Element Grids

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frinks, Neal T.

2016-01-01

Several improvements to the mixed-elementUSM3Ddiscretization and defect-correction schemes have been made. A new methodology for nonlinear iterations, called the Hierarchical Adaptive Nonlinear Iteration Method, has been developed and implemented. The Hierarchical Adaptive Nonlinear Iteration Method provides two additional hierarchies around a simple and approximate preconditioner of USM3D. The hierarchies are a matrix-free linear solver for the exact linearization of Reynolds-averaged Navier-Stokes equations and a nonlinear control of the solution update. Two variants of the Hierarchical Adaptive Nonlinear Iteration Method are assessed on four benchmark cases, namely, a zero-pressure-gradient flat plate, a bump-in-channel configuration, the NACA 0012 airfoil, and a NASA Common Research Model configuration. The new methodology provides a convergence acceleration factor of 1.4 to 13 over the preconditioner-alone method representing the baseline solver technology.

Low-memory iterative density fitting.

PubMed

Grajciar, Lukáš

2015-07-30

A new low-memory modification of the density fitting approximation based on a combination of a continuous fast multipole method (CFMM) and a preconditioned conjugate gradient solver is presented. Iterative conjugate gradient solver uses preconditioners formed from blocks of the Coulomb metric matrix that decrease the number of iterations needed for convergence by up to one order of magnitude. The matrix-vector products needed within the iterative algorithm are calculated using CFMM, which evaluates them with the linear scaling memory requirements only. Compared with the standard density fitting implementation, up to 15-fold reduction of the memory requirements is achieved for the most efficient preconditioner at a cost of only 25% increase in computational time. The potential of the method is demonstrated by performing density functional theory calculations for zeolite fragment with 2592 atoms and 121,248 auxiliary basis functions on a single 12-core CPU workstation. © 2015 Wiley Periodicals, Inc.

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

DOE PAGES

Slaybaugh, R. N.; Ramirez-Zweiger, M.; Pandya, Tara; ...

2018-02-20

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MGmore » Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.« less

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

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

Slaybaugh, R. N.; Ramirez-Zweiger, M.; Pandya, Tara

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MGmore » Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.« less

Albany/FELIX: A parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

DOE PAGES

Tezaur, I. K.; Perego, M.; Salinger, A. G.; ...

2015-04-27

This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, alongmore » with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.« 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.

Advancing parabolic operators in thermodynamic MHD models: Explicit super time-stepping versus implicit schemes with Krylov solvers

NASA Astrophysics Data System (ADS)

Caplan, R. M.; Mikić, Z.; Linker, J. A.; Lionello, R.

2017-05-01

We explore the performance and advantages/disadvantages of using unconditionally stable explicit super time-stepping (STS) algorithms versus implicit schemes with Krylov solvers for integrating parabolic operators in thermodynamic MHD models of the solar corona. Specifically, we compare the second-order Runge-Kutta Legendre (RKL2) STS method with the implicit backward Euler scheme computed using the preconditioned conjugate gradient (PCG) solver with both a point-Jacobi and a non-overlapping domain decomposition ILU0 preconditioner. The algorithms are used to integrate anisotropic Spitzer thermal conduction and artificial kinematic viscosity at time-steps much larger than classic explicit stability criteria allow. A key component of the comparison is the use of an established MHD model (MAS) to compute a real-world simulation on a large HPC cluster. Special attention is placed on the parallel scaling of the algorithms. It is shown that, for a specific problem and model, the RKL2 method is comparable or surpasses the implicit method with PCG solvers in performance and scaling, but suffers from some accuracy limitations. These limitations, and the applicability of RKL methods are briefly discussed.

A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

DOE PAGES

Chacon, Luis; Stanier, Adam John

2016-12-01

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« less

An overview of NSPCG: A nonsymmetric preconditioned conjugate gradient package

NASA Astrophysics Data System (ADS)

Oppe, Thomas C.; Joubert, Wayne D.; Kincaid, David R.

1989-05-01

The most recent research-oriented software package developed as part of the ITPACK Project is called "NSPCG" since it contains many nonsymmetric preconditioned conjugate gradient procedures. It is designed to solve large sparse systems of linear algebraic equations by a variety of different iterative methods. One of the main purposes for the development of the package is to provide a common modular structure for research on iterative methods for nonsymmetric matrices. Another purpose for the development of the package is to investigate the suitability of several iterative methods for vector computers. Since the vectorizability of an iterative method depends greatly on the matrix structure, NSPCG allows great flexibility in the operator representation. The coefficient matrix can be passed in one of several different matrix data storage schemes. These sparse data formats allow matrices with a wide range of structures from highly structured ones such as those with all nonzeros along a relatively small number of diagonals to completely unstructured sparse matrices. Alternatively, the package allows the user to call the accelerators directly with user-supplied routines for performing certain matrix operations. In this case, one can use the data format from an application program and not be required to copy the matrix into one of the package formats. This is particularly advantageous when memory space is limited. Some of the basic preconditioners that are available are point methods such as Jacobi, Incomplete LU Decomposition and Symmetric Successive Overrelaxation as well as block and multicolor preconditioners. The user can select from a large collection of accelerators such as Conjugate Gradient (CG), Chebyshev (SI, for semi-iterative), Generalized Minimal Residual (GMRES), Biconjugate Gradient Squared (BCGS) and many others. The package is modular so that almost any accelerator can be used with almost any preconditioner.

Efficient preconditioning of the electronic structure problem in large scale ab initio molecular dynamics simulations

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

Schiffmann, Florian; VandeVondele, Joost, E-mail: Joost.VandeVondele@mat.ethz.ch

2015-06-28

We present an improved preconditioning scheme for electronic structure calculations based on the orbital transformation method. First, a preconditioner is developed which includes information from the full Kohn-Sham matrix but avoids computationally demanding diagonalisation steps in its construction. This reduces the computational cost of its construction, eliminating a bottleneck in large scale simulations, while maintaining rapid convergence. In addition, a modified form of Hotelling’s iterative inversion is introduced to replace the exact inversion of the preconditioner matrix. This method is highly effective during molecular dynamics (MD), as the solution obtained in earlier MD steps is a suitable initial guess. Filteringmore » small elements during sparse matrix multiplication leads to linear scaling inversion, while retaining robustness, already for relatively small systems. For system sizes ranging from a few hundred to a few thousand atoms, which are typical for many practical applications, the improvements to the algorithm lead to a 2-5 fold speedup per MD step.« less

Analysis of physics-based preconditioning for single-phase subchannel equations

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

Hansel, J. E.; Ragusa, J. C.; Allu, S.

2013-07-01

The (single-phase) subchannel approximations are used throughout nuclear engineering to provide an efficient flow simulation because the computational burden is much smaller than for computational fluid dynamics (CFD) simulations, and empirical relations have been developed and validated to provide accurate solutions in appropriate flow regimes. Here, the subchannel equations have been recast in a residual form suitable for a multi-physics framework. The Eigen spectrum of the Jacobian matrix, along with several potential physics-based preconditioning approaches, are evaluated, and the the potential for improved convergence from preconditioning is assessed. The physics-based preconditioner options include several forms of reduced equations that decouplemore » the subchannels by neglecting crossflow, conduction, and/or both turbulent momentum and energy exchange between subchannels. Eigen-scopy analysis shows that preconditioning moves clusters of eigenvalues away from zero and toward one. A test problem is run with and without preconditioning. Without preconditioning, the solution failed to converge using GMRES, but application of any of the preconditioners allowed the solution to converge. (authors)« less

Fully implicit adaptive mesh refinement solver for 2D MHD

NASA Astrophysics Data System (ADS)

Philip, B.; Chacon, L.; Pernice, M.

2008-11-01

Application of implicit adaptive mesh refinement (AMR) to simulate resistive magnetohydrodynamics is described. Solving this challenging multi-scale, multi-physics problem can improve understanding of reconnection in magnetically-confined plasmas. AMR is employed to resolve extremely thin current sheets, essential for an accurate macroscopic description. Implicit time stepping allows us to accurately follow the dynamical time scale of the developing magnetic field, without being restricted by fast Alfven time scales. At each time step, the large-scale system of nonlinear equations is solved by a Jacobian-free Newton-Krylov method together with a physics-based preconditioner. Each block within the preconditioner is solved optimally using the Fast Adaptive Composite grid method, which can be considered as a multiplicative Schwarz method on AMR grids. We will demonstrate the excellent accuracy and efficiency properties of the method with several challenging reduced MHD applications, including tearing, island coalescence, and tilt instabilities. B. Philip, L. Chac'on, M. Pernice, J. Comput. Phys., in press (2008)

An efficient method for model refinement in diffuse optical tomography

NASA Astrophysics Data System (ADS)

Zirak, A. R.; Khademi, M.

2007-11-01

Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.

Multilevel Preconditioners for Discontinuous Galerkin Approximations of Elliptic Problems with Jump Coefficients

DTIC Science & Technology

2010-12-01

discontinuous coefficients on geometrically nonconforming substructures. Technical Report Serie A 634, Instituto de Matematica Pura e Aplicada, Brazil, 2009...Instituto de Matematica Pura e Aplicada, Brazil, 2010. submitted. [41] M. Dryja, M. V. Sarkis, and O. B. Widlund. Multilevel Schwarz methods for

Efficient numerical calculation of MHD equilibria with magnetic islands, with particular application to saturated neoclassical tearing modes

NASA Astrophysics Data System (ADS)

Raburn, Daniel Louis

We have developed a preconditioned, globalized Jacobian-free Newton-Krylov (JFNK) solver for calculating equilibria with magnetic islands. The solver has been developed in conjunction with the Princeton Iterative Equilibrium Solver (PIES) and includes two notable enhancements over a traditional JFNK scheme: (1) globalization of the algorithm by a sophisticated backtracking scheme, which optimizes between the Newton and steepest-descent directions; and, (2) adaptive preconditioning, wherein information regarding the system Jacobian is reused between Newton iterations to form a preconditioner for our GMRES-like linear solver. We have developed a formulation for calculating saturated neoclassical tearing modes (NTMs) which accounts for the incomplete loss of a bootstrap current due to gradients of multiple physical quantities. We have applied the coupled PIES-JFNK solver to calculate saturated island widths on several shots from the Tokamak Fusion Test Reactor (TFTR) and have found reasonable agreement with experimental measurement.

A Study of Multigrid Preconditioners Using Eigensystem Analysis

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Swanson, R. C.

2005-01-01

The convergence properties of numerical schemes for partial differential equations are studied by examining the eigensystem of the discrete operator. This method of analysis is very general, and allows the effects of boundary conditions and grid nonuniformities to be examined directly. Algorithms for the Laplace equation and a two equation model hyperbolic system are examined.

Spectral element multigrid. Part 2: Theoretical justification

NASA Technical Reports Server (NTRS)

Maday, Yvon; Munoz, Rafael

1988-01-01

A multigrid algorithm is analyzed which is used for solving iteratively the algebraic system resulting from tha approximation of a second order problem by spectral or spectral element methods. The analysis, performed here in the one dimensional case, justifies the good smoothing properties of the Jacobi preconditioner that was presented in Part 1 of this paper.

The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Harada, Kyouji; Morimoto, Munenori; Sakakihara, Michio

2004-03-01

Several preconditioned iterative methods reported in the literature have been used for improving the convergence rate of the Gauss-Seidel method. In this article, on the basis of nonnegative matrix, comparisons between some splittings for such preconditioned matrices are derived. Simple numerical examples are also given.

A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Chen, Hao; Lv, Wen; Zhang, Tongtong

2018-05-01

We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.

StagBL : A Scalable, Portable, High-Performance Discretization and Solver Layer for Geodynamic Simulation

NASA Astrophysics Data System (ADS)

Sanan, P.; Tackley, P. J.; Gerya, T.; Kaus, B. J. P.; May, D.

2017-12-01

StagBL is an open-source parallel solver and discretization library for geodynamic simulation,encapsulating and optimizing operations essential to staggered-grid finite volume Stokes flow solvers.It provides a parallel staggered-grid abstraction with a high-level interface in C and Fortran.On top of this abstraction, tools are available to define boundary conditions and interact with particle systems.Tools and examples to efficiently solve Stokes systems defined on the grid are provided in small (direct solver), medium (simple preconditioners), and large (block factorization and multigrid) model regimes.By working directly with leading application codes (StagYY, I3ELVIS, and LaMEM) and providing an API and examples to integrate with others, StagBL aims to become a community tool supplying scalable, portable, reproducible performance toward novel science in regional- and planet-scale geodynamics and planetary science.By implementing kernels used by many research groups beneath a uniform abstraction layer, the library will enable optimization for modern hardware, thus reducing community barriers to large- or extreme-scale parallel simulation on modern architectures. In particular, the library will include CPU-, Manycore-, and GPU-optimized variants of matrix-free operators and multigrid components.The common layer provides a framework upon which to introduce innovative new tools.StagBL will leverage p4est to provide distributed adaptive meshes, and incorporate a multigrid convergence analysis tool.These options, in addition to a wealth of solver options provided by an interface to PETSc, will make the most modern solution techniques available from a common interface. StagBL in turn provides a PETSc interface, DMStag, to its central staggered grid abstraction.We present public version 0.5 of StagBL, including preliminary integration with application codes and demonstrations with its own demonstration application, StagBLDemo. Central to StagBL is the notion of an uninterrupted pipeline from toy/teaching codes to high-performance, extreme-scale solves. StagBLDemo replicates the functionality of an advanced MATLAB-style regional geodynamics code, thus providing users with a concrete procedure to exceed the performance and scalability limitations of smaller-scale tools.

Preconditioner Circuit Analysis

DTIC Science & Technology

2011-09-01

S) Matthew J. Nye 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Postgraduate School Monterey, CA 939435–000 8. PERFORMING... ORGANIZATION REPORT NUMBER 9. SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS(ES) N/A 10. SPONSORING/MONITORING AGENCY REPORT NUMBER 11...of the simulations and the theoretical computations. D. THESIS ORGANIZATION This thesis is organized into four chapters. The theoretical

An extended basis inexact shift-invert Lanczos for the efficient solution of large-scale generalized eigenproblems

NASA Astrophysics Data System (ADS)

Rewieński, M.; Lamecki, A.; Mrozowski, M.

2013-09-01

This paper proposes a technique, based on the Inexact Shift-Invert Lanczos (ISIL) method with Inexact Jacobi Orthogonal Component Correction (IJOCC) refinement, and a preconditioned conjugate-gradient (PCG) linear solver with multilevel preconditioner, for finding several eigenvalues for generalized symmetric eigenproblems. Several eigenvalues are found by constructing (with the ISIL process) an extended projection basis. Presented results of numerical experiments confirm the technique can be effectively applied to challenging, large-scale problems characterized by very dense spectra, such as resonant cavities with spatial dimensions which are large with respect to wavelengths of the resonating electromagnetic fields. It is also shown that the proposed scheme based on inexact linear solves delivers superior performance, as compared to methods which rely on exact linear solves, indicating tremendous potential of the 'inexact solve' concept. Finally, the scheme which generates an extended projection basis is found to provide a cost-efficient alternative to classical deflation schemes when several eigenvalues are computed.

A Partitioning Algorithm for Block-Diagonal Matrices With Overlap

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

Guy Antoine Atenekeng Kahou; Laura Grigori; Masha Sosonkina

2008-02-02

We present a graph partitioning algorithm that aims at partitioning a sparse matrix into a block-diagonal form, such that any two consecutive blocks overlap. We denote this form of the matrix as the overlapped block-diagonal matrix. The partitioned matrix is suitable for applying the explicit formulation of Multiplicative Schwarz preconditioner (EFMS) described in [3]. The graph partitioning algorithm partitions the graph of the input matrix into K partitions, such that every partition {Omega}{sub i} has at most two neighbors {Omega}{sub i-1} and {Omega}{sub i+1}. First, an ordering algorithm, such as the reverse Cuthill-McKee algorithm, that reduces the matrix profile ismore » performed. An initial overlapped block-diagonal partition is obtained from the profile of the matrix. An iterative strategy is then used to further refine the partitioning by allowing nodes to be transferred between neighboring partitions. Experiments are performed on matrices arising from real-world applications to show the feasibility and usefulness of this approach.« less

BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields

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

Oh, Duk -Soon; Widlund, Olof B.; Zampini, Stefano

Here, a BDDC domain decomposition preconditioner is defined by a coarse component, expressed in terms of primal constraints, a weighted average across the interface between the subdomains, and local components given in terms of solvers of local subdomain problems. BDDC methods for vector field problems discretized with Raviart-Thomas finite elements are introduced. The methods are based on a new type of weighted average an adaptive selection of primal constraints developed to deal with coefficients with high contrast even inside individual subdomains. For problems with very many subdomains, a third level of the preconditioner is introduced. Assuming that the subdomains aremore » all built from elements of a coarse triangulation of the given domain, and that in each subdomain the material parameters are consistent, one obtains a bound for the preconditioned linear system's condition number which is independent of the values and jumps of these parameters across the subdomains' interface. Numerical experiments, using the PETSc library, are also presented which support the theory and show the algorithms' effectiveness even for problems not covered by the theory. Also included are experiments with Brezzi-Douglas-Marini finite-element approximations.« less

A model reduction approach to numerical inversion for a parabolic partial differential equation

NASA Astrophysics Data System (ADS)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

BDDC algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields

DOE PAGES

Oh, Duk -Soon; Widlund, Olof B.; Zampini, Stefano; ...

2017-06-21

Here, a BDDC domain decomposition preconditioner is defined by a coarse component, expressed in terms of primal constraints, a weighted average across the interface between the subdomains, and local components given in terms of solvers of local subdomain problems. BDDC methods for vector field problems discretized with Raviart-Thomas finite elements are introduced. The methods are based on a new type of weighted average an adaptive selection of primal constraints developed to deal with coefficients with high contrast even inside individual subdomains. For problems with very many subdomains, a third level of the preconditioner is introduced. Assuming that the subdomains aremore » all built from elements of a coarse triangulation of the given domain, and that in each subdomain the material parameters are consistent, one obtains a bound for the preconditioned linear system's condition number which is independent of the values and jumps of these parameters across the subdomains' interface. Numerical experiments, using the PETSc library, are also presented which support the theory and show the algorithms' effectiveness even for problems not covered by the theory. Also included are experiments with Brezzi-Douglas-Marini finite-element approximations.« less

Recent advances in nonlinear implicit, electrostatic particle-in-cell (PIC) algorithms

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; Barnes, Daniel

2012-10-01

An implicit 1D electrostatic PIC algorithmfootnotetextChen, Chac'on, Barnes, J. Comput. Phys. 230 (2011) has been developed that satisfies exact energy and charge conservation. The algorithm employs a kinetic-enslaved Jacobian-free Newton-Krylov methodfootnotetextIbid. that ensures nonlinear convergence while taking timesteps comparable to the dynamical timescale of interest. Here we present two main improvements of the algorithm. The first is the formulation of a preconditioner based on linearized fluid equations, which are closed using available particle information. The computational benefit is that solving the fluid system is much cheaper than the kinetic one. The effectiveness of the preconditioner in accelerating nonlinear iterations on challenging problems will be demonstrated. A second improvement is the generalization of Ref. 1 to curvilinear meshes,footnotetextChac'on, Chen, Barnes, J. Comput. Phys. submitted (2012) with a hybrid particle update of positions and velocities in logical and physical space respectively.footnotetextSwift, J. Comp. Phys., 126 (1996) The curvilinear algorithm remains exactly charge and energy-conserving, and can be extended to multiple dimensions. We demonstrate the accuracy and efficiency of the algorithm with a 1D ion-acoustic shock wave simulation.

DVS-SOFTWARE: An Effective Tool for Applying Highly Parallelized Hardware To Computational Geophysics

NASA Astrophysics Data System (ADS)

Herrera, I.; Herrera, G. S.

2015-12-01

Most geophysical systems are macroscopic physical systems. The behavior prediction of such systems is carried out by means of computational models whose basic models are partial differential equations (PDEs) [1]. Due to the enormous size of the discretized version of such PDEs it is necessary to apply highly parallelized super-computers. For them, at present, the most efficient software is based on non-overlapping domain decomposition methods (DDM). However, a limiting feature of the present state-of-the-art techniques is due to the kind of discretizations used in them. Recently, I. Herrera and co-workers using 'non-overlapping discretizations' have produced the DVS-Software which overcomes this limitation [2]. The DVS-software can be applied to a great variety of geophysical problems and achieves very high parallel efficiencies (90%, or so [3]). It is therefore very suitable for effectively applying the most advanced parallel supercomputers available at present. In a parallel talk, in this AGU Fall Meeting, Graciela Herrera Z. will present how this software is being applied to advance MOD-FLOW. Key Words: Parallel Software for Geophysics, High Performance Computing, HPC, Parallel Computing, Domain Decomposition Methods (DDM)REFERENCES [1]. Herrera Ismael and George F. Pinder, Mathematical Modelling in Science and Engineering: An axiomatic approach", John Wiley, 243p., 2012. [2]. Herrera, I., de la Cruz L.M. and Rosas-Medina A. "Non Overlapping Discretization Methods for Partial, Differential Equations". NUMER METH PART D E, 30: 1427-1454, 2014, DOI 10.1002/num 21852. (Open source) [3]. Herrera, I., & Contreras Iván "An Innovative Tool for Effectively Applying Highly Parallelized Software To Problems of Elasticity". Geofísica Internacional, 2015 (In press)

Architecting the Finite Element Method Pipeline for the GPU.

PubMed

Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T

2014-02-01

The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.

Identification of immiscible NAPL contaminant sources in aquifers by a modified two-level saturation based imperialist competitive algorithm.

PubMed

Ghafouri, H R; Mosharaf-Dehkordi, M; Afzalan, B

2017-07-01

A simulation-optimization model is proposed for identifying the characteristics of local immiscible NAPL contaminant sources inside aquifers. This model employs the UTCHEM 9.0 software as its simulator for solving the governing equations associated with the multi-phase flow in porous media. As the optimization model, a novel two-level saturation based Imperialist Competitive Algorithm (ICA) is proposed to estimate the parameters of contaminant sources. The first level consists of three parallel independent ICAs and plays as a pre-conditioner for the second level which is a single modified ICA. The ICA in the second level is modified by dividing each country into a number of provinces (smaller parts). Similar to countries in the classical ICA, these provinces are optimized by the assimilation, competition, and revolution steps in the ICA. To increase the diversity of populations, a new approach named knock the base method is proposed. The performance and accuracy of the simulation-optimization model is assessed by solving a set of two and three-dimensional problems considering the effects of different parameters such as the grid size, rock heterogeneity and designated monitoring networks. The obtained numerical results indicate that using this simulation-optimization model provides accurate results at a less number of iterations when compared with the model employing the classical one-level ICA. Copyright © 2017 Elsevier B.V. All rights reserved.

Scan line graphics generation on the massively parallel processor

NASA Technical Reports Server (NTRS)

Dorband, John E.

1988-01-01

Described here is how researchers implemented a scan line graphics generation algorithm on the Massively Parallel Processor (MPP). Pixels are computed in parallel and their results are applied to the Z buffer in large groups. To perform pixel value calculations, facilitate load balancing across the processors and apply the results to the Z buffer efficiently in parallel requires special virtual routing (sort computation) techniques developed by the author especially for use on single-instruction multiple-data (SIMD) architectures.

M-step preconditioned conjugate gradient methods

NASA Technical Reports Server (NTRS)

Adams, L.

1983-01-01

Preconditioned conjugate gradient methods for solving sparse symmetric and positive finite systems of linear equations are described. Necessary and sufficient conditions are given for when these preconditioners can be used and an analysis of their effectiveness is given. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.

A modified conjugate gradient method based on the Tikhonov system for computerized tomography (CT).

PubMed

Wang, Qi; Wang, Huaxiang

2011-04-01

During the past few decades, computerized tomography (CT) was widely used for non-destructive testing (NDT) and non-destructive examination (NDE) in the industrial area because of its characteristics of non-invasiveness and visibility. Recently, CT technology has been applied to multi-phase flow measurement. Using the principle of radiation attenuation measurements along different directions through the investigated object with a special reconstruction algorithm, cross-sectional information of the scanned object can be worked out. It is a typical inverse problem and has always been a challenge for its nonlinearity and ill-conditions. The Tikhonov regulation method is widely used for similar ill-posed problems. However, the conventional Tikhonov method does not provide reconstructions with qualities good enough, the relative errors between the reconstructed images and the real distribution should be further reduced. In this paper, a modified conjugate gradient (CG) method is applied to a Tikhonov system (MCGT method) for reconstructing CT images. The computational load is dominated by the number of independent measurements m, and a preconditioner is imported to lower the condition number of the Tikhonov system. Both simulation and experiment results indicate that the proposed method can reduce the computational time and improve the quality of image reconstruction. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Transport synthetic acceleration with opposing reflecting boundary conditions

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

Zika, M.R.; Adams, M.L.

2000-02-01

The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iteratingmore » on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.« less

A multilevel preconditioner for domain decomposition boundary systems

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

Bramble, J.H.; Pasciak, J.E.; Xu, Jinchao.

1991-12-11

In this note, we consider multilevel preconditioning of the reduced boundary systems which arise in non-overlapping domain decomposition methods. It will be shown that the resulting preconditioned systems have condition numbers which be bounded in the case of multilevel spaces on the whole domain and grow at most proportional to the number of levels in the case of multilevel boundary spaces without multilevel extensions into the interior.

Fractional Step Like Schemes for Free Surface Problems with Thermal Coupling Using the Lagrangian PFEM

NASA Astrophysics Data System (ADS)

Aubry, R.; Oñate, E.; Idelsohn, S. R.

2006-09-01

The method presented in Aubry et al. (Comput Struc 83:1459-1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of motion is extended to three dimensions (3D) with particular emphasis on mass conservation. A modified fractional step (FS) based on the pressure Schur complement (Turek 1999), and related to the class of algebraic splittings Quarteroni et al. (Comput Methods Appl Mech Eng 188:505-526, 2000), is used and a new advantage of the splittings of the equations compared with the classical FS is highlighted for free surface problems. The temperature is semi-coupled with the displacement, which is the main variable in a Lagrangian description. Comparisons for various mesh Reynolds numbers are performed with the classical FS, an algebraic splitting and a monolithic solution, in order to illustrate the behaviour of the Uzawa operator and the mass conservation. As the classical fractional step is equivalent to one iteration of the Uzawa algorithm performed with a standard Laplacian as a preconditioner, it will behave well only in a Reynold mesh number domain where the preconditioner is efficient. Numerical results are provided to assess the superiority of the modified algebraic splitting to the classical FS.

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

DOE PAGES

Svyatsky, Daniil; Lipnikov, Konstantin

2017-03-18

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

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

Svyatsky, Daniil; Lipnikov, Konstantin

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

Efficient Coupling of Fluid-Plasma and Monte-Carlo-Neutrals Models for Edge Plasma Transport

NASA Astrophysics Data System (ADS)

Dimits, A. M.; Cohen, B. I.; Friedman, A.; Joseph, I.; Lodestro, L. L.; Rensink, M. E.; Rognlien, T. D.; Sjogreen, B.; Stotler, D. P.; Umansky, M. V.

2017-10-01

UEDGE has been valuable for modeling transport in the tokamak edge and scrape-off layer due in part to its efficient fully implicit solution of coupled fluid neutrals and plasma models. We are developing an implicit coupling of the kinetic Monte-Carlo (MC) code DEGAS-2, as the neutrals model component, to the UEDGE plasma component, based on an extension of the Jacobian-free Newton-Krylov (JFNK) method to MC residuals. The coupling components build on the methods and coding already present in UEDGE. For the linear Krylov iterations, a procedure has been developed to ``extract'' a good preconditioner from that of UEDGE. This preconditioner may also be used to greatly accelerate the convergence rate of a relaxed fixed-point iteration, which may provide a useful ``intermediate'' algorithm. The JFNK method also requires calculation of Jacobian-vector products, for which any finite-difference procedure is inaccurate when a MC component is present. A semi-analytical procedure that retains the standard MC accuracy and fully kinetic neutrals physics is therefore being developed. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and LDRD project 15-ERD-059, by PPPL under Contract DE-AC02-09CH11466, and supported in part by the U.S. DOE, OFES.

A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation.

PubMed

Gumerov, Nail A; Duraiswami, Ramani

2009-01-01

The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001 less, similarkD less, similar500 are presented and shown to perform close to theoretical expectations.

Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods

NASA Astrophysics Data System (ADS)

Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco

2015-04-01

The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface resistivity. The Hessian of the regularization term is used as preconditioner which requires an additional PDE solution in each iteration step. As it turns out, the relevant PDEs are naturally formulated in the finite element framework. Using the domain decomposition method provided in Escript, the inversion scheme has been parallelized for distributed memory computers with multi-core shared memory nodes. We show numerical examples from simple layered models to complex 3D models and compare with the results from other methods. The inversion scheme is furthermore tested on a field data example to characterise localised freshwater discharge in a coastal environment.. References: L. Gross and C. Kemp (2013) Large Scale Joint Inversion of Geophysical Data using the Finite Element Method in escript. ASEG Extended Abstracts 2013, http://dx.doi.org/10.1071/ASEG2013ab306

Parallel workflow tools to facilitate human brain MRI post-processing

PubMed Central

Cui, Zaixu; Zhao, Chenxi; Gong, Gaolang

2015-01-01

Multi-modal magnetic resonance imaging (MRI) techniques are widely applied in human brain studies. To obtain specific brain measures of interest from MRI datasets, a number of complex image post-processing steps are typically required. Parallel workflow tools have recently been developed, concatenating individual processing steps and enabling fully automated processing of raw MRI data to obtain the final results. These workflow tools are also designed to make optimal use of available computational resources and to support the parallel processing of different subjects or of independent processing steps for a single subject. Automated, parallel MRI post-processing tools can greatly facilitate relevant brain investigations and are being increasingly applied. In this review, we briefly summarize these parallel workflow tools and discuss relevant issues. PMID:26029043

Applying Parallel Processing Techniques to Tether Dynamics Simulation

NASA Technical Reports Server (NTRS)

Wells, B. Earl

1996-01-01

The focus of this research has been to determine the effectiveness of applying parallel processing techniques to a sizable real-world problem, the simulation of the dynamics associated with a tether which connects two objects in low earth orbit, and to explore the degree to which the parallelization process can be automated through the creation of new software tools. The goal has been to utilize this specific application problem as a base to develop more generally applicable techniques.

Combustion Stability Innovations for Liquid Rocket

DTIC Science & Technology

2010-01-31

waves within the pipe . Acoustic time for one pass = 0.003 sec. Closed end The following figure shows the second harmonic of the quarter wave mode at...waveguides at the center of the test section. The two drivers at either end can operate at sync or at a specified phase difference. The effect of close ...preserve conservation in real time. The preconditioner operates on the inner loop driving the solution to the next time level. Sufficient number of inner

Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa

2017-12-01

Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.

Fully anisotropic 3-D EM modelling on a Lebedev grid with a multigrid pre-conditioner

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil V.; de la Kethulle de Ryhove, Sébastien; Bratteland, Tarjei

2016-12-01

We present a numerical algorithm for 3-D electromagnetic (EM) simulations in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3-D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For synthetic data corresponding to a 3-D model with a TTI anticlinal structure, a standard vertical transverse isotropic (VTI) inversion is not able to image a resistor, while for a 3-D model with a TTI synclinal structure it produces a false resistive anomaly. However, if the VTI forward solver used in the inversion is replaced by the proposed TTI solver with perfect knowledge of the strike and dip of the dipping structures, the resulting resistivity images become consistent with the true models.

Parallel pivoting combined with parallel reduction

NASA Technical Reports Server (NTRS)

Alaghband, Gita

1987-01-01

Parallel algorithms for triangularization of large, sparse, and unsymmetric matrices are presented. The method combines the parallel reduction with a new parallel pivoting technique, control over generations of fill-ins and a check for numerical stability, all done in parallel with the work being distributed over the active processes. The parallel technique uses the compatibility relation between pivots to identify parallel pivot candidates and uses the Markowitz number of pivots to minimize fill-in. This technique is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds.

Ion manipulation method and device

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

Anderson, Gordon A.; Baker, Erin M.; Smith, Richard D.

2017-11-07

An ion manipulation method and device is disclosed. The device includes a pair of substantially parallel surfaces. An array of inner electrodes is contained within, and extends substantially along the length of, each parallel surface. The device includes a first outer array of electrodes and a second outer array of electrodes. Each outer array of electrodes is positioned on either side of the inner electrodes, and is contained within and extends substantially along the length of each parallel surface. A DC voltage is applied to the first and second outer array of electrodes. A RF voltage, with a superimposed electricmore » field, is applied to the inner electrodes by applying the DC voltages to each electrode. Ions either move between the parallel surfaces within an ion confinement area or along paths in the direction of the electric field, or can be trapped in the ion confinement area.« less

Ion manipulation device

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

Anderson, Gordon A.; Baker, Erin M.; Smith, Richard D.

2018-05-08

An ion manipulation method and device is disclosed. The device includes a pair of substantially parallel surfaces. An array of inner electrodes is contained within, and extends substantially along the length of, each parallel surface. The device includes a first outer array of electrodes and a second outer array of electrodes. Each outer array of electrodes is positioned on either side of the inner electrodes, and is contained within and extends substantially along the length of each parallel surface. A DC voltage is applied to the first and second outer array of electrodes. A RF voltage, with a superimposed electricmore » field, is applied to the inner electrodes by applying the DC voltages to each electrode. Ions either move between the parallel surfaces within an ion confinement area or along paths in the direction of the electric field, or can be trapped in the ion confinement area.« less

Parallel Implicit Runge-Kutta Methods Applied to Coupled Orbit/Attitude Propagation

NASA Astrophysics Data System (ADS)

Hatten, Noble; Russell, Ryan P.

2017-12-01

A variable-step Gauss-Legendre implicit Runge-Kutta (GLIRK) propagator is applied to coupled orbit/attitude propagation. Concepts previously shown to improve efficiency in 3DOF propagation are modified and extended to the 6DOF problem, including the use of variable-fidelity dynamics models. The impact of computing the stage dynamics of a single step in parallel is examined using up to 23 threads and 22 associated GLIRK stages; one thread is reserved for an extra dynamics function evaluation used in the estimation of the local truncation error. Efficiency is found to peak for typical examples when using approximately 8 to 12 stages for both serial and parallel implementations. Accuracy and efficiency compare favorably to explicit Runge-Kutta and linear-multistep solvers for representative scenarios. However, linear-multistep methods are found to be more efficient for some applications, particularly in a serial computing environment, or when parallelism can be applied across multiple trajectories.

Adaptive Implicit Non-Equilibrium Radiation Diffusion

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

Philip, Bobby; Wang, Zhen; Berrill, Mark A

2013-01-01

We describe methods for accurate and efficient long term time integra- tion of non-equilibrium radiation diffusion systems: implicit time integration for effi- cient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while control- ling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

Generalized Preconditioned Locally Harmonic Residual Eigensolver (GPLHR) v0.1

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

VECHARYNSKI, EUGENE; YANG, CHAO

The software contains a MATLAB implementation of the Generalized Preconditioned Locally Harmonic Residual (GPLHR) method for solving standard and generalized non-Hermitian eigenproblems. The method is particularly useful for computing a subset of eigenvalues, and their eigen- or Schur vectors, closest to a given shift. The proposed method is based on block iterations and can take advantage of a preconditioner if it is available. It does not need to perform exact shift-and-invert transformation. Standard and generalized eigenproblems are handled in a unified framework.

Runtime support for parallelizing data mining algorithms

NASA Astrophysics Data System (ADS)

Jin, Ruoming; Agrawal, Gagan

2002-03-01

With recent technological advances, shared memory parallel machines have become more scalable, and offer large main memories and high bus bandwidths. They are emerging as good platforms for data warehousing and data mining. In this paper, we focus on shared memory parallelization of data mining algorithms. We have developed a series of techniques for parallelization of data mining algorithms, including full replication, full locking, fixed locking, optimized full locking, and cache-sensitive locking. Unlike previous work on shared memory parallelization of specific data mining algorithms, all of our techniques apply to a large number of common data mining algorithms. In addition, we propose a reduction-object based interface for specifying a data mining algorithm. We show how our runtime system can apply any of the technique we have developed starting from a common specification of the algorithm.

Parallel Architecture, Parallel Acquisition Cross-Linguistic Evidence from Nominal and Verbal Domains

ERIC Educational Resources Information Center

Sutton, Brett R.

2017-01-01

This dissertation explores parallels between Complementizer Phrase (CP) and Determiner Phrase (DP) semantics, syntax, and morphology--including similarities in case-assignment, subject-verb and possessor-possessum agreement, subject and possessor semantics, and overall syntactic structure--in first language acquisition. Applying theoretical…

ParaBTM: A Parallel Processing Framework for Biomedical Text Mining on Supercomputers.

PubMed

Xing, Yuting; Wu, Chengkun; Yang, Xi; Wang, Wei; Zhu, En; Yin, Jianping

2018-04-27

A prevailing way of extracting valuable information from biomedical literature is to apply text mining methods on unstructured texts. However, the massive amount of literature that needs to be analyzed poses a big data challenge to the processing efficiency of text mining. In this paper, we address this challenge by introducing parallel processing on a supercomputer. We developed paraBTM, a runnable framework that enables parallel text mining on the Tianhe-2 supercomputer. It employs a low-cost yet effective load balancing strategy to maximize the efficiency of parallel processing. We evaluated the performance of paraBTM on several datasets, utilizing three types of named entity recognition tasks as demonstration. Results show that, in most cases, the processing efficiency can be greatly improved with parallel processing, and the proposed load balancing strategy is simple and effective. In addition, our framework can be readily applied to other tasks of biomedical text mining besides NER.

Vacuum chamber for ion manipulation device

DOEpatents

Chen, Tsung-Chi; Tang, Keqi; Ibrahim, Yehia M; Smith, Richard D; Anderson, Gordon A; Baker, Erin M

2014-12-09

An ion manipulation method and device is disclosed. The device includes a pair of substantially parallel surfaces. An array of inner electrodes is contained within, and extends substantially along the length of, each parallel surface. The device includes a first outer array of electrodes and a second outer array of electrodes. Each outer array of electrodes is positioned on either side of the inner electrodes, and is contained within and extends substantially along the length of each parallel surface. A DC voltage is applied to the first and second outer array of electrodes. A RF voltage, with a superimposed electric field, is applied to the inner electrodes by applying the DC voltages to each electrode. Ions either move between the parallel surfaces within an ion confinement area or along paths in the direction of the electric field, or can be trapped in the ion confinement area. A predetermined number of pairs of surfaces are disposed in one or more chambers, forming a multiple-layer ion mobility cyclotron device.

Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction

PubMed Central

Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

2012-01-01

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constrain involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the preconditioned alternating projection algorithm. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality. PMID:23271835

Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG

DOE PAGES

Shadid, J. N.; Pawlowski, R. P.; Cyr, E. C.; ...

2016-02-10

Here, we discuss that the computational solution of the governing balance equations for mass, momentum, heat transfer and magnetic induction for resistive magnetohydrodynamics (MHD) systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fully-implicit stabilized unstructured finite element (FE) capability for 3D incompressible resistive MHD. The discussion considers the development of a stabilized FE formulation in context of the variational multiscale (VMS) method,more » and describes the scalable implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, that include MHD duct flows, an unstable hydromagnetic Kelvin–Helmholtz shear layer, and a 3D island coalescence problem used to model magnetic reconnection. Initial results that explore the scaling of the solution methods are also presented on up to 128K processors for problems with up to 1.8B unknowns on a CrayXK7.« less

SymPix: A Spherical Grid for Efficient Sampling of Rotationally Invariant Operators

NASA Astrophysics Data System (ADS)

Seljebotn, D. S.; Eriksen, H. K.

2016-02-01

We present SymPix, a special-purpose spherical grid optimized for efficiently sampling rotationally invariant linear operators. This grid is conceptually similar to the Gauss-Legendre (GL) grid, aligning sample points with iso-latitude rings located on Legendre polynomial zeros. Unlike the GL grid, however, the number of grid points per ring varies as a function of latitude, avoiding expensive oversampling near the poles and ensuring nearly equal sky area per grid point. The ratio between the number of grid points in two neighboring rings is required to be a low-order rational number (3, 2, 1, 4/3, 5/4, or 6/5) to maintain a high degree of symmetries. Our main motivation for this grid is to solve linear systems using multi-grid methods, and to construct efficient preconditioners through pixel-space sampling of the linear operator in question. As a benchmark and representative example, we compute a preconditioner for a linear system that involves the operator \\widehat{{\\boldsymbol{D}}}+{\\widehat{{\\boldsymbol{B}}}}T{{\\boldsymbol{N}}}-1\\widehat{{\\boldsymbol{B}}}, where \\widehat{{\\boldsymbol{B}}} and \\widehat{{\\boldsymbol{D}}} may be described as both local and rotationally invariant operators, and {\\boldsymbol{N}} is diagonal in the pixel domain. For a bandwidth limit of {{\\ell }}{max} = 3000, we find that our new SymPix implementation yields average speed-ups of 360 and 23 for {\\widehat{{\\boldsymbol{B}}}}T{{\\boldsymbol{N}}}-1\\widehat{{\\boldsymbol{B}}} and \\widehat{{\\boldsymbol{D}}}, respectively, compared with the previous state-of-the-art implementation.

Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction

NASA Astrophysics Data System (ADS)

Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

2012-11-01

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constraint involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the PAPA. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

NASA Astrophysics Data System (ADS)

Chen, Hui; Deng, Ju-Zhi; Yin, Min; Yin, Chang-Chun; Tang, Wen-Wu

2017-03-01

To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

IETI – Isogeometric Tearing and Interconnecting

PubMed Central

Kleiss, Stefan K.; Pechstein, Clemens; Jüttler, Bert; Tomar, Satyendra

2012-01-01

Finite Element Tearing and Interconnecting (FETI) methods are a powerful approach to designing solvers for large-scale problems in computational mechanics. The numerical simulation problem is subdivided into a number of independent sub-problems, which are then coupled in appropriate ways. NURBS- (Non-Uniform Rational B-spline) based isogeometric analysis (IGA) applied to complex geometries requires to represent the computational domain as a collection of several NURBS geometries. Since there is a natural decomposition of the computational domain into several subdomains, NURBS-based IGA is particularly well suited for using FETI methods. This paper proposes the new IsogEometric Tearing and Interconnecting (IETI) method, which combines the advanced solver design of FETI with the exact geometry representation of IGA. We describe the IETI framework for two classes of simple model problems (Poisson and linearized elasticity) and discuss the coupling of the subdomains along interfaces (both for matching interfaces and for interfaces with T-joints, i.e. hanging nodes). Special attention is paid to the construction of a suitable preconditioner for the iterative linear solver used for the interface problem. We report several computational experiments to demonstrate the performance of the proposed IETI method. PMID:24511167

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

NASA Astrophysics Data System (ADS)

Heinkenschloss, Matthias

2005-01-01

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

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

Helmholtz and parabolic equation solutions to a benchmark problem in ocean acoustics.

PubMed

Larsson, Elisabeth; Abrahamsson, Leif

2003-05-01

The Helmholtz equation (HE) describes wave propagation in applications such as acoustics and electromagnetics. For realistic problems, solving the HE is often too expensive. Instead, approximations like the parabolic wave equation (PE) are used. For low-frequency shallow-water environments, one persistent problem is to assess the accuracy of the PE model. In this work, a recently developed HE solver that can handle a smoothly varying bathymetry, variable material properties, and layered materials, is used for an investigation of the errors in PE solutions. In the HE solver, a preconditioned Krylov subspace method is applied to the discretized equations. The preconditioner combines domain decomposition and fast transform techniques. A benchmark problem with upslope-downslope propagation over a penetrable lossy seamount is solved. The numerical experiments show that, for the same bathymetry, a soft and slow bottom gives very similar HE and PE solutions, whereas the PE model is far from accurate for a hard and fast bottom. A first attempt to estimate the error is made by computing the relative deviation from the energy balance for the PE solution. This measure gives an indication of the magnitude of the error, but cannot be used as a strict error bound.

Scalable subsurface inverse modeling of huge data sets with an application to tracer concentration breakthrough data from magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Lee, Jonghyun; Yoon, Hongkyu; Kitanidis, Peter K.; Werth, Charles J.; Valocchi, Albert J.

2016-07-01

Characterizing subsurface properties is crucial for reliable and cost-effective groundwater supply management and contaminant remediation. With recent advances in sensor technology, large volumes of hydrogeophysical and geochemical data can be obtained to achieve high-resolution images of subsurface properties. However, characterization with such a large amount of information requires prohibitive computational costs associated with "big data" processing and numerous large-scale numerical simulations. To tackle such difficulties, the principal component geostatistical approach (PCGA) has been proposed as a "Jacobian-free" inversion method that requires much smaller forward simulation runs for each iteration than the number of unknown parameters and measurements needed in the traditional inversion methods. PCGA can be conveniently linked to any multiphysics simulation software with independent parallel executions. In this paper, we extend PCGA to handle a large number of measurements (e.g., 106 or more) by constructing a fast preconditioner whose computational cost scales linearly with the data size. For illustration, we characterize the heterogeneous hydraulic conductivity (K) distribution in a laboratory-scale 3-D sand box using about 6 million transient tracer concentration measurements obtained using magnetic resonance imaging. Since each individual observation has little information on the K distribution, the data were compressed by the zeroth temporal moment of breakthrough curves, which is equivalent to the mean travel time under the experimental setting. Only about 2000 forward simulations in total were required to obtain the best estimate with corresponding estimation uncertainty, and the estimated K field captured key patterns of the original packing design, showing the efficiency and effectiveness of the proposed method.

Parallel Computational Fluid Dynamics: Current Status and Future Requirements

NASA Technical Reports Server (NTRS)

Simon, Horst D.; VanDalsem, William R.; Dagum, Leonardo; Kutler, Paul (Technical Monitor)

1994-01-01

One or the key objectives of the Applied Research Branch in the Numerical Aerodynamic Simulation (NAS) Systems Division at NASA Allies Research Center is the accelerated introduction of highly parallel machines into a full operational environment. In this report we discuss the performance results obtained from the implementation of some computational fluid dynamics (CFD) applications on the Connection Machine CM-2 and the Intel iPSC/860. We summarize some of the experiences made so far with the parallel testbed machines at the NAS Applied Research Branch. Then we discuss the long term computational requirements for accomplishing some of the grand challenge problems in computational aerosciences. We argue that only massively parallel machines will be able to meet these grand challenge requirements, and we outline the computer science and algorithm research challenges ahead.

A New Coarsening Operator for the Optimal Preconditioning of the Dual and Primal Domain Decomposition Methods: Application to Problems with Severe Coefficient Jumps

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Rixen, Daniel

1996-01-01

We present an optimal preconditioning algorithm that is equally applicable to the dual (FETI) and primal (Balancing) Schur complement domain decomposition methods, and which successfully addresses the problems of subdomain heterogeneities including the effects of large jumps of coefficients. The proposed preconditioner is derived from energy principles and embeds a new coarsening operator that propagates the error globally and accelerates convergence. The resulting iterative solver is illustrated with the solution of highly heterogeneous elasticity problems.

ASDTIC control and standardized interface circuits applied to buck, parallel and buck-boost dc to dc power converters

NASA Technical Reports Server (NTRS)

Schoenfeld, A. D.; Yu, Y.

1973-01-01

Versatile standardized pulse modulation nondissipatively regulated control signal processing circuits were applied to three most commonly used dc to dc power converter configurations: (1) the series switching buck-regulator, (2) the pulse modulated parallel inverter, and (3) the buck-boost converter. The unique control concept and the commonality of control functions for all switching regulators have resulted in improved static and dynamic performance and control circuit standardization. New power-circuit technology was also applied to enhance reliability and to achieve optimum weight and efficiency.

Amélioration des performances d'une implantation parallélovectorielle du gradient conjugué par extension du schéma de stockage matriciel

NASA Astrophysics Data System (ADS)

Magnin, H.; Coulomb, J. L.

1993-03-01

Electromagnetic field computation with the Finite Element (FE) method implies solving of large linear systems of equations. Performances and memory capacities of today computers allow to achieve three-dimensional FE discretizations of electromagnetic problems, but the number of unknowns grows high. So, to improve time to the numerical solution of the linear system(s) thus arising, the use of parallel and/or vector computers has to be envisaged. In this paper, the main constitutive steps of the Pre-conditioned Conjugate Gradient algorithm (PCG) are analysed. After a short recall of our previous work concerning their improvement by use of vector and parallel computations, we show some speedup limitations due to the sparse row-wise matrix storage scheme employed. Then, an extension of this matrix representation is proposed, leading to introduce redundant storage of non-zero coefficients. In spite of the “memory waste” thus implied, it is shown how this extension can be successfully employed to increase the speedup due to parallelism and vectorization on the whole algorithm, and in particular to derive a parallel preconditioner. La résolution par la méthode des éléments finis des équations de l'électromagnétisme conduit à résoudre de grands systèmes d'équations linéaires. Les capacités mémoire et les performances actuelles des systèmes informatiques permettent de traiter les problèmes électromagnétiques par discrétisation tridimensionnelle, mais alors le nombre d'inconnues devient très élevé. Ainsi, la résolution en un temps raisonnable des équations linéaires associées à de telles discrétisations conduit à envisager l'emploi d'ordinateurs à architecture parallèle. Dans cet article, les différentes étapes constitutives de l'algorithme du gradient conjugué préconditionné (GCP) sont analysées. Après un court rappel de nos travaux antérieurs concemant leur amélioration par utilisation de traitements parallèles et vectoriels, nous montrons les limitations du gain de temps dues au mode de stockage matriciel utilisé : la représentation creuse dite “Morse”. Nous proposons alors une extension de ce mode de stockage, conduisant à l'introduction de redondance au niveau du rangement des termes matriciels en mémoire. Malgré le “gaspillage” mémoire ainsi occasionné, il apparait que cette extension peut être mise à profit pour augmenter sensiblement les gains par parallélisation et vectorisation de l'ensemble de l'algorithme du gradient conjugué, et notamment pour la réalisation d'un pré-conditionnement parallèle.

Ion manipulation device with electrical breakdown protection

DOEpatents

Chen, Tsung-Chi; Tang, Keqi; Ibrahim, Yehia M; Smith, Richard D; Anderson, Gordon A; Baker, Erin M

2014-12-02

An ion manipulation method and device is disclosed. The device includes a pair of substantially parallel surfaces. An array of inner electrodes is contained within, and extends substantially along the length of, each parallel surface. The device includes a first outer array of electrodes and a second outer array of electrodes. Each outer array of electrodes is positioned on either side of the inner electrodes, and is contained within and extends substantially along the length of each parallel surface. A DC voltage is applied to the first and second outer array of electrodes. A RF voltage, with a superimposed electric field, is applied to the inner electrodes by applying the DC voltages to each electrode. Ions either move between the parallel surfaces within an ion confinement area or along paths in the direction of the electric field, or can be trapped in the ion confinement area. The surfaces are housed in a chamber, and at least one electrically insulative shield is coupled to an inner surface of the chamber for increasing a mean-free-path between two adjacent electrodes in the chamber.

Parallel and Serial Grouping of Image Elements in Visual Perception

ERIC Educational Resources Information Center

Houtkamp, Roos; Roelfsema, Pieter R.

2010-01-01

The visual system groups image elements that belong to an object and segregates them from other objects and the background. Important cues for this grouping process are the Gestalt criteria, and most theories propose that these are applied in parallel across the visual scene. Here, we find that Gestalt grouping can indeed occur in parallel in some…

Applications of New Surrogate Global Optimization Algorithms including Efficient Synchronous and Asynchronous Parallelism for Calibration of Expensive Nonlinear Geophysical Simulation Models.

NASA Astrophysics Data System (ADS)

Shoemaker, C. A.; Pang, M.; Akhtar, T.; Bindel, D.

2016-12-01

New parallel surrogate global optimization algorithms are developed and applied to objective functions that are expensive simulations (possibly with multiple local minima). The algorithms can be applied to most geophysical simulations, including those with nonlinear partial differential equations. The optimization does not require simulations be parallelized. Asynchronous (and synchronous) parallel execution is available in the optimization toolbox "pySOT". The parallel algorithms are modified from serial to eliminate fine grained parallelism. The optimization is computed with open source software pySOT, a Surrogate Global Optimization Toolbox that allows user to pick the type of surrogate (or ensembles), the search procedure on surrogate, and the type of parallelism (synchronous or asynchronous). pySOT also allows the user to develop new algorithms by modifying parts of the code. In the applications here, the objective function takes up to 30 minutes for one simulation, and serial optimization can take over 200 hours. Results from Yellowstone (NSF) and NCSS (Singapore) supercomputers are given for groundwater contaminant hydrology simulations with applications to model parameter estimation and decontamination management. All results are compared with alternatives. The first results are for optimization of pumping at many wells to reduce cost for decontamination of groundwater at a superfund site. The optimization runs with up to 128 processors. Superlinear speed up is obtained for up to 16 processors, and efficiency with 64 processors is over 80%. Each evaluation of the objective function requires the solution of nonlinear partial differential equations to describe the impact of spatially distributed pumping and model parameters on model predictions for the spatial and temporal distribution of groundwater contaminants. The second application uses an asynchronous parallel global optimization for groundwater quality model calibration. The time for a single objective function evaluation varies unpredictably, so efficiency is improved with asynchronous parallel calculations to improve load balancing. The third application (done at NCSS) incorporates new global surrogate multi-objective parallel search algorithms into pySOT and applies it to a large watershed calibration problem.

Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach

DOE PAGES

Usabiaga, Florencio Balboa; Kallemov, Bakytzhan; Delmotte, Blaise; ...

2016-01-12

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest numbermore » of iterations that is essentially independent of the number of particles. Key to the efficiency of the method is a technique for fast computation of the product of the blob-blob mobility matrix and a vector. For unbounded suspensions, we rely on existing analytical expressions for the Rotne-Prager-Yamakawa tensor combined with a fast multipole method (FMM) to obtain linear scaling in the number of particles. For suspensions sedimented against a single no-slip boundary, we use a direct summation on a graphical processing unit (GPU), which gives quadratic asymptotic scaling with the number of particles. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently developed rigid-body immersed boundary method by B. Kallemov, A. P. S. Bhalla, B. E. Griffith, and A. Donev (Commun. Appl. Math. Comput. Sci. 11 (2016), no. 1, 79-141) to suspensions of freely moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid-body equations converges in a bounded number of iterations regardless of the system size. In our approach, each iteration only requires a few cycles of a geometric multigrid solver for the Poisson equation, and an application of the block-diagonal preconditioner, leading to linear scaling with the number of particles. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.« less

Feynman’s clock, a new variational principle, and parallel-in-time quantum dynamics

PubMed Central

McClean, Jarrod R.; Parkhill, John A.; Aspuru-Guzik, Alán

2013-01-01

We introduce a discrete-time variational principle inspired by the quantum clock originally proposed by Feynman and use it to write down quantum evolution as a ground-state eigenvalue problem. The construction allows one to apply ground-state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover, this formalism naturally leads to an algorithm to parallelize quantum simulation over time. We draw an explicit connection between previously known time-dependent variational principles and the time-embedded variational principle presented. Sample calculations are presented, applying the idea to a hydrogen molecule and the spin degrees of freedom of a model inorganic compound, demonstrating the parallel speedup of our method as well as its flexibility in applying ground-state methodologies. Finally, we take advantage of the unique perspective of this variational principle to examine the error of basis approximations in quantum dynamics. PMID:24062428

Ultrasonically-assisted Thermal Stir Welding System

NASA Technical Reports Server (NTRS)

Ding, R. Jeffrey (Inventor)

2014-01-01

A welding head assembly has a work piece disposed between its containment plates' opposing surfaces with the work piece being maintained in a plastic state thereof at least in a vicinity of the welding head assembly's stir rod as the rod is rotated about its longitudinal axis. The welding head assembly and the work piece experience relative movement there between in a direction perpendicular to the rod's longitudinal axis as the work piece is subjected to a compressive force applied by the containment plates. A first source coupled to the first containment plate applies a first ultrasonic wave thereto such that the first ultrasonic wave propagates parallel to the direction of relative movement. A second source coupled to the second containment plate applies a second ultrasonic wave thereto such that the second ultrasonic wave propagates parallel to the direction of relative movement.propagates parallel to the direction of relative movement.

Time Parallel Solution of Linear Partial Differential Equations on the Intel Touchstone Delta Supercomputer

NASA Technical Reports Server (NTRS)

Toomarian, N.; Fijany, A.; Barhen, J.

1993-01-01

Evolutionary partial differential equations are usually solved by decretization in time and space, and by applying a marching in time procedure to data and algorithms potentially parallelized in the spatial domain.

Rough Electrode Creates Excess Capacitance in Thin-Film Capacitors

PubMed Central

2017-01-01

The parallel-plate capacitor equation is widely used in contemporary material research for nanoscale applications and nanoelectronics. To apply this equation, flat and smooth electrodes are assumed for a capacitor. This essential assumption is often violated for thin-film capacitors because the formation of nanoscale roughness at the electrode interface is very probable for thin films grown via common deposition methods. In this work, we experimentally and theoretically show that the electrical capacitance of thin-film capacitors with realistic interface roughness is significantly larger than the value predicted by the parallel-plate capacitor equation. The degree of the deviation depends on the strength of the roughness, which is described by three roughness parameters for a self-affine fractal surface. By applying an extended parallel-plate capacitor equation that includes the roughness parameters of the electrode, we are able to calculate the excess capacitance of the electrode with weak roughness. Moreover, we introduce the roughness parameter limits for which the simple parallel-plate capacitor equation is sufficiently accurate for capacitors with one rough electrode. Our results imply that the interface roughness beyond the proposed limits cannot be dismissed unless the independence of the capacitance from the interface roughness is experimentally demonstrated. The practical protocols suggested in our work for the reliable use of the parallel-plate capacitor equation can be applied as general guidelines in various fields of interest. PMID:28745040

Rough Electrode Creates Excess Capacitance in Thin-Film Capacitors.

PubMed

Torabi, Solmaz; Cherry, Megan; Duijnstee, Elisabeth A; Le Corre, Vincent M; Qiu, Li; Hummelen, Jan C; Palasantzas, George; Koster, L Jan Anton

2017-08-16

The parallel-plate capacitor equation is widely used in contemporary material research for nanoscale applications and nanoelectronics. To apply this equation, flat and smooth electrodes are assumed for a capacitor. This essential assumption is often violated for thin-film capacitors because the formation of nanoscale roughness at the electrode interface is very probable for thin films grown via common deposition methods. In this work, we experimentally and theoretically show that the electrical capacitance of thin-film capacitors with realistic interface roughness is significantly larger than the value predicted by the parallel-plate capacitor equation. The degree of the deviation depends on the strength of the roughness, which is described by three roughness parameters for a self-affine fractal surface. By applying an extended parallel-plate capacitor equation that includes the roughness parameters of the electrode, we are able to calculate the excess capacitance of the electrode with weak roughness. Moreover, we introduce the roughness parameter limits for which the simple parallel-plate capacitor equation is sufficiently accurate for capacitors with one rough electrode. Our results imply that the interface roughness beyond the proposed limits cannot be dismissed unless the independence of the capacitance from the interface roughness is experimentally demonstrated. The practical protocols suggested in our work for the reliable use of the parallel-plate capacitor equation can be applied as general guidelines in various fields of interest.

Partitioning and packing mathematical simulation models for calculation on parallel computers

NASA Technical Reports Server (NTRS)

Arpasi, D. J.; Milner, E. J.

1986-01-01

The development of multiprocessor simulations from a serial set of ordinary differential equations describing a physical system is described. Degrees of parallelism (i.e., coupling between the equations) and their impact on parallel processing are discussed. The problem of identifying computational parallelism within sets of closely coupled equations that require the exchange of current values of variables is described. A technique is presented for identifying this parallelism and for partitioning the equations for parallel solution on a multiprocessor. An algorithm which packs the equations into a minimum number of processors is also described. The results of the packing algorithm when applied to a turbojet engine model are presented in terms of processor utilization.

A heterogeneous computing accelerated SCE-UA global optimization method using OpenMP, OpenCL, CUDA, and OpenACC.

PubMed

Kan, Guangyuan; He, Xiaoyan; Ding, Liuqian; Li, Jiren; Liang, Ke; Hong, Yang

2017-10-01

The shuffled complex evolution optimization developed at the University of Arizona (SCE-UA) has been successfully applied in various kinds of scientific and engineering optimization applications, such as hydrological model parameter calibration, for many years. The algorithm possesses good global optimality, convergence stability and robustness. However, benchmark and real-world applications reveal the poor computational efficiency of the SCE-UA. This research aims at the parallelization and acceleration of the SCE-UA method based on powerful heterogeneous computing technology. The parallel SCE-UA is implemented on Intel Xeon multi-core CPU (by using OpenMP and OpenCL) and NVIDIA Tesla many-core GPU (by using OpenCL, CUDA, and OpenACC). The serial and parallel SCE-UA were tested based on the Griewank benchmark function. Comparison results indicate the parallel SCE-UA significantly improves computational efficiency compared to the original serial version. The OpenCL implementation obtains the best overall acceleration results however, with the most complex source code. The parallel SCE-UA has bright prospects to be applied in real-world applications.

Scalable subsurface inverse modeling of huge data sets with an application to tracer concentration breakthrough data from magnetic resonance imaging

DOE PAGES

Lee, Jonghyun; Yoon, Hongkyu; Kitanidis, Peter K.; ...

2016-06-09

When characterizing subsurface properties is crucial for reliable and cost-effective groundwater supply management and contaminant remediation. With recent advances in sensor technology, large volumes of hydro-geophysical and geochemical data can be obtained to achieve high-resolution images of subsurface properties. However, characterization with such a large amount of information requires prohibitive computational costs associated with “big data” processing and numerous large-scale numerical simulations. To tackle such difficulties, the Principal Component Geostatistical Approach (PCGA) has been proposed as a “Jacobian-free” inversion method that requires much smaller forward simulation runs for each iteration than the number of unknown parameters and measurements needed inmore » the traditional inversion methods. PCGA can be conveniently linked to any multi-physics simulation software with independent parallel executions. In our paper, we extend PCGA to handle a large number of measurements (e.g. 106 or more) by constructing a fast preconditioner whose computational cost scales linearly with the data size. For illustration, we characterize the heterogeneous hydraulic conductivity (K) distribution in a laboratory-scale 3-D sand box using about 6 million transient tracer concentration measurements obtained using magnetic resonance imaging. Since each individual observation has little information on the K distribution, the data was compressed by the zero-th temporal moment of breakthrough curves, which is equivalent to the mean travel time under the experimental setting. Moreover, only about 2,000 forward simulations in total were required to obtain the best estimate with corresponding estimation uncertainty, and the estimated K field captured key patterns of the original packing design, showing the efficiency and effectiveness of the proposed method. This article is protected by copyright. All rights reserved.« less

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

Lee, Jonghyun; Yoon, Hongkyu; Kitanidis, Peter K.

When characterizing subsurface properties is crucial for reliable and cost-effective groundwater supply management and contaminant remediation. With recent advances in sensor technology, large volumes of hydro-geophysical and geochemical data can be obtained to achieve high-resolution images of subsurface properties. However, characterization with such a large amount of information requires prohibitive computational costs associated with “big data” processing and numerous large-scale numerical simulations. To tackle such difficulties, the Principal Component Geostatistical Approach (PCGA) has been proposed as a “Jacobian-free” inversion method that requires much smaller forward simulation runs for each iteration than the number of unknown parameters and measurements needed inmore » the traditional inversion methods. PCGA can be conveniently linked to any multi-physics simulation software with independent parallel executions. In our paper, we extend PCGA to handle a large number of measurements (e.g. 106 or more) by constructing a fast preconditioner whose computational cost scales linearly with the data size. For illustration, we characterize the heterogeneous hydraulic conductivity (K) distribution in a laboratory-scale 3-D sand box using about 6 million transient tracer concentration measurements obtained using magnetic resonance imaging. Since each individual observation has little information on the K distribution, the data was compressed by the zero-th temporal moment of breakthrough curves, which is equivalent to the mean travel time under the experimental setting. Moreover, only about 2,000 forward simulations in total were required to obtain the best estimate with corresponding estimation uncertainty, and the estimated K field captured key patterns of the original packing design, showing the efficiency and effectiveness of the proposed method. This article is protected by copyright. All rights reserved.« less

Identification of immiscible NAPL contaminant sources in aquifers by a modified two-level saturation based imperialist competitive algorithm

NASA Astrophysics Data System (ADS)

Ghafouri, H. R.; Mosharaf-Dehkordi, M.; Afzalan, B.

2017-07-01

A simulation-optimization model is proposed for identifying the characteristics of local immiscible NAPL contaminant sources inside aquifers. This model employs the UTCHEM 9.0 software as its simulator for solving the governing equations associated with the multi-phase flow in porous media. As the optimization model, a novel two-level saturation based Imperialist Competitive Algorithm (ICA) is proposed to estimate the parameters of contaminant sources. The first level consists of three parallel independent ICAs and plays as a pre-conditioner for the second level which is a single modified ICA. The ICA in the second level is modified by dividing each country into a number of provinces (smaller parts). Similar to countries in the classical ICA, these provinces are optimized by the assimilation, competition, and revolution steps in the ICA. To increase the diversity of populations, a new approach named knock the base method is proposed. The performance and accuracy of the simulation-optimization model is assessed by solving a set of two and three-dimensional problems considering the effects of different parameters such as the grid size, rock heterogeneity and designated monitoring networks. The obtained numerical results indicate that using this simulation-optimization model provides accurate results at a less number of iterations when compared with the model employing the classical one-level ICA. A model is proposed to identify characteristics of immiscible NAPL contaminant sources. The contaminant is immiscible in water and multi-phase flow is simulated. The model is a multi-level saturation-based optimization algorithm based on ICA. Each answer string in second level is divided into a set of provinces. Each ICA is modified by incorporating a new knock the base model.

Conjugate gradient coupled with multigrid for an indefinite problem

NASA Technical Reports Server (NTRS)

Gozani, J.; Nachshon, A.; Turkel, E.

1984-01-01

An iterative algorithm for the Helmholtz equation is presented. This scheme was based on the preconditioned conjugate gradient method for the normal equations. The preconditioning is one cycle of a multigrid method for the discrete Laplacian. The smoothing algorithm is red-black Gauss-Seidel and is constructed so it is a symmetric operator. The total number of iterations needed by the algorithm is independent of h. By varying the number of grids, the number of iterations depends only weakly on k when k(3)h(2) is constant. Comparisons with a SSOR preconditioner are presented.

Rapidly converging multigrid reconstruction of cone-beam tomographic data

NASA Astrophysics Data System (ADS)

Myers, Glenn R.; Kingston, Andrew M.; Latham, Shane J.; Recur, Benoit; Li, Thomas; Turner, Michael L.; Beeching, Levi; Sheppard, Adrian P.

2016-10-01

In the context of large-angle cone-beam tomography (CBCT), we present a practical iterative reconstruction (IR) scheme designed for rapid convergence as required for large datasets. The robustness of the reconstruction is provided by the "space-filling" source trajectory along which the experimental data is collected. The speed of convergence is achieved by leveraging the highly isotropic nature of this trajectory to design an approximate deconvolution filter that serves as a pre-conditioner in a multi-grid scheme. We demonstrate this IR scheme for CBCT and compare convergence to that of more traditional techniques.

Performance issues for iterative solvers in device simulation

NASA Technical Reports Server (NTRS)

Fan, Qing; Forsyth, P. A.; Mcmacken, J. R. F.; Tang, Wei-Pai

1994-01-01

Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods still suffer from reliability problems. The linear systems which appear in numerical simulation of semiconductor devices are notoriously ill-conditioned. In order to produce robust algorithms for practical problems, careful attention must be given to many implementation issues. This paper concentrates on strategies for developing robust preconditioners. In addition, effective data structures and convergence check issues are also discussed. These algorithms are compared with a standard direct sparse matrix solver on a variety of problems.

Augmenting the one-shot framework by additional constraints

DOE PAGES

Bosse, Torsten

2016-05-12

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. Finally, a retardation analysis and the local convergence of the method in terms of necessary and sufficient conditions are given, which depend on key characteristics of the underlying problem and the quality of the utilized preconditioner.

Augmenting the one-shot framework by additional constraints

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

Bosse, Torsten

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. Finally, a retardation analysis and the local convergence of the method in terms of necessary and sufficient conditions are given, which depend on key characteristics of the underlying problem and the quality of the utilized preconditioner.

Big Data: A Parallel Particle Swarm Optimization-Back-Propagation Neural Network Algorithm Based on MapReduce.

PubMed

Cao, Jianfang; Cui, Hongyan; Shi, Hao; Jiao, Lijuan

2016-01-01

A back-propagation (BP) neural network can solve complicated random nonlinear mapping problems; therefore, it can be applied to a wide range of problems. However, as the sample size increases, the time required to train BP neural networks becomes lengthy. Moreover, the classification accuracy decreases as well. To improve the classification accuracy and runtime efficiency of the BP neural network algorithm, we proposed a parallel design and realization method for a particle swarm optimization (PSO)-optimized BP neural network based on MapReduce on the Hadoop platform using both the PSO algorithm and a parallel design. The PSO algorithm was used to optimize the BP neural network's initial weights and thresholds and improve the accuracy of the classification algorithm. The MapReduce parallel programming model was utilized to achieve parallel processing of the BP algorithm, thereby solving the problems of hardware and communication overhead when the BP neural network addresses big data. Datasets on 5 different scales were constructed using the scene image library from the SUN Database. The classification accuracy of the parallel PSO-BP neural network algorithm is approximately 92%, and the system efficiency is approximately 0.85, which presents obvious advantages when processing big data. The algorithm proposed in this study demonstrated both higher classification accuracy and improved time efficiency, which represents a significant improvement obtained from applying parallel processing to an intelligent algorithm on big data.

On the utility of threads for data parallel programming

NASA Technical Reports Server (NTRS)

Fahringer, Thomas; Haines, Matthew; Mehrotra, Piyush

1995-01-01

Threads provide a useful programming model for asynchronous behavior because of their ability to encapsulate units of work that can then be scheduled for execution at runtime, based on the dynamic state of a system. Recently, the threaded model has been applied to the domain of data parallel scientific codes, and initial reports indicate that the threaded model can produce performance gains over non-threaded approaches, primarily through the use of overlapping useful computation with communication latency. However, overlapping computation with communication is possible without the benefit of threads if the communication system supports asynchronous primitives, and this comparison has not been made in previous papers. This paper provides a critical look at the utility of lightweight threads as applied to data parallel scientific programming.

Parallel tempering for the traveling salesman problem

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

Percus, Allon; Wang, Richard; Hyman, Jeffrey

We explore the potential of parallel tempering as a combinatorial optimization method, applying it to the traveling salesman problem. We compare simulation results of parallel tempering with a benchmark implementation of simulated annealing, and study how different choices of parameters affect the relative performance of the two methods. We find that a straightforward implementation of parallel tempering can outperform simulated annealing in several crucial respects. When parameters are chosen appropriately, both methods yield close approximation to the actual minimum distance for an instance with 200 nodes. However, parallel tempering yields more consistently accurate results when a series of independent simulationsmore » are performed. Our results suggest that parallel tempering might offer a simple but powerful alternative to simulated annealing for combinatorial optimization problems.« less

Hypercube Expert System Shell - Applying Production Parallelism.

DTIC Science & Technology

1989-12-01

possible processor organizations, or int( rconntction n thod,, for par- allel architetures . The following are examples of commonlv used interconnection...this timing analysis because match speed-up avaiiah& from production parallelism is proportional to the average number of affected produclions1 ( 11:5

Use of the preconditioned conjugate gradient algorithm as a generic solver for mixed-model equations in animal breeding applications.

PubMed

Tsuruta, S; Misztal, I; Strandén, I

2001-05-01

Utility of the preconditioned conjugate gradient algorithm with a diagonal preconditioner for solving mixed-model equations in animal breeding applications was evaluated with 16 test problems. The problems included single- and multiple-trait analyses, with data on beef, dairy, and swine ranging from small examples to national data sets. Multiple-trait models considered low and high genetic correlations. Convergence was based on relative differences between left- and right-hand sides. The ordering of equations was fixed effects followed by random effects, with no special ordering within random effects. The preconditioned conjugate gradient program implemented with double precision converged for all models. However, when implemented in single precision, the preconditioned conjugate gradient algorithm did not converge for seven large models. The preconditioned conjugate gradient and successive overrelaxation algorithms were subsequently compared for 13 of the test problems. The preconditioned conjugate gradient algorithm was easy to implement with the iteration on data for general models. However, successive overrelaxation requires specific programming for each set of models. On average, the preconditioned conjugate gradient algorithm converged in three times fewer rounds of iteration than successive overrelaxation. With straightforward implementations, programs using the preconditioned conjugate gradient algorithm may be two or more times faster than those using successive overrelaxation. However, programs using the preconditioned conjugate gradient algorithm would use more memory than would comparable implementations using successive overrelaxation. Extensive optimization of either algorithm can influence rankings. The preconditioned conjugate gradient implemented with iteration on data, a diagonal preconditioner, and in double precision may be the algorithm of choice for solving mixed-model equations when sufficient memory is available and ease of implementation is essential.

Direct reconstruction of cardiac PET kinetic parametric images using a preconditioned conjugate gradient approach

PubMed Central

Rakvongthai, Yothin; Ouyang, Jinsong; Guerin, Bastien; Li, Quanzheng; Alpert, Nathaniel M.; El Fakhri, Georges

2013-01-01

Purpose: Our research goal is to develop an algorithm to reconstruct cardiac positron emission tomography (PET) kinetic parametric images directly from sinograms and compare its performance with the conventional indirect approach. Methods: Time activity curves of a NCAT phantom were computed according to a one-tissue compartmental kinetic model with realistic kinetic parameters. The sinograms at each time frame were simulated using the activity distribution for the time frame. The authors reconstructed the parametric images directly from the sinograms by optimizing a cost function, which included the Poisson log-likelihood and a spatial regularization terms, using the preconditioned conjugate gradient (PCG) algorithm with the proposed preconditioner. The proposed preconditioner is a diagonal matrix whose diagonal entries are the ratio of the parameter and the sensitivity of the radioactivity associated with parameter. The authors compared the reconstructed parametric images using the direct approach with those reconstructed using the conventional indirect approach. Results: At the same bias, the direct approach yielded significant relative reduction in standard deviation by 12%–29% and 32%–70% for 50 × 106 and 10 × 106 detected coincidences counts, respectively. Also, the PCG method effectively reached a constant value after only 10 iterations (with numerical convergence achieved after 40–50 iterations), while more than 500 iterations were needed for CG. Conclusions: The authors have developed a novel approach based on the PCG algorithm to directly reconstruct cardiac PET parametric images from sinograms, and yield better estimation of kinetic parameters than the conventional indirect approach, i.e., curve fitting of reconstructed images. The PCG method increases the convergence rate of reconstruction significantly as compared to the conventional CG method. PMID:24089922

A Spectral Element Discretisation on Unstructured Triangle / Tetrahedral Meshes for Elastodynamics

NASA Astrophysics Data System (ADS)

May, Dave A.; Gabriel, Alice-A.

2017-04-01

The spectral element method (SEM) defined over quadrilateral and hexahedral element geometries has proven to be a fast, accurate and scalable approach to study wave propagation phenomena. In the context of regional scale seismology and or simulations incorporating finite earthquake sources, the geometric restrictions associated with hexahedral elements can limit the applicability of the classical quad./hex. SEM. Here we describe a continuous Galerkin spectral element discretisation defined over unstructured meshes composed of triangles (2D), or tetrahedra (3D). The method uses a stable, nodal basis constructed from PKD polynomials and thus retains the spectral accuracy and low dispersive properties of the classical SEM, in addition to the geometric versatility provided by unstructured simplex meshes. For the particular basis and quadrature rule we have adopted, the discretisation results in a mass matrix which is not diagonal, thereby mandating linear solvers be utilised. To that end, we have developed efficient solvers and preconditioners which are robust with respect to the polynomial order (p), and possess high arithmetic intensity. Furthermore, we also consider using implicit time integrators, together with a p-multigrid preconditioner to circumvent the CFL condition. Implicit time integrators become particularly relevant when considering solving problems on poor quality meshes, or meshes containing elements with a widely varying range of length scales - both of which frequently arise when meshing non-trivial geometries. We demonstrate the applicability of the new method by examining a number of two- and three-dimensional wave propagation scenarios. These scenarios serve to characterise the accuracy and cost of the new method. Lastly, we will assess the potential benefits of using implicit time integrators for regional scale wave propagation simulations.

Direct reconstruction of cardiac PET kinetic parametric images using a preconditioned conjugate gradient approach.

PubMed

Rakvongthai, Yothin; Ouyang, Jinsong; Guerin, Bastien; Li, Quanzheng; Alpert, Nathaniel M; El Fakhri, Georges

2013-10-01

Our research goal is to develop an algorithm to reconstruct cardiac positron emission tomography (PET) kinetic parametric images directly from sinograms and compare its performance with the conventional indirect approach. Time activity curves of a NCAT phantom were computed according to a one-tissue compartmental kinetic model with realistic kinetic parameters. The sinograms at each time frame were simulated using the activity distribution for the time frame. The authors reconstructed the parametric images directly from the sinograms by optimizing a cost function, which included the Poisson log-likelihood and a spatial regularization terms, using the preconditioned conjugate gradient (PCG) algorithm with the proposed preconditioner. The proposed preconditioner is a diagonal matrix whose diagonal entries are the ratio of the parameter and the sensitivity of the radioactivity associated with parameter. The authors compared the reconstructed parametric images using the direct approach with those reconstructed using the conventional indirect approach. At the same bias, the direct approach yielded significant relative reduction in standard deviation by 12%-29% and 32%-70% for 50 × 10(6) and 10 × 10(6) detected coincidences counts, respectively. Also, the PCG method effectively reached a constant value after only 10 iterations (with numerical convergence achieved after 40-50 iterations), while more than 500 iterations were needed for CG. The authors have developed a novel approach based on the PCG algorithm to directly reconstruct cardiac PET parametric images from sinograms, and yield better estimation of kinetic parameters than the conventional indirect approach, i.e., curve fitting of reconstructed images. The PCG method increases the convergence rate of reconstruction significantly as compared to the conventional CG method.

Comparison of an algebraic multigrid algorithm to two iterative solvers used for modeling ground water flow and transport

USGS Publications Warehouse

Detwiler, R.L.; Mehl, S.; Rajaram, H.; Cheung, W.W.

2002-01-01

Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.

Methods of parallel computation applied on granular simulations

NASA Astrophysics Data System (ADS)

Martins, Gustavo H. B.; Atman, Allbens P. F.

2017-06-01

Every year, parallel computing has becoming cheaper and more accessible. As consequence, applications were spreading over all research areas. Granular materials is a promising area for parallel computing. To prove this statement we study the impact of parallel computing in simulations of the BNE (Brazil Nut Effect). This property is due the remarkable arising of an intruder confined to a granular media when vertically shaken against gravity. By means of DEM (Discrete Element Methods) simulations, we study the code performance testing different methods to improve clock time. A comparison between serial and parallel algorithms, using OpenMP® is also shown. The best improvement was obtained by optimizing the function that find contacts using Verlet's cells.

Parallel computation using boundary elements in solid mechanics

NASA Technical Reports Server (NTRS)

Chien, L. S.; Sun, C. T.

1990-01-01

The inherent parallelism of the boundary element method is shown. The boundary element is formulated by assuming the linear variation of displacements and tractions within a line element. Moreover, MACSYMA symbolic program is employed to obtain the analytical results for influence coefficients. Three computational components are parallelized in this method to show the speedup and efficiency in computation. The global coefficient matrix is first formed concurrently. Then, the parallel Gaussian elimination solution scheme is applied to solve the resulting system of equations. Finally, and more importantly, the domain solutions of a given boundary value problem are calculated simultaneously. The linear speedups and high efficiencies are shown for solving a demonstrated problem on Sequent Symmetry S81 parallel computing system.

Big Data: A Parallel Particle Swarm Optimization-Back-Propagation Neural Network Algorithm Based on MapReduce

PubMed Central

Cao, Jianfang; Cui, Hongyan; Shi, Hao; Jiao, Lijuan

2016-01-01

A back-propagation (BP) neural network can solve complicated random nonlinear mapping problems; therefore, it can be applied to a wide range of problems. However, as the sample size increases, the time required to train BP neural networks becomes lengthy. Moreover, the classification accuracy decreases as well. To improve the classification accuracy and runtime efficiency of the BP neural network algorithm, we proposed a parallel design and realization method for a particle swarm optimization (PSO)-optimized BP neural network based on MapReduce on the Hadoop platform using both the PSO algorithm and a parallel design. The PSO algorithm was used to optimize the BP neural network’s initial weights and thresholds and improve the accuracy of the classification algorithm. The MapReduce parallel programming model was utilized to achieve parallel processing of the BP algorithm, thereby solving the problems of hardware and communication overhead when the BP neural network addresses big data. Datasets on 5 different scales were constructed using the scene image library from the SUN Database. The classification accuracy of the parallel PSO-BP neural network algorithm is approximately 92%, and the system efficiency is approximately 0.85, which presents obvious advantages when processing big data. The algorithm proposed in this study demonstrated both higher classification accuracy and improved time efficiency, which represents a significant improvement obtained from applying parallel processing to an intelligent algorithm on big data. PMID:27304987

AdiosStMan: Parallelizing Casacore Table Data System using Adaptive IO System

NASA Astrophysics Data System (ADS)

Wang, R.; Harris, C.; Wicenec, A.

2016-07-01

In this paper, we investigate the Casacore Table Data System (CTDS) used in the casacore and CASA libraries, and methods to parallelize it. CTDS provides a storage manager plugin mechanism for third-party developers to design and implement their own CTDS storage managers. Having this in mind, we looked into various storage backend techniques that can possibly enable parallel I/O for CTDS by implementing new storage managers. After carrying on benchmarks showing the excellent parallel I/O throughput of the Adaptive IO System (ADIOS), we implemented an ADIOS based parallel CTDS storage manager. We then applied the CASA MSTransform frequency split task to verify the ADIOS Storage Manager. We also ran a series of performance tests to examine the I/O throughput in a massively parallel scenario.

Curious parallels and curious connections--phylogenetic thinking in biology and historical linguistics.

PubMed

Atkinson, Quentin D; Gray, Russell D

2005-08-01

In The Descent of Man (1871), Darwin observed "curious parallels" between the processes of biological and linguistic evolution. These parallels mean that evolutionary biologists and historical linguists seek answers to similar questions and face similar problems. As a result, the theory and methodology of the two disciplines have evolved in remarkably similar ways. In addition to Darwin's curious parallels of process, there are a number of equally curious parallels and connections between the development of methods in biology and historical linguistics. Here we briefly review the parallels between biological and linguistic evolution and contrast the historical development of phylogenetic methods in the two disciplines. We then look at a number of recent studies that have applied phylogenetic methods to language data and outline some current problems shared by the two fields.

Parallelized Stochastic Cutoff Method for Long-Range Interacting Systems

NASA Astrophysics Data System (ADS)

Endo, Eishin; Toga, Yuta; Sasaki, Munetaka

2015-07-01

We present a method of parallelizing the stochastic cutoff (SCO) method, which is a Monte-Carlo method for long-range interacting systems. After interactions are eliminated by the SCO method, we subdivide a lattice into noninteracting interpenetrating sublattices. This subdivision enables us to parallelize the Monte-Carlo calculation in the SCO method. Such subdivision is found by numerically solving the vertex coloring of a graph created by the SCO method. We use an algorithm proposed by Kuhn and Wattenhofer to solve the vertex coloring by parallel computation. This method was applied to a two-dimensional magnetic dipolar system on an L × L square lattice to examine its parallelization efficiency. The result showed that, in the case of L = 2304, the speed of computation increased about 102 times by parallel computation with 288 processors.

Parallel rendering

NASA Technical Reports Server (NTRS)

Crockett, Thomas W.

1995-01-01

This article provides a broad introduction to the subject of parallel rendering, encompassing both hardware and software systems. The focus is on the underlying concepts and the issues which arise in the design of parallel rendering algorithms and systems. We examine the different types of parallelism and how they can be applied in rendering applications. Concepts from parallel computing, such as data decomposition, task granularity, scalability, and load balancing, are considered in relation to the rendering problem. We also explore concepts from computer graphics, such as coherence and projection, which have a significant impact on the structure of parallel rendering algorithms. Our survey covers a number of practical considerations as well, including the choice of architectural platform, communication and memory requirements, and the problem of image assembly and display. We illustrate the discussion with numerous examples from the parallel rendering literature, representing most of the principal rendering methods currently used in computer graphics.

An interfering Go/No-go task does not affect accuracy in a Concealed Information Test.

PubMed

Ambach, Wolfgang; Stark, Rudolf; Peper, Martin; Vaitl, Dieter

2008-04-01

Following the idea that response inhibition processes play a central role in concealing information, the present study investigated the influence of a Go/No-go task as an interfering mental activity, performed parallel to the Concealed Information Test (CIT), on the detectability of concealed information. 40 undergraduate students participated in a mock-crime experiment and simultaneously performed a CIT and a Go/No-go task. Electrodermal activity (EDA), respiration line length (RLL), heart rate (HR) and finger pulse waveform length (FPWL) were registered. Reaction times were recorded as behavioral measures in the Go/No-go task as well as in the CIT. As a within-subject control condition, the CIT was also applied without an additional task. The parallel task did not influence the mean differences of the physiological measures of the mock-crime-related probe and the irrelevant items. This finding might possibly be due to the fact that the applied parallel task induced a tonic rather than a phasic mental activity, which did not influence differential responding to CIT items. No physiological evidence for an interaction between the parallel task and sub-processes of deception (e.g. inhibition) was found. Subjects' performance in the Go/No-go parallel task did not contribute to the detection of concealed information. Generalizability needs further investigations of different variations of the parallel task.

The interaction of turbulence with parallel and perpendicular shocks

NASA Astrophysics Data System (ADS)

Adhikari, L.; Zank, G. P.; Hunana, P.; Hu, Q.

2016-11-01

Interplanetary shocks exist in most astrophysical flows, and modify the properties of the background flow. We apply the Zank et al 2012 six coupled turbulence transport model equations to study the interaction of turbulence with parallel and perpendicular shock waves in the solar wind. We model the 1D structure of a stationary perpendicular or parallel shock wave using a hyperbolic tangent function and the Rankine-Hugoniot conditions. A reduced turbulence transport model (the 4-equation model) is applied to parallel and perpendicular shock waves, and solved using a 4th- order Runge Kutta method. We compare the model results with ACE spacecraft observations. We identify one quasi-parallel and one quasi-perpendicular event in the ACE spacecraft data sets, and compute various turbulent observed values such as the fluctuating magnetic and kinetic energy, the energy in forward and backward propagating modes, the total turbulent energy in the upstream and downstream of the shock. We also calculate the error associated with each turbulent observed value, and fit the observed values by a least square method and use a Fourier series fitting function. We find that the theoretical results are in reasonable agreement with observations. The energy in turbulent fluctuations is enhanced and the correlation length is approximately constant at the shock. Similarly, the normalized cross helicity increases across a perpendicular shock, and decreases across a parallel shock.

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

Kargupta, H.; Stafford, B.; Hamzaoglu, I.

This paper describes an experimental parallel/distributed data mining system PADMA (PArallel Data Mining Agents) that uses software agents for local data accessing and analysis and a web based interface for interactive data visualization. It also presents the results of applying PADMA for detecting patterns in unstructured texts of postmortem reports and laboratory test data for Hepatitis C patients.

Pattern Recognition by Retina-Like Devices.

ERIC Educational Resources Information Center

Weiman, Carl F. R.; Rothstein, Jerome

This study has investigated some pattern recognition capabilities of devices consisting of arrays of cooperating elements acting in parallel. The problem of recognizing straight lines in general position on the quadratic lattice has been completely solved by applying parallel acting algorithms to a special code for lines on the lattice. The…

Efficient conjugate gradient algorithms for computation of the manipulator forward dynamics

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheid, Robert E.

1989-01-01

The applicability of conjugate gradient algorithms for computation of the manipulator forward dynamics is investigated. The redundancies in the previously proposed conjugate gradient algorithm are analyzed. A new version is developed which, by avoiding these redundancies, achieves a significantly greater efficiency. A preconditioned conjugate gradient algorithm is also presented. A diagonal matrix whose elements are the diagonal elements of the inertia matrix is proposed as the preconditioner. In order to increase the computational efficiency, an algorithm is developed which exploits the synergism between the computation of the diagonal elements of the inertia matrix and that required by the conjugate gradient algorithm.

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

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

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

An object-oriented approach to nested data parallelism

NASA Technical Reports Server (NTRS)

Sheffler, Thomas J.; Chatterjee, Siddhartha

1994-01-01

This paper describes an implementation technique for integrating nested data parallelism into an object-oriented language. Data-parallel programming employs sets of data called 'collections' and expresses parallelism as operations performed over the elements of a collection. When the elements of a collection are also collections, then there is the possibility for 'nested data parallelism.' Few current programming languages support nested data parallelism however. In an object-oriented framework, a collection is a single object. Its type defines the parallel operations that may be applied to it. Our goal is to design and build an object-oriented data-parallel programming environment supporting nested data parallelism. Our initial approach is built upon three fundamental additions to C++. We add new parallel base types by implementing them as classes, and add a new parallel collection type called a 'vector' that is implemented as a template. Only one new language feature is introduced: the 'foreach' construct, which is the basis for exploiting elementwise parallelism over collections. The strength of the method lies in the compilation strategy, which translates nested data-parallel C++ into ordinary C++. Extracting the potential parallelism in nested 'foreach' constructs is called 'flattening' nested parallelism. We show how to flatten 'foreach' constructs using a simple program transformation. Our prototype system produces vector code which has been successfully run on workstations, a CM-2, and a CM-5.

A framework for grand scale parallelization of the combined finite discrete element method in 2d

NASA Astrophysics Data System (ADS)

Lei, Z.; Rougier, E.; Knight, E. E.; Munjiza, A.

2014-09-01

Within the context of rock mechanics, the Combined Finite-Discrete Element Method (FDEM) has been applied to many complex industrial problems such as block caving, deep mining techniques (tunneling, pillar strength, etc.), rock blasting, seismic wave propagation, packing problems, dam stability, rock slope stability, rock mass strength characterization problems, etc. The reality is that most of these were accomplished in a 2D and/or single processor realm. In this work a hardware independent FDEM parallelization framework has been developed using the Virtual Parallel Machine for FDEM, (V-FDEM). With V-FDEM, a parallel FDEM software can be adapted to different parallel architecture systems ranging from just a few to thousands of cores.

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.

Binary zone-plate array for a parallel joint transform correlator applied to face recognition.

PubMed

Kodate, K; Hashimoto, A; Thapliya, R

1999-05-10

Taking advantage of small aberrations, high efficiency, and compactness, we developed a new, to our knowledge, design procedure for a binary zone-plate array (BZPA) and applied it to a parallel joint transform correlator for the recognition of the human face. Pairs of reference and unknown images of faces are displayed on a liquid-crystal spatial light modulator (SLM), Fourier transformed by the BZPA, intensity recorded on an optically addressable SLM, and inversely Fourier transformed to obtain correlation signals. Consideration of the bandwidth allows the relations among the channel number, the numerical aperture of the zone plates, and the pattern size to be determined. Experimentally a five-channel parallel correlator was implemented and tested successfully with a 100-person database. The design and the fabrication of a 20-channel BZPA for phonetic character recognition are also included.

Accelerating global optimization of aerodynamic shapes using a new surrogate-assisted parallel genetic algorithm

NASA Astrophysics Data System (ADS)

Ebrahimi, Mehdi; Jahangirian, Alireza

2017-12-01

An efficient strategy is presented for global shape optimization of wing sections with a parallel genetic algorithm. Several computational techniques are applied to increase the convergence rate and the efficiency of the method. A variable fidelity computational evaluation method is applied in which the expensive Navier-Stokes flow solver is complemented by an inexpensive multi-layer perceptron neural network for the objective function evaluations. A population dispersion method that consists of two phases, of exploration and refinement, is developed to improve the convergence rate and the robustness of the genetic algorithm. Owing to the nature of the optimization problem, a parallel framework based on the master/slave approach is used. The outcomes indicate that the method is able to find the global optimum with significantly lower computational time in comparison to the conventional genetic algorithm.

Newton-like methods for Navier-Stokes solution

NASA Astrophysics Data System (ADS)

Qin, N.; Xu, X.; Richards, B. E.

1992-12-01

The paper reports on Newton-like methods called SFDN-alpha-GMRES and SQN-alpha-GMRES methods that have been devised and proven as powerful schemes for large nonlinear problems typical of viscous compressible Navier-Stokes solutions. They can be applied using a partially converged solution from a conventional explicit or approximate implicit method. Developments have included the efficient parallelization of the schemes on a distributed memory parallel computer. The methods are illustrated using a RISC workstation and a transputer parallel system respectively to solve a hypersonic vortical flow.

Use of gamma ray radiation to parallel the plates of a Fabry-Perot interferometer

NASA Technical Reports Server (NTRS)

Skinner, Wilbert R.; Hays, Paul B.; Anderson, Sally M.

1987-01-01

The use of gamma radiation to parallel the plates of a Fabry-Perot etalon is examined. The method for determining the etalon parallelism, and the procedure for irradiating the posts are described. Changes in effective gap for the etalon over the surface are utilized to measure the parallelism of the Fabry-Perot etalon. An example in which this technique is applied to an etalon of fused silica plates, which are 132 mm in diameter and coded with zinc sulfide and cryolite, with Zerodur spaces 2 cm in length. The effect of the irradiation of the posts on the thermal performance of the etalon is investigated.

Electric field control of the skyrmion lattice in Cu2OSeO3

NASA Astrophysics Data System (ADS)

White, J. S.; Levatić, I.; Omrani, A. A.; Egetenmeyer, N.; Prša, K.; Živković, I.; Gavilano, J. L.; Kohlbrecher, J.; Bartkowiak, M.; Berger, H.; Rønnow, H. M.

2012-10-01

Small-angle neutron scattering has been employed to study the influence of applied electric (E-)fields on the skyrmion lattice in the chiral lattice magnetoelectric Cu2OSeO3. Using an experimental geometry with the E-field parallel to the [111] axis, and the magnetic field parallel to the [1\\bar {1}0] axis, we demonstrate that the effect of applying an E-field is to controllably rotate the skyrmion lattice around the magnetic field axis. Our results are an important first demonstration for a microscopic coupling between applied E-fields and the skyrmions in an insulator, and show that the general emergent properties of skyrmions may be tailored according to the properties of the host system.

A three-dimensional spectral algorithm for simulations of transition and turbulence

NASA Technical Reports Server (NTRS)

Zang, T. A.; Hussaini, M. Y.

1985-01-01

A spectral algorithm for simulating three dimensional, incompressible, parallel shear flows is described. It applies to the channel, to the parallel boundary layer, and to other shear flows with one wall bounded and two periodic directions. Representative applications to the channel and to the heated boundary layer are presented.

Parallel Performance of a Combustion Chemistry Simulation

DOE PAGES

Skinner, Gregg; Eigenmann, Rudolf

1995-01-01

We used a description of a combustion simulation's mathematical and computational methods to develop a version for parallel execution. The result was a reasonable performance improvement on small numbers of processors. We applied several important programming techniques, which we describe, in optimizing the application. This work has implications for programming languages, compiler design, and software engineering.

The Influence of Shape on the Output Potential of ZnO Nanostructures: Sensitivity to Parallel versus Perpendicular Forces.

PubMed

Cardoso, José; Oliveira, Filipe F; Proenca, Mariana P; Ventura, João

2018-05-22

With the consistent shrinking of devices, micro-systems are, nowadays, widely used in areas such as biomedics, electronics, automobiles, and measurement devices. As devices shrunk, so too did their energy consumptions, opening the way for the use of nanogenerators (NGs) as power sources. In particular, to harvest energy from an object's motion (mechanical vibrations, torsional forces, or pressure), present NGs are mainly composed of piezoelectric materials in which, upon an applied compressive or strain force, an electrical field is produced that can be used to power a device. The focus of this work is to simulate the piezoelectric effect in different ZnO nanostructures to optimize the output potential generated by a nanodevice. In these simulations, cylindrical nanowires, nanomushrooms, and nanotrees were created, and the influence of the nanostructures' shape on the output potential was studied as a function of applied parallel and perpendicular forces. The obtained results demonstrated that the output potential is linearly proportional to the applied force and that perpendicular forces are more efficient in all structures. However, nanotrees were found to have an increased sensitivity to parallel applied forces, which resulted in a large enhancement of the output efficiency. These results could then open a new path to increase the efficiency of piezoelectric nanogenerators.

Modification of crystal anisotropy and enhancement of magnetic moment of Co-doped SnO2 thin films annealed under magnetic field

PubMed Central

2014-01-01

Co-doped SnO2 thin films were grown by sputtering technique on SiO2/Si(001) substrates at room temperature, and then, thermal treatments with and without an applied magnetic field (HTT) were performed in vacuum at 600°C for 20 min. HTT was applied parallel and perpendicular to the substrate surface. Magnetic M(H) measurements reveal the coexistence of a strong antiferromagnetic (AFM) signal and a ferromagnetic (FM) component. The AFM component has a Néel temperature higher than room temperature, the spin axis lies parallel to the substrate surface, and the highest magnetic moment m =7 μB/Co at. is obtained when HTT is applied parallel to the substrate surface. Our results show an enhancement of FM moment per Co+2 from 0.06 to 0.42 μB/Co at. for the sample on which HTT was applied perpendicular to the surface. The FM order is attributed to the coupling of Co+2 ions through electrons trapped at the site of oxygen vacancies, as described by the bound magnetic polaron model. Our results suggest that FM order is aligned along [101] direction of Co-doped SnO2 nanocrystals, which is proposed to be the easy magnetization axis. PMID:25489286

High order parallel numerical schemes for solving incompressible flows

NASA Technical Reports Server (NTRS)

Lin, Avi; Milner, Edward J.; Liou, May-Fun; Belch, Richard A.

1992-01-01

The use of parallel computers for numerically solving flow fields has gained much importance in recent years. This paper introduces a new high order numerical scheme for computational fluid dynamics (CFD) specifically designed for parallel computational environments. A distributed MIMD system gives the flexibility of treating different elements of the governing equations with totally different numerical schemes in different regions of the flow field. The parallel decomposition of the governing operator to be solved is the primary parallel split. The primary parallel split was studied using a hypercube like architecture having clusters of shared memory processors at each node. The approach is demonstrated using examples of simple steady state incompressible flows. Future studies should investigate the secondary split because, depending on the numerical scheme that each of the processors applies and the nature of the flow in the specific subdomain, it may be possible for a processor to seek better, or higher order, schemes for its particular subcase.

Parallel computing works

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

Not Available

An account of the Caltech Concurrent Computation Program (C{sup 3}P), a five year project that focused on answering the question: Can parallel computers be used to do large-scale scientific computations '' As the title indicates, the question is answered in the affirmative, by implementing numerous scientific applications on real parallel computers and doing computations that produced new scientific results. In the process of doing so, C{sup 3}P helped design and build several new computers, designed and implemented basic system software, developed algorithms for frequently used mathematical computations on massively parallel machines, devised performance models and measured the performance of manymore » computers, and created a high performance computing facility based exclusively on parallel computers. While the initial focus of C{sup 3}P was the hypercube architecture developed by C. Seitz, many of the methods developed and lessons learned have been applied successfully on other massively parallel architectures.« less

Synthesizing parallel imaging applications using the CAP (computer-aided parallelization) tool

NASA Astrophysics Data System (ADS)

Gennart, Benoit A.; Mazzariol, Marc; Messerli, Vincent; Hersch, Roger D.

1997-12-01

Imaging applications such as filtering, image transforms and compression/decompression require vast amounts of computing power when applied to large data sets. These applications would potentially benefit from the use of parallel processing. However, dedicated parallel computers are expensive and their processing power per node lags behind that of the most recent commodity components. Furthermore, developing parallel applications remains a difficult task: writing and debugging the application is difficult (deadlocks), programs may not be portable from one parallel architecture to the other, and performance often comes short of expectations. In order to facilitate the development of parallel applications, we propose the CAP computer-aided parallelization tool which enables application programmers to specify at a high-level of abstraction the flow of data between pipelined-parallel operations. In addition, the CAP tool supports the programmer in developing parallel imaging and storage operations. CAP enables combining efficiently parallel storage access routines and image processing sequential operations. This paper shows how processing and I/O intensive imaging applications must be implemented to take advantage of parallelism and pipelining between data access and processing. This paper's contribution is (1) to show how such implementations can be compactly specified in CAP, and (2) to demonstrate that CAP specified applications achieve the performance of custom parallel code. The paper analyzes theoretically the performance of CAP specified applications and demonstrates the accuracy of the theoretical analysis through experimental measurements.

MPI, HPF or OpenMP: A Study with the NAS Benchmarks

NASA Technical Reports Server (NTRS)

Jin, Hao-Qiang; Frumkin, Michael; Hribar, Michelle; Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)

1999-01-01

Porting applications to new high performance parallel and distributed platforms is a challenging task. Writing parallel code by hand is time consuming and costly, but the task can be simplified by high level languages and would even better be automated by parallelizing tools and compilers. The definition of HPF (High Performance Fortran, based on data parallel model) and OpenMP (based on shared memory parallel model) standards has offered great opportunity in this respect. Both provide simple and clear interfaces to language like FORTRAN and simplify many tedious tasks encountered in writing message passing programs. In our study we implemented the parallel versions of the NAS Benchmarks with HPF and OpenMP directives. Comparison of their performance with the MPI implementation and pros and cons of different approaches will be discussed along with experience of using computer-aided tools to help parallelize these benchmarks. Based on the study,potentials of applying some of the techniques to realistic aerospace applications will be presented

MPI, HPF or OpenMP: A Study with the NAS Benchmarks

NASA Technical Reports Server (NTRS)

Jin, H.; Frumkin, M.; Hribar, M.; Waheed, A.; Yan, J.; Saini, Subhash (Technical Monitor)

1999-01-01

Porting applications to new high performance parallel and distributed platforms is a challenging task. Writing parallel code by hand is time consuming and costly, but this task can be simplified by high level languages and would even better be automated by parallelizing tools and compilers. The definition of HPF (High Performance Fortran, based on data parallel model) and OpenMP (based on shared memory parallel model) standards has offered great opportunity in this respect. Both provide simple and clear interfaces to language like FORTRAN and simplify many tedious tasks encountered in writing message passing programs. In our study, we implemented the parallel versions of the NAS Benchmarks with HPF and OpenMP directives. Comparison of their performance with the MPI implementation and pros and cons of different approaches will be discussed along with experience of using computer-aided tools to help parallelize these benchmarks. Based on the study, potentials of applying some of the techniques to realistic aerospace applications will be presented.

Wavelet-like bases for thin-wire integral equations in electromagnetics

NASA Astrophysics Data System (ADS)

Francomano, E.; Tortorici, A.; Toscano, E.; Ala, G.; Viola, F.

2005-03-01

In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rossow, C.-C.

2008-01-01

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Sound transmission through a poroelastic layered panel

NASA Astrophysics Data System (ADS)

Nagler, Loris; Rong, Ping; Schanz, Martin; von Estorff, Otto

2014-04-01

Multi-layered panels are often used to improve the acoustics in cars, airplanes, rooms, etc. For such an application these panels include porous and/or fibrous layers. The proposed numerical method is an approach to simulate the acoustical behavior of such multi-layered panels. The model assumes plate-like structures and, hence, combines plate theories for the different layers. The poroelastic layer is modelled with a recently developed plate theory. This theory uses a series expansion in thickness direction with subsequent analytical integration in this direction to reduce the three dimensions to two. The same idea is used to model either air gaps or fibrous layers. The latter are modeled as equivalent fluid and can be handled like an air gap, i.e., a kind of `air plate' is used. The coupling of the layers is done by using the series expansion to express the continuity conditions on the surfaces of the plates. The final system is solved with finite elements, where domain decomposition techniques in combination with preconditioned iterative solvers are applied to solve the final system of equations. In a large frequency range, the comparison with measurements shows very good agreement. From the numerical solution process it can be concluded that different preconditioners for the different layers are necessary. A reuse of the Krylov subspace of the iterative solvers pays if several excitations have to be computed but not that much in the loop over the frequencies.

Parallel tiled Nussinov RNA folding loop nest generated using both dependence graph transitive closure and loop skewing.

PubMed

Palkowski, Marek; Bielecki, Wlodzimierz

2017-06-02

RNA secondary structure prediction is a compute intensive task that lies at the core of several search algorithms in bioinformatics. Fortunately, the RNA folding approaches, such as the Nussinov base pair maximization, involve mathematical operations over affine control loops whose iteration space can be represented by the polyhedral model. Polyhedral compilation techniques have proven to be a powerful tool for optimization of dense array codes. However, classical affine loop nest transformations used with these techniques do not optimize effectively codes of dynamic programming of RNA structure predictions. The purpose of this paper is to present a novel approach allowing for generation of a parallel tiled Nussinov RNA loop nest exposing significantly higher performance than that of known related code. This effect is achieved due to improving code locality and calculation parallelization. In order to improve code locality, we apply our previously published technique of automatic loop nest tiling to all the three loops of the Nussinov loop nest. This approach first forms original rectangular 3D tiles and then corrects them to establish their validity by means of applying the transitive closure of a dependence graph. To produce parallel code, we apply the loop skewing technique to a tiled Nussinov loop nest. The technique is implemented as a part of the publicly available polyhedral source-to-source TRACO compiler. Generated code was run on modern Intel multi-core processors and coprocessors. We present the speed-up factor of generated Nussinov RNA parallel code and demonstrate that it is considerably faster than related codes in which only the two outer loops of the Nussinov loop nest are tiled.

Third-order linearization for self-beating filtered microwave photonic systems using a dual parallel Mach-Zehnder modulator.

PubMed

Pérez, Daniel; Gasulla, Ivana; Capmany, José; Fandiño, Javier S; Muñoz, Pascual; Alavi, Hossein

2016-09-05

We develop, analyze and apply a linearization technique based on dual parallel Mach-Zehnder modulator to self-beating microwave photonics systems. The approach enables broadband low-distortion transmission and reception at expense of a moderate electrical power penalty yielding a small optical power penalty (<1 dB).

A mode-matching analysis of dielectric-filled resonant cavities coupled to terahertz parallel-plate waveguides.

PubMed

Astley, Victoria; Reichel, Kimberly S; Jones, Jonathan; Mendis, Rajind; Mittleman, Daniel M

2012-09-10

We use the mode-matching technique to study parallel-plate waveguide resonant cavities that are filled with a dielectric. We apply the generalized scattering matrix theory to calculate the power transmission through the waveguide-cavities. We compare the analytical results to experimental data to confirm the validity of this approach.

Discrimination of portraits using a hybrid parallel joint transform correlator system

NASA Astrophysics Data System (ADS)

Inaba, Rieko; Hashimoto, Asako; Kodate, Kashiko

1999-05-01

A hybrid parallel joint transform correlation system is demonstrated through the introduction of a five-channel binary zone plate array and is applied to the discrimination of portraits for a presumed criminal investigation. In order to improve performance, we adopt pe-processing of images with white area of 20%. Furthermore, we discuss the robustness.

Parallel versus Serial Processing Dependencies in the Perisylvian Speech Network: A Granger Analysis of Intracranial EEG Data

ERIC Educational Resources Information Center

Gow, David W., Jr.; Keller, Corey J.; Eskandar, Emad; Meng, Nate; Cash, Sydney S.

2009-01-01

In this work, we apply Granger causality analysis to high spatiotemporal resolution intracranial EEG (iEEG) data to examine how different components of the left perisylvian language network interact during spoken language perception. The specific focus is on the characterization of serial versus parallel processing dependencies in the dominant…

Analysis of Serial and Parallel Algorithms for Use in Molecular Dynamics.. Review and Proposals

NASA Astrophysics Data System (ADS)

Mazzone, A. M.

This work analyzes the stability and accuracy of multistep methods, either for serial or parallel calculations, applied to molecular dynamics simulations. Numerical testing is made by evaluating the equilibrium configurations of mono-elemental crystalline lattices of metallic and semiconducting type (Ag and Si, respectively) and of a cubic CuY compound.

Customizing FP-growth algorithm to parallel mining with Charm++ library

NASA Astrophysics Data System (ADS)

Puścian, Marek

2017-08-01

This paper presents a frequent item mining algorithm that was customized to handle growing data repositories. The proposed solution applies Master Slave scheme to frequent pattern growth technique. Efficient utilization of available computation units is achieved by dynamic reallocation of tasks. Conditional frequent trees are assigned to parallel workers basing on their workload. Proposed enhancements have been successfully implemented using Charm++ library. This paper discusses results of the performance of parallelized FP-growth algorithm against different datasets. The approach has been illustrated with many experiments and measurements performed using multiprocessor and multithreaded computer.

Keldysh formalism for multiple parallel worlds

NASA Astrophysics Data System (ADS)

Ansari, M.; Nazarov, Y. V.

2016-03-01

We present a compact and self-contained review of the recently developed Keldysh formalism for multiple parallel worlds. The formalism has been applied to consistent quantum evaluation of the flows of informational quantities, in particular, to the evaluation of Renyi and Shannon entropy flows. We start with the formulation of the standard and extended Keldysh techniques in a single world in a form convenient for our presentation. We explain the use of Keldysh contours encompassing multiple parallel worlds. In the end, we briefly summarize the concrete results obtained with the method.

Execution of parallel algorithms on a heterogeneous multicomputer

NASA Astrophysics Data System (ADS)

Isenstein, Barry S.; Greene, Jonathon

1995-04-01

Many aerospace/defense sensing and dual-use applications require high-performance computing, extensive high-bandwidth interconnect and realtime deterministic operation. This paper will describe the architecture of a scalable multicomputer that includes DSP and RISC processors. A single chassis implementation is capable of delivering in excess of 10 GFLOPS of DSP processing power with 2 Gbytes/s of realtime sensor I/O. A software approach to implementing parallel algorithms called the Parallel Application System (PAS) is also presented. An example of applying PAS to a DSP application is shown.

Keldysh formalism for multiple parallel worlds

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

Ansari, M.; Nazarov, Y. V., E-mail: y.v.nazarov@tudelft.nl

We present a compact and self-contained review of the recently developed Keldysh formalism for multiple parallel worlds. The formalism has been applied to consistent quantum evaluation of the flows of informational quantities, in particular, to the evaluation of Renyi and Shannon entropy flows. We start with the formulation of the standard and extended Keldysh techniques in a single world in a form convenient for our presentation. We explain the use of Keldysh contours encompassing multiple parallel worlds. In the end, we briefly summarize the concrete results obtained with the method.

A new scheduling algorithm for parallel sparse LU factorization with static pivoting

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

Grigori, Laura; Li, Xiaoye S.

2002-08-20

In this paper we present a static scheduling algorithm for parallel sparse LU factorization with static pivoting. The algorithm is divided into mapping and scheduling phases, using the symmetric pruned graphs of L' and U to represent dependencies. The scheduling algorithm is designed for driving the parallel execution of the factorization on a distributed-memory architecture. Experimental results and comparisons with SuperLU{_}DIST are reported after applying this algorithm on real world application matrices on an IBM SP RS/6000 distributed memory machine.

Native-Speakerism, Stereotyping and the Collusion of Applied Linguistics

ERIC Educational Resources Information Center

Kabel, Ahmed

2009-01-01

Although, in recent years there have been several advances in critical applied linguistics which have attempted to problematize the ideological underpinnings of language practices, there have in parallel been resistances mounted on the part of traditional applied linguistics that adamantly oppose any form of coming to terms with the political and…

Multiple solution of linear algebraic systems by an iterative method with recomputed preconditioner in the analysis of microstrip structures

NASA Astrophysics Data System (ADS)

Ahunov, Roman R.; Kuksenko, Sergey P.; Gazizov, Talgat R.

2016-06-01

A multiple solution of linear algebraic systems with dense matrix by iterative methods is considered. To accelerate the process, the recomputing of the preconditioning matrix is used. A priory condition of the recomputing based on change of the arithmetic mean of the current solution time during the multiple solution is proposed. To confirm the effectiveness of the proposed approach, the numerical experiments using iterative methods BiCGStab and CGS for four different sets of matrices on two examples of microstrip structures are carried out. For solution of 100 linear systems the acceleration up to 1.6 times, compared to the approach without recomputing, is obtained.

Off-diagonal Jacobian support for Nodal BCs

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

Peterson, John W.; Andrs, David; Gaston, Derek R.

In this brief note, we describe the implementation of o-diagonal Jacobian computations for nodal boundary conditions in the Multiphysics Object Oriented Simulation Environment (MOOSE) [1] framework. There are presently a number of applications [2{5] based on the MOOSE framework that solve complicated physical systems of partial dierential equations whose boundary conditions are often highly nonlinear. Accurately computing the on- and o-diagonal Jacobian and preconditioner entries associated to these constraints is crucial for enabling ecient numerical solvers in these applications. Two key ingredients are required for properly specifying the Jacobian contributions of nonlinear nodal boundary conditions in MOOSE and nite elementmore » codes in general: 1. The ability to zero out entire Jacobian matrix rows after \

Parallel simulation of tsunami inundation on a large-scale supercomputer

NASA Astrophysics Data System (ADS)

Oishi, Y.; Imamura, F.; Sugawara, D.

2013-12-01

An accurate prediction of tsunami inundation is important for disaster mitigation purposes. One approach is to approximate the tsunami wave source through an instant inversion analysis using real-time observation data (e.g., Tsushima et al., 2009) and then use the resulting wave source data in an instant tsunami inundation simulation. However, a bottleneck of this approach is the large computational cost of the non-linear inundation simulation and the computational power of recent massively parallel supercomputers is helpful to enable faster than real-time execution of a tsunami inundation simulation. Parallel computers have become approximately 1000 times faster in 10 years (www.top500.org), and so it is expected that very fast parallel computers will be more and more prevalent in the near future. Therefore, it is important to investigate how to efficiently conduct a tsunami simulation on parallel computers. In this study, we are targeting very fast tsunami inundation simulations on the K computer, currently the fastest Japanese supercomputer, which has a theoretical peak performance of 11.2 PFLOPS. One computing node of the K computer consists of 1 CPU with 8 cores that share memory, and the nodes are connected through a high-performance torus-mesh network. The K computer is designed for distributed-memory parallel computation, so we have developed a parallel tsunami model. Our model is based on TUNAMI-N2 model of Tohoku University, which is based on a leap-frog finite difference method. A grid nesting scheme is employed to apply high-resolution grids only at the coastal regions. To balance the computation load of each CPU in the parallelization, CPUs are first allocated to each nested layer in proportion to the number of grid points of the nested layer. Using CPUs allocated to each layer, 1-D domain decomposition is performed on each layer. In the parallel computation, three types of communication are necessary: (1) communication to adjacent neighbours for the finite difference calculation, (2) communication between adjacent layers for the calculations to connect each layer, and (3) global communication to obtain the time step which satisfies the CFL condition in the whole domain. A preliminary test on the K computer showed the parallel efficiency on 1024 cores was 57% relative to 64 cores. We estimate that the parallel efficiency will be considerably improved by applying a 2-D domain decomposition instead of the present 1-D domain decomposition in future work. The present parallel tsunami model was applied to the 2011 Great Tohoku tsunami. The coarsest resolution layer covers a 758 km × 1155 km region with a 405 m grid spacing. A nesting of five layers was used with the resolution ratio of 1/3 between nested layers. The finest resolution region has 5 m resolution and covers most of the coastal region of Sendai city. To complete 2 hours of simulation time, the serial (non-parallel) computation took approximately 4 days on a workstation. To complete the same simulation on 1024 cores of the K computer, it took 45 minutes which is more than two times faster than real-time. This presentation discusses the updated parallel computational performance and the efficient use of the K computer when considering the characteristics of the tsunami inundation simulation model in relation to the characteristics and capabilities of the K computer.

F-Nets and Software Cabling: Deriving a Formal Model and Language for Portable Parallel Programming

NASA Technical Reports Server (NTRS)

DiNucci, David C.; Saini, Subhash (Technical Monitor)

1998-01-01

Parallel programming is still being based upon antiquated sequence-based definitions of the terms "algorithm" and "computation", resulting in programs which are architecture dependent and difficult to design and analyze. By focusing on obstacles inherent in existing practice, a more portable model is derived here, which is then formalized into a model called Soviets which utilizes a combination of imperative and functional styles. This formalization suggests more general notions of algorithm and computation, as well as insights into the meaning of structured programming in a parallel setting. To illustrate how these principles can be applied, a very-high-level graphical architecture-independent parallel language, called Software Cabling, is described, with many of the features normally expected from today's computer languages (e.g. data abstraction, data parallelism, and object-based programming constructs).

Hierarchical Fuzzy Control Applied to Parallel Connected UPS Inverters Using Average Current Sharing Scheme

NASA Astrophysics Data System (ADS)

Singh, Santosh Kumar; Ghatak Choudhuri, Sumit

2018-05-01

Parallel connection of UPS inverters to enhance power rating is a widely accepted practice. Inter-modular circulating currents appear when multiple inverter modules are connected in parallel to supply variable critical load. Interfacing of modules henceforth requires an intensive design, using proper control strategy. The potentiality of human intuitive Fuzzy Logic (FL) control with imprecise system model is well known and thus can be utilised in parallel-connected UPS systems. Conventional FL controller is computational intensive, especially with higher number of input variables. This paper proposes application of Hierarchical-Fuzzy Logic control for parallel connected Multi-modular inverters system for reduced computational burden on the processor for a given switching frequency. Simulated results in MATLAB environment and experimental verification using Texas TMS320F2812 DSP are included to demonstrate feasibility of the proposed control scheme.

Parallel steady state studies on a milliliter scale accelerate fed-batch bioprocess design for recombinant protein production with Escherichia coli.

PubMed

Schmideder, Andreas; Cremer, Johannes H; Weuster-Botz, Dirk

2016-11-01

In general, fed-batch processes are applied for recombinant protein production with Escherichia coli (E. coli). However, state of the art methods for identifying suitable reaction conditions suffer from severe drawbacks, i.e. direct transfer of process information from parallel batch studies is often defective and sequential fed-batch studies are time-consuming and cost-intensive. In this study, continuously operated stirred-tank reactors on a milliliter scale were applied to identify suitable reaction conditions for fed-batch processes. Isopropyl β-d-1-thiogalactopyranoside (IPTG) induction strategies were varied in parallel-operated stirred-tank bioreactors to study the effects on the continuous production of the recombinant protein photoactivatable mCherry (PAmCherry) with E. coli. Best-performing induction strategies were transferred from the continuous processes on a milliliter scale to liter scale fed-batch processes. Inducing recombinant protein expression by dynamically increasing the IPTG concentration to 100 µM led to an increase in the product concentration of 21% (8.4 g L -1 ) compared to an implemented high-performance production process with the most frequently applied induction strategy by a single addition of 1000 µM IPGT. Thus, identifying feasible reaction conditions for fed-batch processes in parallel continuous studies on a milliliter scale was shown to be a powerful, novel method to accelerate bioprocess design in a cost-reducing manner. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1426-1435, 2016. © 2016 American Institute of Chemical Engineers.

True Shear Parallel Plate Viscometer

NASA Technical Reports Server (NTRS)

Ethridge, Edwin; Kaukler, William

2010-01-01

This viscometer (which can also be used as a rheometer) is designed for use with liquids over a large temperature range. The device consists of horizontally disposed, similarly sized, parallel plates with a precisely known gap. The lower plate is driven laterally with a motor to apply shear to the liquid in the gap. The upper plate is freely suspended from a double-arm pendulum with a sufficiently long radius to reduce height variations during the swing to negligible levels. A sensitive load cell measures the shear force applied by the liquid to the upper plate. Viscosity is measured by taking the ratio of shear stress to shear rate.

A Parallel Genetic Algorithm for Automated Electronic Circuit Design

NASA Technical Reports Server (NTRS)

Lohn, Jason D.; Colombano, Silvano P.; Haith, Gary L.; Stassinopoulos, Dimitris; Norvig, Peter (Technical Monitor)

2000-01-01

We describe a parallel genetic algorithm (GA) that automatically generates circuit designs using evolutionary search. A circuit-construction programming language is introduced and we show how evolution can generate practical analog circuit designs. Our system allows circuit size (number of devices), circuit topology, and device values to be evolved. We present experimental results as applied to analog filter and amplifier design tasks.

Stiffness modeling of compliant parallel mechanisms and applications in the performance analysis of a decoupled parallel compliant stage

NASA Astrophysics Data System (ADS)

Jiang, Yao; Li, Tie-Min; Wang, Li-Ping

2015-09-01

This paper investigates the stiffness modeling of compliant parallel mechanism (CPM) based on the matrix method. First, the general compliance matrix of a serial flexure chain is derived. The stiffness modeling of CPMs is next discussed in detail, considering the relative positions of the applied load and the selected displacement output point. The derived stiffness models have simple and explicit forms, and the input, output, and coupling stiffness matrices of the CPM can easily be obtained. The proposed analytical model is applied to the stiffness modeling and performance analysis of an XY parallel compliant stage with input and output decoupling characteristics. Then, the key geometrical parameters of the stage are optimized to obtain the minimum input decoupling degree. Finally, a prototype of the compliant stage is developed and its input axial stiffness, coupling characteristics, positioning resolution, and circular contouring performance are tested. The results demonstrate the excellent performance of the compliant stage and verify the effectiveness of the proposed theoretical model. The general stiffness models provided in this paper will be helpful for performance analysis, especially in determining coupling characteristics, and the structure optimization of the CPM.

Multirate-based fast parallel algorithms for 2-D DHT-based real-valued discrete Gabor transform.

PubMed

Tao, Liang; Kwan, Hon Keung

2012-07-01

Novel algorithms for the multirate and fast parallel implementation of the 2-D discrete Hartley transform (DHT)-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented in this paper. A 2-D multirate-based analysis convolver bank is designed for the 2-D RDGT, and a 2-D multirate-based synthesis convolver bank is designed for the 2-D inverse RDGT. The parallel channels in each of the two convolver banks have a unified structure and can apply the 2-D fast DHT algorithm to speed up their computations. The computational complexity of each parallel channel is low and is independent of the Gabor oversampling rate. All the 2-D RDGT coefficients of an image are computed in parallel during the analysis process and can be reconstructed in parallel during the synthesis process. The computational complexity and time of the proposed parallel algorithms are analyzed and compared with those of the existing fastest algorithms for 2-D discrete Gabor transforms. The results indicate that the proposed algorithms are the fastest, which make them attractive for real-time image processing.

Opus: A Coordination Language for Multidisciplinary Applications

NASA Technical Reports Server (NTRS)

Chapman, Barbara; Haines, Matthew; Mehrotra, Piyush; Zima, Hans; vanRosendale, John

1997-01-01

Data parallel languages, such as High Performance fortran, can be successfully applied to a wide range of numerical applications. However, many advanced scientific and engineering applications are multidisciplinary and heterogeneous in nature, and thus do not fit well into the data parallel paradigm. In this paper we present Opus, a language designed to fill this gap. The central concept of Opus is a mechanism called ShareD Abstractions (SDA). An SDA can be used as a computation server, i.e., a locus of computational activity, or as a data repository for sharing data between asynchronous tasks. SDAs can be internally data parallel, providing support for the integration of data and task parallelism as well as nested task parallelism. They can thus be used to express multidisciplinary applications in a natural and efficient way. In this paper we describe the features of the language through a series of examples and give an overview of the runtime support required to implement these concepts in parallel and distributed environments.

A parallel simulated annealing algorithm for standard cell placement on a hypercube computer

NASA Technical Reports Server (NTRS)

Jones, Mark Howard

1987-01-01

A parallel version of a simulated annealing algorithm is presented which is targeted to run on a hypercube computer. A strategy for mapping the cells in a two dimensional area of a chip onto processors in an n-dimensional hypercube is proposed such that both small and large distance moves can be applied. Two types of moves are allowed: cell exchanges and cell displacements. The computation of the cost function in parallel among all the processors in the hypercube is described along with a distributed data structure that needs to be stored in the hypercube to support parallel cost evaluation. A novel tree broadcasting strategy is used extensively in the algorithm for updating cell locations in the parallel environment. Studies on the performance of the algorithm on example industrial circuits show that it is faster and gives better final placement results than the uniprocessor simulated annealing algorithms. An improved uniprocessor algorithm is proposed which is based on the improved results obtained from parallelization of the simulated annealing algorithm.

Parallelism between gradient temperature raman spectroscopy and differential scanning calorimetry results

USDA-ARS?s Scientific Manuscript database

Temperature dependent Raman spectroscopy (TDR) applies the temperature gradients utilized in differential scanning calorimetry (DSC) to Raman spectroscopy, providing a straightforward technique to identify molecular rearrangements that occur just prior to phase transitions. Herein we apply TDR and D...

Line-drawing algorithms for parallel machines

NASA Technical Reports Server (NTRS)

Pang, Alex T.

1990-01-01

The fact that conventional line-drawing algorithms, when applied directly on parallel machines, can lead to very inefficient codes is addressed. It is suggested that instead of modifying an existing algorithm for a parallel machine, a more efficient implementation can be produced by going back to the invariants in the definition. Popular line-drawing algorithms are compared with two alternatives; distance to a line (a point is on the line if sufficiently close to it) and intersection with a line (a point on the line if an intersection point). For massively parallel single-instruction-multiple-data (SIMD) machines (with thousands of processors and up), the alternatives provide viable line-drawing algorithms. Because of the pixel-per-processor mapping, their performance is independent of the line length and orientation.

Improving parallel I/O autotuning with performance modeling

DOE PAGES

Behzad, Babak; Byna, Surendra; Wild, Stefan M.; ...

2014-01-01

Various layers of the parallel I/O subsystem offer tunable parameters for improving I/O performance on large-scale computers. However, searching through a large parameter space is challenging. We are working towards an autotuning framework for determining the parallel I/O parameters that can achieve good I/O performance for different data write patterns. In this paper, we characterize parallel I/O and discuss the development of predictive models for use in effectively reducing the parameter space. Furthermore, applying our technique on tuning an I/O kernel derived from a large-scale simulation code shows that the search time can be reduced from 12 hours to 2more » hours, while achieving 54X I/O performance speedup.« less

Dynamic modeling of parallel robots for computed-torque control implementation

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

Codourey, A.

1998-12-01

In recent years, increased interest in parallel robots has been observed. Their control with modern theory, such as the computed-torque method, has, however, been restrained, essentially due to the difficulty in establishing a simple dynamic model that can be calculated in real time. In this paper, a simple method based on the virtual work principle is proposed for modeling parallel robots. The mass matrix of the robot, needed for decoupling control strategies, does not explicitly appear in the formulation; however, it can be computed separately, based on kinetic energy considerations. The method is applied to the DELTA parallel robot, leadingmore » to a very efficient model that has been implemented in a real-time computed-torque control algorithm.« less

Portable parallel stochastic optimization for the design of aeropropulsion components

NASA Technical Reports Server (NTRS)

Sues, Robert H.; Rhodes, G. S.

1994-01-01

This report presents the results of Phase 1 research to develop a methodology for performing large-scale Multi-disciplinary Stochastic Optimization (MSO) for the design of aerospace systems ranging from aeropropulsion components to complete aircraft configurations. The current research recognizes that such design optimization problems are computationally expensive, and require the use of either massively parallel or multiple-processor computers. The methodology also recognizes that many operational and performance parameters are uncertain, and that uncertainty must be considered explicitly to achieve optimum performance and cost. The objective of this Phase 1 research was to initialize the development of an MSO methodology that is portable to a wide variety of hardware platforms, while achieving efficient, large-scale parallelism when multiple processors are available. The first effort in the project was a literature review of available computer hardware, as well as review of portable, parallel programming environments. The first effort was to implement the MSO methodology for a problem using the portable parallel programming language, Parallel Virtual Machine (PVM). The third and final effort was to demonstrate the example on a variety of computers, including a distributed-memory multiprocessor, a distributed-memory network of workstations, and a single-processor workstation. Results indicate the MSO methodology can be well-applied towards large-scale aerospace design problems. Nearly perfect linear speedup was demonstrated for computation of optimization sensitivity coefficients on both a 128-node distributed-memory multiprocessor (the Intel iPSC/860) and a network of workstations (speedups of almost 19 times achieved for 20 workstations). Very high parallel efficiencies (75 percent for 31 processors and 60 percent for 50 processors) were also achieved for computation of aerodynamic influence coefficients on the Intel. Finally, the multi-level parallelization strategy that will be needed for large-scale MSO problems was demonstrated to be highly efficient. The same parallel code instructions were used on both platforms, demonstrating portability. There are many applications for which MSO can be applied, including NASA's High-Speed-Civil Transport, and advanced propulsion systems. The use of MSO will reduce design and development time and testing costs dramatically.

An embedded multi-core parallel model for real-time stereo imaging

NASA Astrophysics Data System (ADS)

He, Wenjing; Hu, Jian; Niu, Jingyu; Li, Chuanrong; Liu, Guangyu

2018-04-01

The real-time processing based on embedded system will enhance the application capability of stereo imaging for LiDAR and hyperspectral sensor. The task partitioning and scheduling strategies for embedded multiprocessor system starts relatively late, compared with that for PC computer. In this paper, aimed at embedded multi-core processing platform, a parallel model for stereo imaging is studied and verified. After analyzing the computing amount, throughout capacity and buffering requirements, a two-stage pipeline parallel model based on message transmission is established. This model can be applied to fast stereo imaging for airborne sensors with various characteristics. To demonstrate the feasibility and effectiveness of the parallel model, a parallel software was designed using test flight data, based on the 8-core DSP processor TMS320C6678. The results indicate that the design performed well in workload distribution and had a speed-up ratio up to 6.4.

A software architecture for multidisciplinary applications: Integrating task and data parallelism

NASA Technical Reports Server (NTRS)

Chapman, Barbara; Mehrotra, Piyush; Vanrosendale, John; Zima, Hans

1994-01-01

Data parallel languages such as Vienna Fortran and HPF can be successfully applied to a wide range of numerical applications. However, many advanced scientific and engineering applications are of a multidisciplinary and heterogeneous nature and thus do not fit well into the data parallel paradigm. In this paper we present new Fortran 90 language extensions to fill this gap. Tasks can be spawned as asynchronous activities in a homogeneous or heterogeneous computing environment; they interact by sharing access to Shared Data Abstractions (SDA's). SDA's are an extension of Fortran 90 modules, representing a pool of common data, together with a set of Methods for controlled access to these data and a mechanism for providing persistent storage. Our language supports the integration of data and task parallelism as well as nested task parallelism and thus can be used to express multidisciplinary applications in a natural and efficient way.

An interactive parallel programming environment applied in atmospheric science

NASA Technical Reports Server (NTRS)

vonLaszewski, G.

1996-01-01

This article introduces an interactive parallel programming environment (IPPE) that simplifies the generation and execution of parallel programs. One of the tasks of the environment is to generate message-passing parallel programs for homogeneous and heterogeneous computing platforms. The parallel programs are represented by using visual objects. This is accomplished with the help of a graphical programming editor that is implemented in Java and enables portability to a wide variety of computer platforms. In contrast to other graphical programming systems, reusable parts of the programs can be stored in a program library to support rapid prototyping. In addition, runtime performance data on different computing platforms is collected in a database. A selection process determines dynamically the software and the hardware platform to be used to solve the problem in minimal wall-clock time. The environment is currently being tested on a Grand Challenge problem, the NASA four-dimensional data assimilation system.

Fast hydrological model calibration based on the heterogeneous parallel computing accelerated shuffled complex evolution method

NASA Astrophysics Data System (ADS)

Kan, Guangyuan; He, Xiaoyan; Ding, Liuqian; Li, Jiren; Hong, Yang; Zuo, Depeng; Ren, Minglei; Lei, Tianjie; Liang, Ke

2018-01-01

Hydrological model calibration has been a hot issue for decades. The shuffled complex evolution method developed at the University of Arizona (SCE-UA) has been proved to be an effective and robust optimization approach. However, its computational efficiency deteriorates significantly when the amount of hydrometeorological data increases. In recent years, the rise of heterogeneous parallel computing has brought hope for the acceleration of hydrological model calibration. This study proposed a parallel SCE-UA method and applied it to the calibration of a watershed rainfall-runoff model, the Xinanjiang model. The parallel method was implemented on heterogeneous computing systems using OpenMP and CUDA. Performance testing and sensitivity analysis were carried out to verify its correctness and efficiency. Comparison results indicated that heterogeneous parallel computing-accelerated SCE-UA converged much more quickly than the original serial version and possessed satisfactory accuracy and stability for the task of fast hydrological model calibration.

Analyzing Tropical Waves Using the Parallel Ensemble Empirical Model Decomposition Method: Preliminary Results from Hurricane Sandy

NASA Technical Reports Server (NTRS)

Shen, Bo-Wen; Cheung, Samson; Li, Jui-Lin F.; Wu, Yu-ling

2013-01-01

In this study, we discuss the performance of the parallel ensemble empirical mode decomposition (EMD) in the analysis of tropical waves that are associated with tropical cyclone (TC) formation. To efficiently analyze high-resolution, global, multiple-dimensional data sets, we first implement multilevel parallelism into the ensemble EMD (EEMD) and obtain a parallel speedup of 720 using 200 eight-core processors. We then apply the parallel EEMD (PEEMD) to extract the intrinsic mode functions (IMFs) from preselected data sets that represent (1) idealized tropical waves and (2) large-scale environmental flows associated with Hurricane Sandy (2012). Results indicate that the PEEMD is efficient and effective in revealing the major wave characteristics of the data, such as wavelengths and periods, by sifting out the dominant (wave) components. This approach has a potential for hurricane climate study by examining the statistical relationship between tropical waves and TC formation.

Parallel, Asynchronous Executive (PAX): System concepts, facilities, and architecture

NASA Technical Reports Server (NTRS)

Jones, W. H.

1983-01-01

The Parallel, Asynchronous Executive (PAX) is a software operating system simulation that allows many computers to work on a single problem at the same time. PAX is currently implemented on a UNIVAC 1100/42 computer system. Independent UNIVAC runstreams are used to simulate independent computers. Data are shared among independent UNIVAC runstreams through shared mass-storage files. PAX has achieved the following: (1) applied several computing processes simultaneously to a single, logically unified problem; (2) resolved most parallel processor conflicts by careful work assignment; (3) resolved by means of worker requests to PAX all conflicts not resolved by work assignment; (4) provided fault isolation and recovery mechanisms to meet the problems of an actual parallel, asynchronous processing machine. Additionally, one real-life problem has been constructed for the PAX environment. This is CASPER, a collection of aerodynamic and structural dynamic problem simulation routines. CASPER is not discussed in this report except to provide examples of parallel-processing techniques.

A Framework for Parallel Unstructured Grid Generation for Complex Aerodynamic Simulations

NASA Technical Reports Server (NTRS)

Zagaris, George; Pirzadeh, Shahyar Z.; Chrisochoides, Nikos

2009-01-01

A framework for parallel unstructured grid generation targeting both shared memory multi-processors and distributed memory architectures is presented. The two fundamental building-blocks of the framework consist of: (1) the Advancing-Partition (AP) method used for domain decomposition and (2) the Advancing Front (AF) method used for mesh generation. Starting from the surface mesh of the computational domain, the AP method is applied recursively to generate a set of sub-domains. Next, the sub-domains are meshed in parallel using the AF method. The recursive nature of domain decomposition naturally maps to a divide-and-conquer algorithm which exhibits inherent parallelism. For the parallel implementation, the Master/Worker pattern is employed to dynamically balance the varying workloads of each task on the set of available CPUs. Performance results by this approach are presented and discussed in detail as well as future work and improvements.

Increasing the perceptual salience of relationships in parallel coordinate plots.

PubMed

Harter, Jonathan M; Wu, Xunlei; Alabi, Oluwafemi S; Phadke, Madhura; Pinto, Lifford; Dougherty, Daniel; Petersen, Hannah; Bass, Steffen; Taylor, Russell M

2012-01-01

We present three extensions to parallel coordinates that increase the perceptual salience of relationships between axes in multivariate data sets: (1) luminance modulation maintains the ability to preattentively detect patterns in the presence of overplotting, (2) adding a one-vs.-all variable display highlights relationships between one variable and all others, and (3) adding a scatter plot within the parallel-coordinates display preattentively highlights clusters and spatial layouts without strongly interfering with the parallel-coordinates display. These techniques can be combined with one another and with existing extensions to parallel coordinates, and two of them generalize beyond cases with known-important axes. We applied these techniques to two real-world data sets (relativistic heavy-ion collision hydrodynamics and weather observations with statistical principal component analysis) as well as the popular car data set. We present relationships discovered in the data sets using these methods.

A parallel graded-mesh FDTD algorithm for human-antenna interaction problems.

PubMed

Catarinucci, Luca; Tarricone, Luciano

2009-01-01

The finite difference time domain method (FDTD) is frequently used for the numerical solution of a wide variety of electromagnetic (EM) problems and, among them, those concerning human exposure to EM fields. In many practical cases related to the assessment of occupational EM exposure, large simulation domains are modeled and high space resolution adopted, so that strong memory and central processing unit power requirements have to be satisfied. To better afford the computational effort, the use of parallel computing is a winning approach; alternatively, subgridding techniques are often implemented. However, the simultaneous use of subgridding schemes and parallel algorithms is very new. In this paper, an easy-to-implement and highly-efficient parallel graded-mesh (GM) FDTD scheme is proposed and applied to human-antenna interaction problems, demonstrating its appropriateness in dealing with complex occupational tasks and showing its capability to guarantee the advantages of a traditional subgridding technique without affecting the parallel FDTD performance.

Reliability of a Parallel Pipe Network

NASA Technical Reports Server (NTRS)

Herrera, Edgar; Chamis, Christopher (Technical Monitor)

2001-01-01

The goal of this NASA-funded research is to advance research and education objectives in theoretical and computational probabilistic structural analysis, reliability, and life prediction methods for improved aerospace and aircraft propulsion system components. Reliability methods are used to quantify response uncertainties due to inherent uncertainties in design variables. In this report, several reliability methods are applied to a parallel pipe network. The observed responses are the head delivered by a main pump and the head values of two parallel lines at certain flow rates. The probability that the flow rates in the lines will be less than their specified minimums will be discussed.

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

Weston, Brian T.

This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations ofmore » the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser-induced phase change problems in 2D and 3D.« less

Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains.

PubMed

Balzani, Daniel; Deparis, Simone; Fausten, Simon; Forti, Davide; Heinlein, Alexander; Klawonn, Axel; Quarteroni, Alfio; Rheinbach, Oliver; Schröder, Joerg

2016-10-01

The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid-structure interactions and on the other hand the use of a material model for the vessel wall that is able to capture the relevant features of the material behavior. One of the main contributions of this paper is the application of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid-structure interaction, together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. The fluid-structure interaction problem is solved using a monolithic approach; that is, the nonlinear system is solved (after time and space discretizations) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple - but nonsymmetric - curved geometry is proposed that is demonstrated to be suitable as a benchmark testbed for fluid-structure interaction simulations in biomechanics where nonlinear structural models are used. Based on the curved benchmark geometry, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. It turns out that often-used standard displacement elements with linear shape functions are not sufficient to provide good approximations of the arterial wall stresses, whereas for standard displacement elements or F-bar formulations with quadratic shape functions, suitable results are obtained. For the time discretization, a second-order backward differentiation formula scheme is used. It is shown that the curved geometry enables the analysis of non-rotationally symmetric distributions of the mechanical fields. For instance, the maximal shear stresses in the fluid-structure interface are found to be higher in the inner curve that corresponds to clinical observations indicating a high plaque nucleation probability at such locations. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

An Extension of a Parallel-Distributed Processing Framework of Reading Aloud in Japanese: Human Nonword Reading Accuracy Does Not Require a Sequential Mechanism

ERIC Educational Resources Information Center

Ikeda, Kenji; Ueno, Taiji; Ito, Yuichi; Kitagami, Shinji; Kawaguchi, Jun

2017-01-01

Humans can pronounce a nonword (e.g., rint). Some researchers have interpreted this behavior as requiring a sequential mechanism by which a grapheme-phoneme correspondence rule is applied to each grapheme in turn. However, several parallel-distributed processing (PDP) models in English have simulated human nonword reading accuracy without a…

An equivalent viscoelastic model for rock mass with parallel joints

NASA Astrophysics Data System (ADS)

Li, Jianchun; Ma, Guowei; Zhao, Jian

2010-03-01

An equivalent viscoelastic medium model is proposed for rock mass with parallel joints. A concept of "virtual wave source (VWS)" is proposed to take into account the wave reflections between the joints. The equivalent model can be effectively applied to analyze longitudinal wave propagation through discontinuous media with parallel joints. Parameters in the equivalent viscoelastic model are derived analytically based on longitudinal wave propagation across a single rock joint. The proposed model is then verified by applying identical incident waves to the discontinuous and equivalent viscoelastic media at one end to compare the output waves at the other end. When the wavelength of the incident wave is sufficiently long compared to the joint spacing, the effect of the VWS on wave propagation in rock mass is prominent. The results from the equivalent viscoelastic medium model are very similar to those determined from the displacement discontinuity method. Frequency dependence and joint spacing effect on the equivalent viscoelastic model and the VWS method are discussed.

Graphics Processing Unit Assisted Thermographic Compositing

NASA Technical Reports Server (NTRS)

Ragasa, Scott; McDougal, Matthew; Russell, Sam

2012-01-01

Objective: To develop a software application utilizing general purpose graphics processing units (GPUs) for the analysis of large sets of thermographic data. Background: Over the past few years, an increasing effort among scientists and engineers to utilize the GPU in a more general purpose fashion is allowing for supercomputer level results at individual workstations. As data sets grow, the methods to work them grow at an equal, and often great, pace. Certain common computations can take advantage of the massively parallel and optimized hardware constructs of the GPU to allow for throughput that was previously reserved for compute clusters. These common computations have high degrees of data parallelism, that is, they are the same computation applied to a large set of data where the result does not depend on other data elements. Signal (image) processing is one area were GPUs are being used to greatly increase the performance of certain algorithms and analysis techniques. Technical Methodology/Approach: Apply massively parallel algorithms and data structures to the specific analysis requirements presented when working with thermographic data sets.

The Fortran-P Translator: Towards Automatic Translation of Fortran 77 Programs for Massively Parallel Processors

DOE PAGES

O'keefe, Matthew; Parr, Terence; Edgar, B. Kevin; ...

1995-01-01

Massively parallel processors (MPPs) hold the promise of extremely high performance that, if realized, could be used to study problems of unprecedented size and complexity. One of the primary stumbling blocks to this promise has been the lack of tools to translate application codes to MPP form. In this article we show how applications codes written in a subset of Fortran 77, called Fortran-P, can be translated to achieve good performance on several massively parallel machines. This subset can express codes that are self-similar, where the algorithm applied to the global data domain is also applied to each subdomain. Wemore » have found many codes that match the Fortran-P programming style and have converted them using our tools. We believe a self-similar coding style will accomplish what a vectorizable style has accomplished for vector machines by allowing the construction of robust, user-friendly, automatic translation systems that increase programmer productivity and generate fast, efficient code for MPPs.« less

Distensibility and pressure-flow relationship of the pulmonary circulation. II. Multibranched model.

PubMed

Bshouty, Z; Younes, M

1990-04-01

The contribution of distensibility and recruitment to the distinctive behavior of the pulmonary circulation is not known. To examine this question we developed a multibranched model in which an arterial vascular bed bifurcates sequentially up to 8 parallel channels that converge and reunite at the venous side to end in the left atrium. Eight resistors representing the capillary bed separate the arterial and venous beds. The elastic behavior of capillaries and extra-alveolar vessels was modeled after Fung and Sobin (Circ. Res. 30: 451-490, 1972) and Smith and Mitzner (J. Appl. Physiol. 48: 450-467, 1980), respectively. Forces acting on each component are modified and calculated individually, thus enabling the user to explore the effects of parallel and longitudinal heterogeneities in applied forces (e.g., gravity, vasomotor tone). Model predictions indicate that the contribution of distensibility to nonlinearities in the pressure-flow (P-F) and atrial-pulmonary arterial pressure (Pla-Ppa) relationships is substantial, whereas gravity-related recruitment contributes very little to these relationships. In addition, Pla-Ppa relationships, obtained at a constant flow, have no discriminating ability in identifying the presence or absence of a waterfall along the circulation. The P-F relationship is routinely shifted in a parallel fashion, within the physiological flow range, whenever extra forces (e.g., lung volume, tone) are applied uniformly at one or more branching levels, regardless of whether a waterfall is created. For a given applied force, the magnitude of parallel shift varies with proportion of the circulation subjected to the added force and with Pla.

High voltage pulse generator

DOEpatents

Fasching, George E.

1977-03-08

An improved high-voltage pulse generator has been provided which is especially useful in ultrasonic testing of rock core samples. An N number of capacitors are charged in parallel to V volts and at the proper instance are coupled in series to produce a high-voltage pulse of N times V volts. Rapid switching of the capacitors from the paralleled charging configuration to the series discharging configuration is accomplished by using silicon-controlled rectifiers which are chain self-triggered following the initial triggering of a first one of the rectifiers connected between the first and second of the plurality of charging capacitors. A timing and triggering circuit is provided to properly synchronize triggering pulses to the first SCR at a time when the charging voltage is not being applied to the parallel-connected charging capacitors. Alternate circuits are provided for controlling the application of the charging voltage from a charging circuit to be applied to the parallel capacitors which provides a selection of at least two different intervals in which the charging voltage is turned "off" to allow the SCR's connecting the capacitors in series to turn "off" before recharging begins. The high-voltage pulse-generating circuit including the N capacitors and corresponding SCR's which connect the capacitors in series when triggered "on" further includes diodes and series-connected inductors between the parallel-connected charging capacitors which allow sufficiently fast charging of the capacitors for a high pulse repetition rate and yet allow considerable control of the decay time of the high-voltage pulses from the pulse-generating circuit.

An application of analyzing the trajectories of two disorders: A parallel piecewise growth model of substance use and attention-deficit/hyperactivity disorder.

PubMed

Mamey, Mary Rose; Barbosa-Leiker, Celestina; McPherson, Sterling; Burns, G Leonard; Parks, Craig; Roll, John

2015-12-01

Researchers often want to examine 2 comorbid conditions simultaneously. One strategy to do so is through the use of parallel latent growth curve modeling (LGCM). This statistical technique allows for the simultaneous evaluation of 2 disorders to determine the explanations and predictors of change over time. Additionally, a piecewise model can help identify whether there are more than 2 growth processes within each disorder (e.g., during a clinical trial). A parallel piecewise LGCM was applied to self-reported attention-deficit/hyperactivity disorder (ADHD) and self-reported substance use symptoms in 303 adolescents enrolled in cognitive-behavioral therapy treatment for a substance use disorder and receiving either oral-methylphenidate or placebo for ADHD across 16 weeks. Assessing these 2 disorders concurrently allowed us to determine whether elevated levels of 1 disorder predicted elevated levels or increased risk of the other disorder. First, a piecewise growth model measured ADHD and substance use separately. Next, a parallel piecewise LGCM was used to estimate the regressions across disorders to determine whether higher scores at baseline of the disorders (i.e., ADHD or substance use disorder) predicted rates of change in the related disorder. Finally, treatment was added to the model to predict change. While the analyses revealed no significant relationships across disorders, this study explains and applies a parallel piecewise growth model to examine the developmental processes of comorbid conditions over the course of a clinical trial. Strengths of piecewise and parallel LGCMs for other addictions researchers interested in examining dual processes over time are discussed. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

Parallel transmit beamforming using orthogonal frequency division multiplexing applied to harmonic imaging--a feasibility study.

PubMed

Demi, Libertario; Verweij, Martin D; Van Dongen, Koen W A

2012-11-01

Real-time 2-D or 3-D ultrasound imaging systems are currently used for medical diagnosis. To achieve the required data acquisition rate, these systems rely on parallel beamforming, i.e., a single wide-angled beam is used for transmission and several narrow parallel beams are used for reception. When applied to harmonic imaging, the demand for high-amplitude pressure wave fields, necessary to generate the harmonic components, conflicts with the use of a wide-angled beam in transmission because this results in a large spatial decay of the acoustic pressure. To enhance the amplitude of the harmonics, it is preferable to do the reverse: transmit several narrow parallel beams and use a wide-angled beam in reception. Here, this concept is investigated to determine whether it can be used for harmonic imaging. The method proposed in this paper relies on orthogonal frequency division multiplexing (OFDM), which is used to create distinctive parallel beams in transmission. To test the proposed method, a numerical study has been performed, in which the transmit, receive, and combined beam profiles generated by a linear array have been simulated for the second-harmonic component. Compared with standard parallel beamforming, application of the proposed technique results in a gain of 12 dB for the main beam and in a reduction of the side lobes. Experimental verification in water has also been performed. Measurements obtained with a single-element emitting transducer and a hydrophone receiver confirm the possibility of exciting a practical ultrasound transducer with multiple Gaussian modulated pulses, each having a different center frequency, and the capability to generate distinguishable second-harmonic components.

HMC algorithm with multiple time scale integration and mass preconditioning

NASA Astrophysics Data System (ADS)

Urbach, C.; Jansen, K.; Shindler, A.; Wenger, U.

2006-01-01

We present a variant of the HMC algorithm with mass preconditioning (Hasenbusch acceleration) and multiple time scale integration. We have tested this variant for standard Wilson fermions at β=5.6 and at pion masses ranging from 380 to 680 MeV. We show that in this situation its performance is comparable to the recently proposed HMC variant with domain decomposition as preconditioner. We give an update of the "Berlin Wall" figure, comparing the performance of our variant of the HMC algorithm to other published performance data. Advantages of the HMC algorithm with mass preconditioning and multiple time scale integration are that it is straightforward to implement and can be used in combination with a wide variety of lattice Dirac operators.

Preconditioned conjugate residual methods for the solution of spectral equations

NASA Technical Reports Server (NTRS)

Wong, Y. S.; Zang, T. A.; Hussaini, M. Y.

1986-01-01

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

On linearization and preconditioning for radiation diffusion coupled to material thermal conduction equations

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

Feng, Tao, E-mail: fengtao2@mail.ustc.edu.cn; Graduate School of China Academy Engineering Physics, Beijing 100083; An, Hengbin, E-mail: an_hengbin@iapcm.ac.cn

2013-03-01

Jacobian-free Newton–Krylov (JFNK) method is an effective algorithm for solving large scale nonlinear equations. One of the most important advantages of JFNK method is that there is no necessity to form and store the Jacobian matrix of the nonlinear system when JFNK method is employed. However, an approximation of the Jacobian is needed for the purpose of preconditioning. In this paper, JFNK method is employed to solve a class of non-equilibrium radiation diffusion coupled to material thermal conduction equations, and two preconditioners are designed by linearizing the equations in two methods. Numerical results show that the two preconditioning methods canmore » improve the convergence behavior and efficiency of JFNK method.« less

Numerical Solution of the Gyrokinetic Poisson Equation in TEMPEST

NASA Astrophysics Data System (ADS)

Dorr, Milo; Cohen, Bruce; Cohen, Ronald; Dimits, Andris; Hittinger, Jeffrey; Kerbel, Gary; Nevins, William; Rognlien, Thomas; Umansky, Maxim; Xiong, Andrew; Xu, Xueqiao

2006-10-01

The gyrokinetic Poisson (GKP) model in the TEMPEST continuum gyrokinetic edge plasma code yields the electrostatic potential due to the charge density of electrons and an arbitrary number of ion species including the effects of gyroaveraging in the limit kρ1. The TEMPEST equations are integrated as a differential algebraic system involving a nonlinear system solve via Newton-Krylov iteration. The GKP preconditioner block is inverted using a multigrid preconditioned conjugate gradient (CG) algorithm. Electrons are treated as kinetic or adiabatic. The Boltzmann relation in the adiabatic option employs flux surface averaging to maintain neutrality within field lines and is solved self-consistently with the GKP equation. A decomposition procedure circumvents the near singularity of the GKP Jacobian block that otherwise degrades CG convergence.

Parallel dispatch: a new paradigm of electrical power system dispatch

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

Zhang, Jun Jason; Wang, Fei-Yue; Wang, Qiang

Modern power systems are evolving into sociotechnical systems with massive complexity, whose real-time operation and dispatch go beyond human capability. Thus, the need for developing and applying new intelligent power system dispatch tools are of great practical significance. In this paper, we introduce the overall business model of power system dispatch, the top level design approach of an intelligent dispatch system, and the parallel intelligent technology with its dispatch applications. We expect that a new dispatch paradigm, namely the parallel dispatch, can be established by incorporating various intelligent technologies, especially the parallel intelligent technology, to enable secure operation of complexmore » power grids, extend system operators U+02BC capabilities, suggest optimal dispatch strategies, and to provide decision-making recommendations according to power system operational goals.« less

Parallel Monotonic Basin Hopping for Low Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

McCarty, Steven L.; McGuire, Melissa L.

2018-01-01

Monotonic Basin Hopping has been shown to be an effective method of solving low thrust trajectory optimization problems. This paper outlines an extension to the common serial implementation by parallelizing it over any number of available compute cores. The Parallel Monotonic Basin Hopping algorithm described herein is shown to be an effective way to more quickly locate feasible solutions, and improve locally optimal solutions in an automated way without requiring a feasible initial guess. The increased speed achieved through parallelization enables the algorithm to be applied to more complex problems that would otherwise be impractical for a serial implementation. Low thrust cislunar transfers and a hybrid Mars example case demonstrate the effectiveness of the algorithm. Finally, a preliminary scaling study quantifies the expected decrease in solve time compared to a serial implementation.,

Anomalous pinch of turbulent plasmas driven by the magnetic-drift-induced Lorentz force through the Stokes-Einstein relation

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

Wang, Shaojie, E-mail: wangsj@ustc.edu.cn

It is found that the Lorentz force generated by the magnetic drift drives a generic plasma pinch flux of particle, energy and momentum through the Stokes-Einstein relation. The proposed theoretical model applies for both electrons and ions, trapped particles, and passing particles. An anomalous parallel current pinch due to the electrostatic turbulence with long parallel wave-length is predicted.

Symposium on Parallel Computational Methods for Large-scale Structural Analysis and Design, 2nd, Norfolk, VA, US

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O. (Editor); Housner, Jerrold M. (Editor)

1993-01-01

Computing speed is leaping forward by several orders of magnitude each decade. Engineers and scientists gathered at a NASA Langley symposium to discuss these exciting trends as they apply to parallel computational methods for large-scale structural analysis and design. Among the topics discussed were: large-scale static analysis; dynamic, transient, and thermal analysis; domain decomposition (substructuring); and nonlinear and numerical methods.

Base drive for paralleled inverter systems

NASA Technical Reports Server (NTRS)

Nagano, S. (Inventor)

1980-01-01

In a paralleled inverter system, a positive feedback current derived from the total current from all of the modules of the inverter system is applied to the base drive of each of the power transistors of all modules, thereby to provide all modules protection against open or short circuit faults occurring in any of the modules, and force equal current sharing among the modules during turn on of the power transistors.

Scalable High Performance Computing: Direct and Large-Eddy Turbulent Flow Simulations Using Massively Parallel Computers

NASA Technical Reports Server (NTRS)

Morgan, Philip E.

2004-01-01

This final report contains reports of research related to the tasks "Scalable High Performance Computing: Direct and Lark-Eddy Turbulent FLow Simulations Using Massively Parallel Computers" and "Devleop High-Performance Time-Domain Computational Electromagnetics Capability for RCS Prediction, Wave Propagation in Dispersive Media, and Dual-Use Applications. The discussion of Scalable High Performance Computing reports on three objectives: validate, access scalability, and apply two parallel flow solvers for three-dimensional Navier-Stokes flows; develop and validate a high-order parallel solver for Direct Numerical Simulations (DNS) and Large Eddy Simulation (LES) problems; and Investigate and develop a high-order Reynolds averaged Navier-Stokes turbulence model. The discussion of High-Performance Time-Domain Computational Electromagnetics reports on five objectives: enhancement of an electromagnetics code (CHARGE) to be able to effectively model antenna problems; utilize lessons learned in high-order/spectral solution of swirling 3D jets to apply to solving electromagnetics project; transition a high-order fluids code, FDL3DI, to be able to solve Maxwell's Equations using compact-differencing; develop and demonstrate improved radiation absorbing boundary conditions for high-order CEM; and extend high-order CEM solver to address variable material properties. The report also contains a review of work done by the systems engineer.

Automated Long-Term Monitoring of Parallel Microfluidic Operations Applying a Machine Vision-Assisted Positioning Method

PubMed Central

Yip, Hon Ming; Li, John C. S.; Cui, Xin; Gao, Qiannan; Leung, Chi Chiu

2014-01-01

As microfluidics has been applied extensively in many cell and biochemical applications, monitoring the related processes is an important requirement. In this work, we design and fabricate a high-throughput microfluidic device which contains 32 microchambers to perform automated parallel microfluidic operations and monitoring on an automated stage of a microscope. Images are captured at multiple spots on the device during the operations for monitoring samples in microchambers in parallel; yet the device positions may vary at different time points throughout operations as the device moves back and forth on a motorized microscopic stage. Here, we report an image-based positioning strategy to realign the chamber position before every recording of microscopic image. We fabricate alignment marks at defined locations next to the chambers in the microfluidic device as reference positions. We also develop image processing algorithms to recognize the chamber positions in real-time, followed by realigning the chambers to their preset positions in the captured images. We perform experiments to validate and characterize the device functionality and the automated realignment operation. Together, this microfluidic realignment strategy can be a platform technology to achieve precise positioning of multiple chambers for general microfluidic applications requiring long-term parallel monitoring of cell and biochemical activities. PMID:25133248

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions

NASA Astrophysics Data System (ADS)

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-04-01

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. We also show that the strategy is efficient and scales optimally with problem size.

A new scripting library for modeling flow and transport in fractured rock with channel networks

NASA Astrophysics Data System (ADS)

Dessirier, Benoît; Tsang, Chin-Fu; Niemi, Auli

2018-02-01

Deep crystalline bedrock formations are targeted to host spent nuclear fuel owing to their overall low permeability. They are however highly heterogeneous and only a few preferential paths pertaining to a small set of dominant rock fractures usually carry most of the flow or mass fluxes, a behavior known as channeling that needs to be accounted for in the performance assessment of repositories. Channel network models have been developed and used to investigate the effect of channeling. They are usually simpler than discrete fracture networks based on rock fracture mappings and rely on idealized full or sparsely populated lattices of channels. This study reexamines the fundamental parameter structure required to describe a channel network in terms of groundwater flow and solute transport, leading to an extended description suitable for unstructured arbitrary networks of channels. An implementation of this formalism in a Python scripting library is presented and released along with this article. A new algebraic multigrid preconditioner delivers a significant speedup in the flow solution step compared to previous channel network codes. 3D visualization is readily available for verification and interpretation of the results by exporting the results to an open and free dedicated software. The new code is applied to three example cases to verify its results on full uncorrelated lattices of channels, sparsely populated percolation lattices and to exemplify the use of unstructured networks to accommodate knowledge on local rock fractures.

Connectionism, parallel constraint satisfaction processes, and gestalt principles: (re) introducing cognitive dynamics to social psychology.

PubMed

Read, S J; Vanman, E J; Miller, L C

1997-01-01

We argue that recent work in connectionist modeling, in particular the parallel constraint satisfaction processes that are central to many of these models, has great importance for understanding issues of both historical and current concern for social psychologists. We first provide a brief description of connectionist modeling, with particular emphasis on parallel constraint satisfaction processes. Second, we examine the tremendous similarities between parallel constraint satisfaction processes and the Gestalt principles that were the foundation for much of modem social psychology. We propose that parallel constraint satisfaction processes provide a computational implementation of the principles of Gestalt psychology that were central to the work of such seminal social psychologists as Asch, Festinger, Heider, and Lewin. Third, we then describe how parallel constraint satisfaction processes have been applied to three areas that were key to the beginnings of modern social psychology and remain central today: impression formation and causal reasoning, cognitive consistency (balance and cognitive dissonance), and goal-directed behavior. We conclude by discussing implications of parallel constraint satisfaction principles for a number of broader issues in social psychology, such as the dynamics of social thought and the integration of social information within the narrow time frame of social interaction.

Revisiting Parallel Cyclic Reduction and Parallel Prefix-Based Algorithms for Block Tridiagonal System of Equations

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

Seal, Sudip K; Perumalla, Kalyan S; Hirshman, Steven Paul

2013-01-01

Simulations that require solutions of block tridiagonal systems of equations rely on fast parallel solvers for runtime efficiency. Leading parallel solvers that are highly effective for general systems of equations, dense or sparse, are limited in scalability when applied to block tridiagonal systems. This paper presents scalability results as well as detailed analyses of two parallel solvers that exploit the special structure of block tridiagonal matrices to deliver superior performance, often by orders of magnitude. A rigorous analysis of their relative parallel runtimes is shown to reveal the existence of a critical block size that separates the parameter space spannedmore » by the number of block rows, the block size and the processor count, into distinct regions that favor one or the other of the two solvers. Dependence of this critical block size on the above parameters as well as on machine-specific constants is established. These formal insights are supported by empirical results on up to 2,048 cores of a Cray XT4 system. To the best of our knowledge, this is the highest reported scalability for parallel block tridiagonal solvers to date.« less

Marketing Principles as Applied to the Corporate Information Center.

ERIC Educational Resources Information Center

Brown, Suzan A.

Marketing principles, as applied by major businesses around the world, can also be used by information professionals to grow and expand their presence within their own organization. This paper focuses on parallels between marketing in the industrial/research arena, and the needs of information professionals to expand business from existing…

A mechanism for efficient debugging of parallel programs

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

Miller, B.P.; Choi, J.D.

1988-01-01

This paper addresses the design and implementation of an integrated debugging system for parallel programs running on shared memory multi-processors (SMMP). The authors describe the use of flowback analysis to provide information on causal relationships between events in a program's execution without re-executing the program for debugging. The authors introduce a mechanism called incremental tracing that, by using semantic analyses of the debugged program, makes the flowback analysis practical with only a small amount of trace generated during execution. The extend flowback analysis to apply to parallel programs and describe a method to detect race conditions in the interactions ofmore » the co-operating processes.« less

Plasma Generator Using Spiral Conductors

NASA Technical Reports Server (NTRS)

Szatkowski, George N. (Inventor); Dudley, Kenneth L. (Inventor); Ticatch, Larry A. (Inventor); Smith, Laura J. (Inventor); Koppen, Sandra V. (Inventor); Nguyen, Truong X. (Inventor); Ely, Jay J. (Inventor)

2016-01-01

A plasma generator includes a pair of identical spiraled electrical conductors separated by dielectric material. Both spiraled conductors have inductance and capacitance wherein, in the presence of a time-varying electromagnetic field, the spiraled conductors resonate to generate a harmonic electromagnetic field response. The spiraled conductors lie in parallel planes and partially overlap one another in a direction perpendicular to the parallel planes. The geometric centers of the spiraled conductors define endpoints of a line that is non-perpendicular with respect to the parallel planes. A voltage source coupled across the spiraled conductors applies a voltage sufficient to generate a plasma in at least a portion of the dielectric material.

Local and nonlocal parallel heat transport in general magnetic fields

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

Del-Castillo-Negrete, Diego B; Chacon, Luis

2011-01-01

A novel approach for the study of parallel transport in magnetized plasmas is presented. The method avoids numerical pollution issues of grid-based formulations and applies to integrable and chaotic magnetic fields with local or nonlocal parallel closures. In weakly chaotic fields, the method gives the fractal structure of the devil's staircase radial temperature profile. In fully chaotic fields, the temperature exhibits self-similar spatiotemporal evolution with a stretched-exponential scaling function for local closures and an algebraically decaying one for nonlocal closures. It is shown that, for both closures, the effective radial heat transport is incompatible with the quasilinear diffusion model.

A novel milliliter-scale chemostat system for parallel cultivation of microorganisms in stirred-tank bioreactors.

PubMed

Schmideder, Andreas; Severin, Timm Steffen; Cremer, Johannes Heinrich; Weuster-Botz, Dirk

2015-09-20

A pH-controlled parallel stirred-tank bioreactor system was modified for parallel continuous cultivation on a 10 mL-scale by connecting multichannel peristaltic pumps for feeding and medium removal with micro-pipes (250 μm inner diameter). Parallel chemostat processes with Escherichia coli as an example showed high reproducibility with regard to culture volume and flow rates as well as dry cell weight, dissolved oxygen concentration and pH control at steady states (n=8, coefficient of variation <5%). Reliable estimation of kinetic growth parameters of E. coli was easily achieved within one parallel experiment by preselecting ten different steady states. Scalability of milliliter-scale steady state results was demonstrated by chemostat studies with a stirred-tank bioreactor on a liter-scale. Thus, parallel and continuously operated stirred-tank bioreactors on a milliliter-scale facilitate timesaving and cost reducing steady state studies with microorganisms. The applied continuous bioreactor system overcomes the drawbacks of existing miniaturized bioreactors, like poor mass transfer and insufficient process control. Copyright © 2015 Elsevier B.V. All rights reserved.

Parallel software support for computational structural mechanics

NASA Technical Reports Server (NTRS)

Jordan, Harry F.

1987-01-01

The application of the parallel programming methodology known as the Force was conducted. Two application issues were addressed. The first involves the efficiency of the implementation and its completeness in terms of satisfying the needs of other researchers implementing parallel algorithms. Support for, and interaction with, other Computational Structural Mechanics (CSM) researchers using the Force was the main issue, but some independent investigation of the Barrier construct, which is extremely important to overall performance, was also undertaken. Another efficiency issue which was addressed was that of relaxing the strong synchronization condition imposed on the self-scheduled parallel DO loop. The Force was extended by the addition of logical conditions to the cases of a parallel case construct and by the inclusion of a self-scheduled version of this construct. The second issue involved applying the Force to the parallelization of finite element codes such as those found in the NICE/SPAR testbed system. One of the more difficult problems encountered is the determination of what information in COMMON blocks is actually used outside of a subroutine and when a subroutine uses a COMMON block merely as scratch storage for internal temporary results.

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.

Parallel processing in a host plus multiple array processor system for radar

NASA Technical Reports Server (NTRS)

Barkan, B. Z.

1983-01-01

Host plus multiple array processor architecture is demonstrated to yield a modular, fast, and cost-effective system for radar processing. Software methodology for programming such a system is developed. Parallel processing with pipelined data flow among the host, array processors, and discs is implemented. Theoretical analysis of performance is made and experimentally verified. The broad class of problems to which the architecture and methodology can be applied is indicated.

On the equivalence of Gaussian elimination and Gauss-Jordan reduction in solving linear equations

NASA Technical Reports Server (NTRS)

Tsao, Nai-Kuan

1989-01-01

A novel general approach to round-off error analysis using the error complexity concepts is described. This is applied to the analysis of the Gaussian Elimination and Gauss-Jordan scheme for solving linear equations. The results show that the two algorithms are equivalent in terms of our error complexity measures. Thus the inherently parallel Gauss-Jordan scheme can be implemented with confidence if parallel computers are available.

Tough2{_}MP: A parallel version of TOUGH2

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

Zhang, Keni; Wu, Yu-Shu; Ding, Chris

2003-04-09

TOUGH2{_}MP is a massively parallel version of TOUGH2. It was developed for running on distributed-memory parallel computers to simulate large simulation problems that may not be solved by the standard, single-CPU TOUGH2 code. The new code implements an efficient massively parallel scheme, while preserving the full capacity and flexibility of the original TOUGH2 code. The new software uses the METIS software package for grid partitioning and AZTEC software package for linear-equation solving. The standard message-passing interface is adopted for communication among processors. Numerical performance of the current version code has been tested on CRAY-T3E and IBM RS/6000 SP platforms. Inmore » addition, the parallel code has been successfully applied to real field problems of multi-million-cell simulations for three-dimensional multiphase and multicomponent fluid and heat flow, as well as solute transport. In this paper, we will review the development of the TOUGH2{_}MP, and discuss the basic features, modules, and their applications.« less

Parallel computing in genomic research: advances and applications

PubMed Central

Ocaña, Kary; de Oliveira, Daniel

2015-01-01

Today’s genomic experiments have to process the so-called “biological big data” that is now reaching the size of Terabytes and Petabytes. To process this huge amount of data, scientists may require weeks or months if they use their own workstations. Parallelism techniques and high-performance computing (HPC) environments can be applied for reducing the total processing time and to ease the management, treatment, and analyses of this data. However, running bioinformatics experiments in HPC environments such as clouds, grids, clusters, and graphics processing unit requires the expertise from scientists to integrate computational, biological, and mathematical techniques and technologies. Several solutions have already been proposed to allow scientists for processing their genomic experiments using HPC capabilities and parallelism techniques. This article brings a systematic review of literature that surveys the most recently published research involving genomics and parallel computing. Our objective is to gather the main characteristics, benefits, and challenges that can be considered by scientists when running their genomic experiments to benefit from parallelism techniques and HPC capabilities. PMID:26604801

Parallel computing in genomic research: advances and applications.

PubMed

Ocaña, Kary; de Oliveira, Daniel

2015-01-01

Today's genomic experiments have to process the so-called "biological big data" that is now reaching the size of Terabytes and Petabytes. To process this huge amount of data, scientists may require weeks or months if they use their own workstations. Parallelism techniques and high-performance computing (HPC) environments can be applied for reducing the total processing time and to ease the management, treatment, and analyses of this data. However, running bioinformatics experiments in HPC environments such as clouds, grids, clusters, and graphics processing unit requires the expertise from scientists to integrate computational, biological, and mathematical techniques and technologies. Several solutions have already been proposed to allow scientists for processing their genomic experiments using HPC capabilities and parallelism techniques. This article brings a systematic review of literature that surveys the most recently published research involving genomics and parallel computing. Our objective is to gather the main characteristics, benefits, and challenges that can be considered by scientists when running their genomic experiments to benefit from parallelism techniques and HPC capabilities.

Sentence alignment using feed forward neural network.

PubMed

Fattah, Mohamed Abdel; Ren, Fuji; Kuroiwa, Shingo

2006-12-01

Parallel corpora have become an essential resource for work in multi lingual natural language processing. However, sentence aligned parallel corpora are more efficient than non-aligned parallel corpora for cross language information retrieval and machine translation applications. In this paper, we present a new approach to align sentences in bilingual parallel corpora based on feed forward neural network classifier. A feature parameter vector is extracted from the text pair under consideration. This vector contains text features such as length, punctuate score, and cognate score values. A set of manually prepared training data has been assigned to train the feed forward neural network. Another set of data was used for testing. Using this new approach, we could achieve an error reduction of 60% over length based approach when applied on English-Arabic parallel documents. Moreover this new approach is valid for any language pair and it is quite flexible approach since the feature parameter vector may contain more/less or different features than that we used in our system such as lexical match feature.

Convergence issues in domain decomposition parallel computation of hovering rotor

NASA Astrophysics Data System (ADS)

Xiao, Zhongyun; Liu, Gang; Mou, Bin; Jiang, Xiong

2018-05-01

Implicit LU-SGS time integration algorithm has been widely used in parallel computation in spite of its lack of information from adjacent domains. When applied to parallel computation of hovering rotor flows in a rotating frame, it brings about convergence issues. To remedy the problem, three LU factorization-based implicit schemes (consisting of LU-SGS, DP-LUR and HLU-SGS) are investigated comparatively. A test case of pure grid rotation is designed to verify these algorithms, which show that LU-SGS algorithm introduces errors on boundary cells. When partition boundaries are circumferential, errors arise in proportion to grid speed, accumulating along with the rotation, and leading to computational failure in the end. Meanwhile, DP-LUR and HLU-SGS methods show good convergence owing to boundary treatment which are desirable in domain decomposition parallel computations.

A PIPO Boost Converter with Low Ripple and Medium Current Application

NASA Astrophysics Data System (ADS)

Bandri, S.; Sofian, A.; Ismail, F.

2018-04-01

This paper presents a Parallel Input Parallel Output (PIPO) boost converter is proposed to gain power ability of converter, and reduce current inductors. The proposed technique will distribute current for n-parallel inductor and switching component. Four parallel boost converters implement on input voltage 20.5Vdc to generate output voltage 28.8Vdc. The PIPO boost converter applied phase shift pulse width modulation which will compare with conventional PIPO boost converters by using a similar pulse for every switching component. The current ripple reduction shows an advantage PIPO boost converter then conventional boost converter. Varies loads and duty cycle will be simulated and analyzed to verify the performance of PIPO boost converter. Finally, the unbalance of current inductor is able to be verified on four area of duty cycle in less than 0.6.

Efficient parallelization of analytic bond-order potentials for large-scale atomistic simulations

NASA Astrophysics Data System (ADS)

Teijeiro, C.; Hammerschmidt, T.; Drautz, R.; Sutmann, G.

2016-07-01

Analytic bond-order potentials (BOPs) provide a way to compute atomistic properties with controllable accuracy. For large-scale computations of heterogeneous compounds at the atomistic level, both the computational efficiency and memory demand of BOP implementations have to be optimized. Since the evaluation of BOPs is a local operation within a finite environment, the parallelization concepts known from short-range interacting particle simulations can be applied to improve the performance of these simulations. In this work, several efficient parallelization methods for BOPs that use three-dimensional domain decomposition schemes are described. The schemes are implemented into the bond-order potential code BOPfox, and their performance is measured in a series of benchmarks. Systems of up to several millions of atoms are simulated on a high performance computing system, and parallel scaling is demonstrated for up to thousands of processors.

Advancing MODFLOW Applying the Derived Vector Space Method

NASA Astrophysics Data System (ADS)

Herrera, G. S.; Herrera, I.; Lemus-García, M.; Hernandez-Garcia, G. D.

2015-12-01

The most effective domain decomposition methods (DDM) are non-overlapping DDMs. Recently a new approach, the DVS-framework, based on an innovative discretization method that uses a non-overlapping system of nodes (the derived-nodes), was introduced and developed by I. Herrera et al. [1, 2]. Using the DVS-approach a group of four algorithms, referred to as the 'DVS-algorithms', which fulfill the DDM-paradigm (i.e. the solution of global problems is obtained by resolution of local problems exclusively) has been derived. Such procedures are applicable to any boundary-value problem, or system of such equations, for which a standard discretization method is available and then software with a high degree of parallelization can be constructed. In a parallel talk, in this AGU Fall Meeting, Ismael Herrera will introduce the general DVS methodology. The application of the DVS-algorithms has been demonstrated in the solution of several boundary values problems of interest in Geophysics. Numerical examples for a single-equation, for the cases of symmetric, non-symmetric and indefinite problems were demonstrated before [1,2]. For these problems DVS-algorithms exhibited significantly improved numerical performance with respect to standard versions of DDM algorithms. In view of these results our research group is in the process of applying the DVS method to a widely used simulator for the first time, here we present the advances of the application of this method for the parallelization of MODFLOW. Efficiency results for a group of tests will be presented. References [1] I. Herrera, L.M. de la Cruz and A. Rosas-Medina. Non overlapping discretization methods for partial differential equations, Numer Meth Part D E, (2013). [2] Herrera, I., & Contreras Iván "An Innovative Tool for Effectively Applying Highly Parallelized Software To Problems of Elasticity". Geofísica Internacional, 2015 (In press)

Fine-grained parallelization of fitness functions in bioinformatics optimization problems: gene selection for cancer classification and biclustering of gene expression data.

PubMed

Gomez-Pulido, Juan A; Cerrada-Barrios, Jose L; Trinidad-Amado, Sebastian; Lanza-Gutierrez, Jose M; Fernandez-Diaz, Ramon A; Crawford, Broderick; Soto, Ricardo

2016-08-31

Metaheuristics are widely used to solve large combinatorial optimization problems in bioinformatics because of the huge set of possible solutions. Two representative problems are gene selection for cancer classification and biclustering of gene expression data. In most cases, these metaheuristics, as well as other non-linear techniques, apply a fitness function to each possible solution with a size-limited population, and that step involves higher latencies than other parts of the algorithms, which is the reason why the execution time of the applications will mainly depend on the execution time of the fitness function. In addition, it is usual to find floating-point arithmetic formulations for the fitness functions. This way, a careful parallelization of these functions using the reconfigurable hardware technology will accelerate the computation, specially if they are applied in parallel to several solutions of the population. A fine-grained parallelization of two floating-point fitness functions of different complexities and features involved in biclustering of gene expression data and gene selection for cancer classification allowed for obtaining higher speedups and power-reduced computation with regard to usual microprocessors. The results show better performances using reconfigurable hardware technology instead of usual microprocessors, in computing time and power consumption terms, not only because of the parallelization of the arithmetic operations, but also thanks to the concurrent fitness evaluation for several individuals of the population in the metaheuristic. This is a good basis for building accelerated and low-energy solutions for intensive computing scenarios.

Situating Ontario's Colleges between the American and European Models for Providing Opportunity for the Attainment of Baccalaureate Degrees in Applied Fields of Study

ERIC Educational Resources Information Center

Skolnik, Michael L.

2016-01-01

During the last third of the twentieth century, college sectors in many countries took on the role of expanding opportunities for baccalaureate degree attainment in applied fields of study. In many European countries, colleges came to constitute a parallel higher education sector that offered degree programs of an applied nature in contrast to the…

Applied Biomechanics in an Instructional Setting

ERIC Educational Resources Information Center

Hudson, Jackie L.

2006-01-01

Biomechanics is the science of how people move better, meaning more skillfully and more safely. This article places more emphasis on skill rather than safety, though there are many parallels between them. It shares a few features of the author's paradigm of applied biomechanics and discusses an integrated approach toward a middle school football…

Fiscal Models as Reflections of Institutional Philosophies toward Continuing Education.

ERIC Educational Resources Information Center

Thompson, Gordon

Throughout the existence of the Continuing Education Division (CED) at the University of Manitoba, three different fiscal models were applied by University Administration to the CED: the traditional model; the income-target model; and the subsidy model. (1) The traditional model paralleled that applied to faculties and schools. The CED was…

Basic research needed for stimulating the development of behavioral technologies

PubMed Central

Mace, F. Charles

1994-01-01

The costs of disconnection between the basic and applied sectors of behavior analysis are reviewed, and some solutions to these problems are proposed. Central to these solutions are collaborations between basic and applied behavioral scientists in programmatic research that addresses the behavioral basis and solution of human behavior problems. This kind of collaboration parallels the deliberate interactions between basic and applied researchers that have proven to be so profitable in other scientific fields, such as medicine. Basic research questions of particular relevance to the development of behavioral technologies are posed in the following areas: response allocation, resistance to change, countercontrol, formation and differentiation/discrimination of stimulus and response classes, analysis of low-rate behavior, and rule-governed behavior. Three interrelated strategies to build connections between the basic and applied analysis of behavior are identified: (a) the development of nonhuman animal models of human behavior problems using operations that parallel plausible human circumstances, (b) replication of the modeled relations with human subjects in the operant laboratory, and (c) tests of the generality of the model with actual human problems in natural settings. PMID:16812734

Neoclassical parallel flow calculation in the presence of external parallel momentum sources in Heliotron J

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

Nishioka, K.; Nakamura, Y.; Nishimura, S.

A moment approach to calculate neoclassical transport in non-axisymmetric torus plasmas composed of multiple ion species is extended to include the external parallel momentum sources due to unbalanced tangential neutral beam injections (NBIs). The momentum sources that are included in the parallel momentum balance are calculated from the collision operators of background particles with fast ions. This method is applied for the clarification of the physical mechanism of the neoclassical parallel ion flows and the multi-ion species effect on them in Heliotron J NBI plasmas. It is found that parallel ion flow can be determined by the balance between themore » parallel viscosity and the external momentum source in the region where the external source is much larger than the thermodynamic force driven source in the collisional plasmas. This is because the friction between C{sup 6+} and D{sup +} prevents a large difference between C{sup 6+} and D{sup +} flow velocities in such plasmas. The C{sup 6+} flow velocities, which are measured by the charge exchange recombination spectroscopy system, are numerically evaluated with this method. It is shown that the experimentally measured C{sup 6+} impurity flow velocities do not contradict clearly with the neoclassical estimations, and the dependence of parallel flow velocities on the magnetic field ripples is consistent in both results.« less

Advanced mathematical on-line analysis in nuclear experiments. Usage of parallel computing CUDA routines in standard root analysis

NASA Astrophysics Data System (ADS)

Grzeszczuk, A.; Kowalski, S.

2015-04-01

Compute Unified Device Architecture (CUDA) is a parallel computing platform developed by Nvidia for increase speed of graphics by usage of parallel mode for processes calculation. The success of this solution has opened technology General-Purpose Graphic Processor Units (GPGPUs) for applications not coupled with graphics. The GPGPUs system can be applying as effective tool for reducing huge number of data for pulse shape analysis measures, by on-line recalculation or by very quick system of compression. The simplified structure of CUDA system and model of programming based on example Nvidia GForce GTX580 card are presented by our poster contribution in stand-alone version and as ROOT application.

Cross-polarised and parallel-polarised light: Viewing and photography for examination and documentation of biological materials in medicine and forensics.

PubMed

Hanlon, Katharine L

2018-01-01

Cross-polarisation, with regard to visible light, is a process wherein two polarisers with perpendicular orientation to one another are used on the incident and reflected lights. Under cross-polarised light birefringent structures which are otherwise invisible become apparent. Cross-polarised light eliminates glare and specular highlights, allowing for an unobstructed view of subsurface pathology. Parallel-polarisation occurs when the polarisers are rotated to the same orientation. When cross- or parallel-polarisation is applied to photography, images can be generated which aid in visualisation of surface and subsurface elements. Improved access to equipment and education has the potential to benefit practitioners, researchers, investigators and patients.

Fluorous Parallel Synthesis of A Hydantoin/Thiohydantoin Library

PubMed Central

Lu, Yimin; Zhang, Wei

2007-01-01

Fluorous tagging strategy is applied to solution-phase parallel synthesis of a library containing hydantoin and thiohydantoin analogs. Two perfluoroalkyl (Rf)-tagged α-amino esters each react with 6 aromatic aldehydes under reductive amination conditions. Twelve amino esters then each react with 10 isocyanates and isothiocyanates in parallel. The resulting 120 ureas and thioureas undergo spontaneous cyclization to form the corresponding hydantoins and thiohydantoins. The intermediate and final product purifications are performed with solid-phase extraction (SPE) over FluoroFlash™ cartridges, no chromatography is required. Using standard instruments and straightforward SPE technique, one chemist accomplished the 120-member library synthesis in less than 5 working days, including starting material synthesis and product analysis. PMID:15789556

Parallel gene analysis with allele-specific padlock probes and tag microarrays

PubMed Central

Banér, Johan; Isaksson, Anders; Waldenström, Erik; Jarvius, Jonas; Landegren, Ulf; Nilsson, Mats

2003-01-01

Parallel, highly specific analysis methods are required to take advantage of the extensive information about DNA sequence variation and of expressed sequences. We present a scalable laboratory technique suitable to analyze numerous target sequences in multiplexed assays. Sets of padlock probes were applied to analyze single nucleotide variation directly in total genomic DNA or cDNA for parallel genotyping or gene expression analysis. All reacted probes were then co-amplified and identified by hybridization to a standard tag oligonucleotide array. The technique was illustrated by analyzing normal and pathogenic variation within the Wilson disease-related ATP7B gene, both at the level of DNA and RNA, using allele-specific padlock probes. PMID:12930977

Decoupling Principle Analysis and Development of a Parallel Three-Dimensional Force Sensor

PubMed Central

Zhao, Yanzhi; Jiao, Leihao; Weng, Dacheng; Zhang, Dan; Zheng, Rencheng

2016-01-01

In the development of the multi-dimensional force sensor, dimension coupling is the ubiquitous factor restricting the improvement of the measurement accuracy. To effectively reduce the influence of dimension coupling on the parallel multi-dimensional force sensor, a novel parallel three-dimensional force sensor is proposed using a mechanical decoupling principle, and the influence of the friction on dimension coupling is effectively reduced by making the friction rolling instead of sliding friction. In this paper, the mathematical model is established by combining with the structure model of the parallel three-dimensional force sensor, and the modeling and analysis of mechanical decoupling are carried out. The coupling degree (ε) of the designed sensor is defined and calculated, and the calculation results show that the mechanical decoupling parallel structure of the sensor possesses good decoupling performance. A prototype of the parallel three-dimensional force sensor was developed, and FEM analysis was carried out. The load calibration and data acquisition experiment system are built, and then calibration experiments were done. According to the calibration experiments, the measurement accuracy is less than 2.86% and the coupling accuracy is less than 3.02%. The experimental results show that the sensor system possesses high measuring accuracy, which provides a basis for the applied research of the parallel multi-dimensional force sensor. PMID:27649194

Implementation of Hybrid V-Cycle Multilevel Methods for Mixed Finite Element Systems with Penalty

NASA Technical Reports Server (NTRS)

Lai, Chen-Yao G.

1996-01-01

The goal of this paper is the implementation of hybrid V-cycle hierarchical multilevel methods for the indefinite discrete systems which arise when a mixed finite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system containing the small penalty parameter for the velocity unknown alone. We stabilize the hierarchical spatial decomposition approach proposed by Cai, Goldstein, and Pasciak for the reduced system. We demonstrate that the relative condition number of the preconditioner is bounded uniformly with respect to the penalty parameter, the number of levels and possible jumps of the coefficients as long as they occur only across the edges of the coarsest elements.

An incomplete assembly with thresholding algorithm for systems of reaction-diffusion equations in three space dimensions IAT for reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2003-07-01

Solving systems of reaction-diffusion equations in three space dimensions can be prohibitively expensive both in terms of storage and CPU time. Herein, I present a new incomplete assembly procedure that is designed to reduce storage requirements. Incomplete assembly is analogous to incomplete factorization in that only a fixed number of nonzero entries are stored per row and a drop tolerance is used to discard small values. The algorithm is incorporated in a finite element method-of-lines code and tested on a set of reaction-diffusion systems. The effect of incomplete assembly on CPU time and storage and on the performance of the temporal integrator DASPK, algebraic solver GMRES and preconditioner ILUT is studied.

Shape reanalysis and sensitivities utilizing preconditioned iterative boundary solvers

NASA Technical Reports Server (NTRS)

Guru Prasad, K.; Kane, J. H.

1992-01-01

The computational advantages associated with the utilization of preconditined iterative equation solvers are quantified for the reanalysis of perturbed shapes using continuum structural boundary element analysis (BEA). Both single- and multi-zone three-dimensional problems are examined. Significant reductions in computer time are obtained by making use of previously computed solution vectors and preconditioners in subsequent analyses. The effectiveness of this technique is demonstrated for the computation of shape response sensitivities required in shape optimization. Computer times and accuracies achieved using the preconditioned iterative solvers are compared with those obtained via direct solvers and implicit differentiation of the boundary integral equations. It is concluded that this approach employing preconditioned iterative equation solvers in reanalysis and sensitivity analysis can be competitive with if not superior to those involving direct solvers.

Probabilistic Structures Analysis Methods (PSAM) for select space propulsion system components

NASA Technical Reports Server (NTRS)

1991-01-01

The basic formulation for probabilistic finite element analysis is described and demonstrated on a few sample problems. This formulation is based on iterative perturbation that uses the factorized stiffness on the unperturbed system as the iteration preconditioner for obtaining the solution to the perturbed problem. This approach eliminates the need to compute, store and manipulate explicit partial derivatives of the element matrices and force vector, which not only reduces memory usage considerably, but also greatly simplifies the coding and validation tasks. All aspects for the proposed formulation were combined in a demonstration problem using a simplified model of a curved turbine blade discretized with 48 shell elements, and having random pressure and temperature fields with partial correlation, random uniform thickness, and random stiffness at the root.

A domain decomposition approach to implementing fault slip in finite-element models of quasi-static and dynamic crustal deformation

USGS Publications Warehouse

Aagaard, Brad T.; Knepley, M.G.; Williams, C.A.

2013-01-01

We employ a domain decomposition approach with Lagrange multipliers to implement fault slip in a finite-element code, PyLith, for use in both quasi-static and dynamic crustal deformation applications. This integrated approach to solving both quasi-static and dynamic simulations leverages common finite-element data structures and implementations of various boundary conditions, discretization schemes, and bulk and fault rheologies. We have developed a custom preconditioner for the Lagrange multiplier portion of the system of equations that provides excellent scalability with problem size compared to conventional additive Schwarz methods. We demonstrate application of this approach using benchmarks for both quasi-static viscoelastic deformation and dynamic spontaneous rupture propagation that verify the numerical implementation in PyLith.

Multisource least-squares reverse-time migration with structure-oriented filtering

NASA Astrophysics Data System (ADS)

Fan, Jing-Wen; Li, Zhen-Chun; Zhang, Kai; Zhang, Min; Liu, Xue-Tong

2016-09-01

The technology of simultaneous-source acquisition of seismic data excited by several sources can significantly improve the data collection efficiency. However, direct imaging of simultaneous-source data or blended data may introduce crosstalk noise and affect the imaging quality. To address this problem, we introduce a structure-oriented filtering operator as preconditioner into the multisource least-squares reverse-time migration (LSRTM). The structure-oriented filtering operator is a nonstationary filter along structural trends that suppresses crosstalk noise while maintaining structural information. The proposed method uses the conjugate-gradient method to minimize the mismatch between predicted and observed data, while effectively attenuating the interference noise caused by exciting several sources simultaneously. Numerical experiments using synthetic data suggest that the proposed method can suppress the crosstalk noise and produce highly accurate images.

Choosing order of operations to accelerate strip structure analysis in parameter range

NASA Astrophysics Data System (ADS)

Kuksenko, S. P.; Akhunov, R. R.; Gazizov, T. R.

2018-05-01

The paper considers the issue of using iteration methods in solving the sequence of linear algebraic systems obtained in quasistatic analysis of strip structures with the method of moments. Using the analysis of 4 strip structures, the authors have proved that additional acceleration (up to 2.21 times) of the iterative process can be obtained during the process of solving linear systems repeatedly by means of choosing a proper order of operations and a preconditioner. The obtained results can be used to accelerate the process of computer-aided design of various strip structures. The choice of the order of operations to accelerate the process is quite simple, universal and could be used not only for strip structure analysis but also for a wide range of computational problems.

An approach to enhance pnetCDF performance in ...

EPA Pesticide Factsheets

Data intensive simulations are often limited by their I/O (input/output) performance, and "novel" techniques need to be developed in order to overcome this limitation. The software package pnetCDF (parallel network Common Data Form), which works with parallel file systems, was developed to address this issue by providing parallel I/O capability. This study examines the performance of an application-level data aggregation approach which performs data aggregation along either row or column dimension of MPI (Message Passing Interface) processes on a spatially decomposed domain, and then applies the pnetCDF parallel I/O paradigm. The test was done with three different domain sizes which represent small, moderately large, and large data domains, using a small-scale Community Multiscale Air Quality model (CMAQ) mock-up code. The examination includes comparing I/O performance with traditional serial I/O technique, straight application of pnetCDF, and the data aggregation along row and column dimension before applying pnetCDF. After the comparison, "optimal" I/O configurations of this application-level data aggregation approach were quantified. Data aggregation along the row dimension (pnetCDFcr) works better than along the column dimension (pnetCDFcc) although it may perform slightly worse than the straight pnetCDF method with a small number of processors. When the number of processors becomes larger, pnetCDFcr outperforms pnetCDF significantly. If the number of proces

Massively parallel and linear-scaling algorithm for second-order Møller-Plesset perturbation theory applied to the study of supramolecular wires

NASA Astrophysics Data System (ADS)

Kjærgaard, Thomas; Baudin, Pablo; Bykov, Dmytro; Eriksen, Janus Juul; Ettenhuber, Patrick; Kristensen, Kasper; Larkin, Jeff; Liakh, Dmitry; Pawłowski, Filip; Vose, Aaron; Wang, Yang Min; Jørgensen, Poul

2017-03-01

We present a scalable cross-platform hybrid MPI/OpenMP/OpenACC implementation of the Divide-Expand-Consolidate (DEC) formalism with portable performance on heterogeneous HPC architectures. The Divide-Expand-Consolidate formalism is designed to reduce the steep computational scaling of conventional many-body methods employed in electronic structure theory to linear scaling, while providing a simple mechanism for controlling the error introduced by this approximation. Our massively parallel implementation of this general scheme has three levels of parallelism, being a hybrid of the loosely coupled task-based parallelization approach and the conventional MPI +X programming model, where X is either OpenMP or OpenACC. We demonstrate strong and weak scalability of this implementation on heterogeneous HPC systems, namely on the GPU-based Cray XK7 Titan supercomputer at the Oak Ridge National Laboratory. Using the "resolution of the identity second-order Møller-Plesset perturbation theory" (RI-MP2) as the physical model for simulating correlated electron motion, the linear-scaling DEC implementation is applied to 1-aza-adamantane-trione (AAT) supramolecular wires containing up to 40 monomers (2440 atoms, 6800 correlated electrons, 24 440 basis functions and 91 280 auxiliary functions). This represents the largest molecular system treated at the MP2 level of theory, demonstrating an efficient removal of the scaling wall pertinent to conventional quantum many-body methods.

Electrode structure for uniform corona discharge

NASA Technical Reports Server (NTRS)

Gange, R. A.; Steinmetz, C. C.

1976-01-01

Single corona-discharge needle is used to apply uniform charge to thermoplastic medium in holograph-storage system. Needle is connected to flat transparent electrode that is parallel to thermoplastic.

A parallel computational model for GATE simulations.

PubMed

Rannou, F R; Vega-Acevedo, N; El Bitar, Z

2013-12-01

GATE/Geant4 Monte Carlo simulations are computationally demanding applications, requiring thousands of processor hours to produce realistic results. The classical strategy of distributing the simulation of individual events does not apply efficiently for Positron Emission Tomography (PET) experiments, because it requires a centralized coincidence processing and large communication overheads. We propose a parallel computational model for GATE that handles event generation and coincidence processing in a simple and efficient way by decentralizing event generation and processing but maintaining a centralized event and time coordinator. The model is implemented with the inclusion of a new set of factory classes that can run the same executable in sequential or parallel mode. A Mann-Whitney test shows that the output produced by this parallel model in terms of number of tallies is equivalent (but not equal) to its sequential counterpart. Computational performance evaluation shows that the software is scalable and well balanced. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Massively parallel multicanonical simulations

NASA Astrophysics Data System (ADS)

Gross, Jonathan; Zierenberg, Johannes; Weigel, Martin; Janke, Wolfhard

2018-03-01

Generalized-ensemble Monte Carlo simulations such as the multicanonical method and similar techniques are among the most efficient approaches for simulations of systems undergoing discontinuous phase transitions or with rugged free-energy landscapes. As Markov chain methods, they are inherently serial computationally. It was demonstrated recently, however, that a combination of independent simulations that communicate weight updates at variable intervals allows for the efficient utilization of parallel computational resources for multicanonical simulations. Implementing this approach for the many-thread architecture provided by current generations of graphics processing units (GPUs), we show how it can be efficiently employed with of the order of 104 parallel walkers and beyond, thus constituting a versatile tool for Monte Carlo simulations in the era of massively parallel computing. We provide the fully documented source code for the approach applied to the paradigmatic example of the two-dimensional Ising model as starting point and reference for practitioners in the field.

Smart Optical Material Characterization System and Method

NASA Technical Reports Server (NTRS)

Choi, Sang Hyouk (Inventor); Park, Yeonjoon (Inventor)

2015-01-01

Disclosed is a system and method for characterizing optical materials, using steps and equipment for generating a coherent laser light, filtering the light to remove high order spatial components, collecting the filtered light and forming a parallel light beam, splitting the parallel beam into a first direction and a second direction wherein the parallel beam travelling in the second direction travels toward the material sample so that the parallel beam passes through the sample, applying various physical quantities to the sample, reflecting the beam travelling in the first direction to produce a first reflected beam, reflecting the beam that passes through the sample to produce a second reflected beam that travels back through the sample, combining the second reflected beam after it travels back though the sample with the first reflected beam, sensing the light beam produced by combining the first and second reflected beams, and processing the sensed beam to determine sample characteristics and properties.

Cooperative parallel adaptive neighbourhood search for the disjunctively constrained knapsack problem

NASA Astrophysics Data System (ADS)

Quan, Zhe; Wu, Lei

2017-09-01

This article investigates the use of parallel computing for solving the disjunctively constrained knapsack problem. The proposed parallel computing model can be viewed as a cooperative algorithm based on a multi-neighbourhood search. The cooperation system is composed of a team manager and a crowd of team members. The team members aim at applying their own search strategies to explore the solution space. The team manager collects the solutions from the members and shares the best one with them. The performance of the proposed method is evaluated on a group of benchmark data sets. The results obtained are compared to those reached by the best methods from the literature. The results show that the proposed method is able to provide the best solutions in most cases. In order to highlight the robustness of the proposed parallel computing model, a new set of large-scale instances is introduced. Encouraging results have been obtained.

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.

Classification of hyperspectral imagery using MapReduce on a NVIDIA graphics processing unit (Conference Presentation)

NASA Astrophysics Data System (ADS)

Ramirez, Andres; Rahnemoonfar, Maryam

2017-04-01

A hyperspectral image provides multidimensional figure rich in data consisting of hundreds of spectral dimensions. Analyzing the spectral and spatial information of such image with linear and non-linear algorithms will result in high computational time. In order to overcome this problem, this research presents a system using a MapReduce-Graphics Processing Unit (GPU) model that can help analyzing a hyperspectral image through the usage of parallel hardware and a parallel programming model, which will be simpler to handle compared to other low-level parallel programming models. Additionally, Hadoop was used as an open-source version of the MapReduce parallel programming model. This research compared classification accuracy results and timing results between the Hadoop and GPU system and tested it against the following test cases: the CPU and GPU test case, a CPU test case and a test case where no dimensional reduction was applied.

Efficient parallel implementation of active appearance model fitting algorithm on GPU.

PubMed

Wang, Jinwei; Ma, Xirong; Zhu, Yuanping; Sun, Jizhou

2014-01-01

The active appearance model (AAM) is one of the most powerful model-based object detecting and tracking methods which has been widely used in various situations. However, the high-dimensional texture representation causes very time-consuming computations, which makes the AAM difficult to apply to real-time systems. The emergence of modern graphics processing units (GPUs) that feature a many-core, fine-grained parallel architecture provides new and promising solutions to overcome the computational challenge. In this paper, we propose an efficient parallel implementation of the AAM fitting algorithm on GPUs. Our design idea is fine grain parallelism in which we distribute the texture data of the AAM, in pixels, to thousands of parallel GPU threads for processing, which makes the algorithm fit better into the GPU architecture. We implement our algorithm using the compute unified device architecture (CUDA) on the Nvidia's GTX 650 GPU, which has the latest Kepler architecture. To compare the performance of our algorithm with different data sizes, we built sixteen face AAM models of different dimensional textures. The experiment results show that our parallel AAM fitting algorithm can achieve real-time performance for videos even on very high-dimensional textures.

Efficient Parallel Implementation of Active Appearance Model Fitting Algorithm on GPU

PubMed Central

Wang, Jinwei; Ma, Xirong; Zhu, Yuanping; Sun, Jizhou

2014-01-01

The active appearance model (AAM) is one of the most powerful model-based object detecting and tracking methods which has been widely used in various situations. However, the high-dimensional texture representation causes very time-consuming computations, which makes the AAM difficult to apply to real-time systems. The emergence of modern graphics processing units (GPUs) that feature a many-core, fine-grained parallel architecture provides new and promising solutions to overcome the computational challenge. In this paper, we propose an efficient parallel implementation of the AAM fitting algorithm on GPUs. Our design idea is fine grain parallelism in which we distribute the texture data of the AAM, in pixels, to thousands of parallel GPU threads for processing, which makes the algorithm fit better into the GPU architecture. We implement our algorithm using the compute unified device architecture (CUDA) on the Nvidia's GTX 650 GPU, which has the latest Kepler architecture. To compare the performance of our algorithm with different data sizes, we built sixteen face AAM models of different dimensional textures. The experiment results show that our parallel AAM fitting algorithm can achieve real-time performance for videos even on very high-dimensional textures. PMID:24723812

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

Optics Program Modified for Multithreaded Parallel Computing

NASA Technical Reports Server (NTRS)

Lou, John; Bedding, Dave; Basinger, Scott

2006-01-01

A powerful high-performance computer program for simulating and analyzing adaptive and controlled optical systems has been developed by modifying the serial version of the Modeling and Analysis for Controlled Optical Systems (MACOS) program to impart capabilities for multithreaded parallel processing on computing systems ranging from supercomputers down to Symmetric Multiprocessing (SMP) personal computers. The modifications included the incorporation of OpenMP, a portable and widely supported application interface software, that can be used to explicitly add multithreaded parallelism to an application program under a shared-memory programming model. OpenMP was applied to parallelize ray-tracing calculations, one of the major computing components in MACOS. Multithreading is also used in the diffraction propagation of light in MACOS based on pthreads [POSIX Thread, (where "POSIX" signifies a portable operating system for UNIX)]. In tests of the parallelized version of MACOS, the speedup in ray-tracing calculations was found to be linear, or proportional to the number of processors, while the speedup in diffraction calculations ranged from 50 to 60 percent, depending on the type and number of processors. The parallelized version of MACOS is portable, and, to the user, its interface is basically the same as that of the original serial version of MACOS.

Parallel Tensor Compression for Large-Scale Scientific Data.

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

Kolda, Tamara G.; Ballard, Grey; Austin, Woody Nathan

As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that tracks 64 variables per grid point for 128 time steps yields 8 TB of data. By viewing the data as a dense five way tensor, we can compute a Tucker decomposition to find inherent low-dimensional multilinear structure, achieving compression ratios of up to 10000 on real-world data sets with negligible loss in accuracy. So that we can operate on such massive data, we present the first-ever distributed memorymore » parallel implementation for the Tucker decomposition, whose key computations correspond to parallel linear algebra operations, albeit with nonstandard data layouts. Our approach specifies a data distribution for tensors that avoids any tensor data redistribution, either locally or in parallel. We provide accompanying analysis of the computation and communication costs of the algorithms. To demonstrate the compression and accuracy of the method, we apply our approach to real-world data sets from combustion science simulations. We also provide detailed performance results, including parallel performance in both weak and strong scaling experiments.« less

Lattice Boltzmann computation of creeping fluid flow in roll-coating applications

NASA Astrophysics Data System (ADS)

Rajan, Isac; Kesana, Balashanker; Perumal, D. Arumuga

2018-04-01

Lattice Boltzmann Method (LBM) has advanced as a class of Computational Fluid Dynamics (CFD) methods used to solve complex fluid systems and heat transfer problems. It has ever-increasingly attracted the interest of researchers in computational physics to solve challenging problems of industrial and academic importance. In this current study, LBM is applied to simulate the creeping fluid flow phenomena commonly encountered in manufacturing technologies. In particular, we apply this novel method to simulate the fluid flow phenomena associated with the "meniscus roll coating" application. This prevalent industrial problem encountered in polymer processing and thin film coating applications is modelled as standard lid-driven cavity problem to which creeping flow analysis is applied. This incompressible viscous flow problem is studied in various speed ratios, the ratio of upper to lower lid speed in two different configurations of lid movement - parallel and anti-parallel wall motion. The flow exhibits interesting patterns which will help in design of roll coaters.

Parallel pumping of a ferromagnetic nanostripe: Confinement quantization and off-resonant driving

NASA Astrophysics Data System (ADS)

Yarbrough, P. M.; Livesey, K. L.

2018-01-01

The parametric excitation of spin waves in a rectangular, ferromagnetic nanowire in the parallel pump configuration and with an applied field along the long axis of the wire is studied theoretically, using a semi-classical and semi-analytic Hamiltonian approach. We find that as a function of static applied field strength, there are jumps in the pump power needed to excite thermal spin waves. At these jumps, there is the possibility to non-resonantly excite spin waves near kz = 0. Spin waves with negative or positive group velocity and with different standing wave structures across the wire width can be excited by tuning the applied field. By using a magnetostatic Green's function that depends on both the nanowire's width and thickness—rather than just its aspect ratio—we also find that the threshold field strength varies considerably for nanowires with the same aspect ratio but of different sizes. Comparisons between different methods of calculations are made and the advantages and disadvantages of each are discussed.

Target recognition of ladar range images using even-order Zernike moments.

PubMed

Liu, Zheng-Jun; Li, Qi; Xia, Zhi-Wei; Wang, Qi

2012-11-01

Ladar range images have attracted considerable attention in automatic target recognition fields. In this paper, Zernike moments (ZMs) are applied to classify the target of the range image from an arbitrary azimuth angle. However, ZMs suffer from high computational costs. To improve the performance of target recognition based on small samples, even-order ZMs with serial-parallel backpropagation neural networks (BPNNs) are applied to recognize the target of the range image. It is found that the rotation invariance and classified performance of the even-order ZMs are both better than for odd-order moments and for moments compressed by principal component analysis. The experimental results demonstrate that combining the even-order ZMs with serial-parallel BPNNs can significantly improve the recognition rate for small samples.

Use of RORA for Complex Ground-Water Flow Conditions

USGS Publications Warehouse

Rutledge, A.T.

2004-01-01

The RORA computer program for estimating recharge is based on a condition in which ground water flows perpendicular to the nearest stream that receives ground-water discharge. The method, therefore, does not explicitly account for the ground-water-flow component that is parallel to the stream. Hypothetical finite-difference simulations are used to demonstrate effects of complex flow conditions that consist of two components: one that is perpendicular to the stream and one that is parallel to the stream. Results of the simulations indicate that the RORA program can be used if certain constraints are applied in the estimation of the recession index, an input variable to the program. These constraints apply to a mathematical formulation based on aquifer properties, recession of ground-water levels, and recession of streamflow.

The Multi/Plural Turn, Postcolonial Theory, and Neoliberal Multiculturalism: Complicities and Implications for Applied Linguistics

ERIC Educational Resources Information Center

Kubota, Ryuko

2016-01-01

In applied linguistics and language education, an increased focus has been placed on plurality and hybridity to challenge monolingualism, the native speaker norm, and the modernist view of language and language use as unitary and bounded. The multi/plural turn parallels postcolonial theory in that they both support hybridity and fluidity while…

Bridging Theory and Practice in an Applied Retail Track

ERIC Educational Resources Information Center

Lange, Fredrik; Rosengren, Sara; Colliander, Jonas; Hernant, Mikael; Liljedal, Karina T.

2018-01-01

In this article, we present an educational approach that bridges theory and practice: an applied retail track. The track has been co-created by faculty and 10 partnering retail companies and runs in parallel with traditional courses during a 3-year bachelor's degree program in retail management. The underlying pedagogical concept is to move retail…

Integration experiences and performance studies of A COTS parallel archive systems

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

Chen, Hsing-bung; Scott, Cody; Grider, Bary

2010-01-01

Current and future Archive Storage Systems have been asked to (a) scale to very high bandwidths, (b) scale in metadata performance, (c) support policy-based hierarchical storage management capability, (d) scale in supporting changing needs of very large data sets, (e) support standard interface, and (f) utilize commercial-off-the-shelf(COTS) hardware. Parallel file systems have been asked to do the same thing but at one or more orders of magnitude faster in performance. Archive systems continue to move closer to file systems in their design due to the need for speed and bandwidth, especially metadata searching speeds such as more caching and lessmore » robust semantics. Currently the number of extreme highly scalable parallel archive solutions is very small especially those that will move a single large striped parallel disk file onto many tapes in parallel. We believe that a hybrid storage approach of using COTS components and innovative software technology can bring new capabilities into a production environment for the HPC community much faster than the approach of creating and maintaining a complete end-to-end unique parallel archive software solution. In this paper, we relay our experience of integrating a global parallel file system and a standard backup/archive product with a very small amount of additional code to provide a scalable, parallel archive. Our solution has a high degree of overlap with current parallel archive products including (a) doing parallel movement to/from tape for a single large parallel file, (b) hierarchical storage management, (c) ILM features, (d) high volume (non-single parallel file) archives for backup/archive/content management, and (e) leveraging all free file movement tools in Linux such as copy, move, ls, tar, etc. We have successfully applied our working COTS Parallel Archive System to the current world's first petaflop/s computing system, LANL's Roadrunner, and demonstrated its capability to address requirements of future archival storage systems.« less

Integration experiments and performance studies of a COTS parallel archive system

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

Chen, Hsing-bung; Scott, Cody; Grider, Gary

2010-06-16

Current and future Archive Storage Systems have been asked to (a) scale to very high bandwidths, (b) scale in metadata performance, (c) support policy-based hierarchical storage management capability, (d) scale in supporting changing needs of very large data sets, (e) support standard interface, and (f) utilize commercial-off-the-shelf (COTS) hardware. Parallel file systems have been asked to do the same thing but at one or more orders of magnitude faster in performance. Archive systems continue to move closer to file systems in their design due to the need for speed and bandwidth, especially metadata searching speeds such as more caching andmore » less robust semantics. Currently the number of extreme highly scalable parallel archive solutions is very small especially those that will move a single large striped parallel disk file onto many tapes in parallel. We believe that a hybrid storage approach of using COTS components and innovative software technology can bring new capabilities into a production environment for the HPC community much faster than the approach of creating and maintaining a complete end-to-end unique parallel archive software solution. In this paper, we relay our experience of integrating a global parallel file system and a standard backup/archive product with a very small amount of additional code to provide a scalable, parallel archive. Our solution has a high degree of overlap with current parallel archive products including (a) doing parallel movement to/from tape for a single large parallel file, (b) hierarchical storage management, (c) ILM features, (d) high volume (non-single parallel file) archives for backup/archive/content management, and (e) leveraging all free file movement tools in Linux such as copy, move, Is, tar, etc. We have successfully applied our working COTS Parallel Archive System to the current world's first petafiop/s computing system, LANL's Roadrunner machine, and demonstrated its capability to address requirements of future archival storage systems.« less

Molecular-dynamics simulations of self-assembled monolayers (SAM) on parallel computers

NASA Astrophysics Data System (ADS)

Vemparala, Satyavani

The purpose of this dissertation is to investigate the properties of self-assembled monolayers, particularly alkanethiols and Poly (ethylene glycol) terminated alkanethiols. These simulations are based on realistic interatomic potentials and require scalable and portable multiresolution algorithms implemented on parallel computers. Large-scale molecular dynamics simulations of self-assembled alkanethiol monolayer systems have been carried out using an all-atom model involving a million atoms to investigate their structural properties as a function of temperature, lattice spacing and molecular chain-length. Results show that the alkanethiol chains tilt from the surface normal by a collective angle of 25° along next-nearest neighbor direction at 300K. At 350K the system transforms to a disordered phase characterized by small tilt angle, flexible tilt direction, and random distribution of backbone planes. With increasing lattice spacing, a, the tilt angle increases rapidly from a nearly zero value at a = 4.7A to as high as 34° at a = 5.3A at 300K. We also studied the effect of end groups on the tilt structure of SAM films. We characterized the system with respect to temperature, the alkane chain length, lattice spacing, and the length of the end group. We found that the gauche defects were predominant only in the tails, and the gauche defects increased with the temperature and number of EG units. Effect of electric field on the structure of poly (ethylene glycol) (PEG) terminated alkanethiol self assembled monolayer (SAM) on gold has been studied using parallel molecular dynamics method. An applied electric field triggers a conformational transition from all-trans to a mostly gauche conformation. The polarity of the electric field has a significant effect on the surface structure of PEG leading to a profound effect on the hydrophilicity of the surface. The electric field applied anti-parallel to the surface normal causes a reversible transition to an ordered state in which the oxygen atoms are exposed. On the other hand, an electric field applied in a direction parallel to the surface normal introduces considerable disorder in the system and the oxygen atoms are buried inside.

A parallel finite element simulator for ion transport through three-dimensional ion channel systems.

PubMed

Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo

2013-09-15

A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results. Copyright © 2013 Wiley Periodicals, Inc.

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.

A parallel algorithm for 2D visco-acoustic frequency-domain full-waveform inversion: application to a dense OBS data set

NASA Astrophysics Data System (ADS)

Sourbier, F.; Operto, S.; Virieux, J.

2006-12-01

We present a distributed-memory parallel algorithm for 2D visco-acoustic full-waveform inversion of wide-angle seismic data. Our code is written in fortran90 and use MPI for parallelism. The algorithm was applied to real wide-angle data set recorded by 100 OBSs with a 1-km spacing in the eastern-Nankai trough (Japan) to image the deep structure of the subduction zone. Full-waveform inversion is applied sequentially to discrete frequencies by proceeding from the low to the high frequencies. The inverse problem is solved with a classic gradient method. Full-waveform modeling is performed with a frequency-domain finite-difference method. In the frequency-domain, solving the wave equation requires resolution of a large unsymmetric system of linear equations. We use the massively parallel direct solver MUMPS (http://www.enseeiht.fr/irit/apo/MUMPS) for distributed-memory computer to solve this system. The MUMPS solver is based on a multifrontal method for the parallel factorization. The MUMPS algorithm is subdivided in 3 main steps: a symbolic analysis step that performs re-ordering of the matrix coefficients to minimize the fill-in of the matrix during the subsequent factorization and an estimation of the assembly tree of the matrix. Second, the factorization is performed with dynamic scheduling to accomodate numerical pivoting and provides the LU factors distributed over all the processors. Third, the resolution is performed for multiple sources. To compute the gradient of the cost function, 2 simulations per shot are required (one to compute the forward wavefield and one to back-propagate residuals). The multi-source resolutions can be performed in parallel with MUMPS. In the end, each processor stores in core a sub-domain of all the solutions. These distributed solutions can be exploited to compute in parallel the gradient of the cost function. Since the gradient of the cost function is a weighted stack of the shot and residual solutions of MUMPS, each processor computes the corresponding sub-domain of the gradient. In the end, the gradient is centralized on the master processor using a collective communation. The gradient is scaled by the diagonal elements of the Hessian matrix. This scaling is computed only once per frequency before the first iteration of the inversion. Estimation of the diagonal terms of the Hessian requires performing one simulation per non redondant shot and receiver position. The same strategy that the one used for the gradient is used to compute the diagonal Hessian in parallel. This algorithm was applied to a dense wide-angle data set recorded by 100 OBSs in the eastern Nankai trough, offshore Japan. Thirteen frequencies ranging from 3 and 15 Hz were inverted. Tweny iterations per frequency were computed leading to 260 tomographic velocity models of increasing resolution. The velocity model dimensions are 105 km x 25 km corresponding to a finite-difference grid of 4201 x 1001 grid with a 25-m grid interval. The number of shot was 1005 and the number of inverted OBS gathers was 93. The inversion requires 20 days on 6 32-bits bi-processor nodes with 4 Gbytes of RAM memory per node when only the LU factorization is performed in parallel. Preliminary estimations of the time required to perform the inversion with the fully-parallelized code is 6 and 4 days using 20 and 50 processors respectively.

Linearized potential solution for an airfoil in nonuniform parallel streams

NASA Technical Reports Server (NTRS)

Prabhu, R. K.; Tiwari, S. N.

1983-01-01

A small perturbation potential flow theory is applied to the problem of determining the chordwise pressure distribution, lift and pitching moment of a thin airfoil in the middle of five parallel streams. This theory is then extended to the case of an undisturbed stream having a given smooth velocity profile. Two typical examples are considered and the results obtained are compared with available solutions of Euler's equations. The agreement between these two results is not quite satisfactory. Possible reasons for the differences are indicated.

Digital intermediate frequency QAM modulator using parallel processing

DOEpatents

Pao, Hsueh-Yuan [Livermore, CA; Tran, Binh-Nien [San Ramon, CA

2008-05-27

The digital Intermediate Frequency (IF) modulator applies to various modulation types and offers a simple and low cost method to implement a high-speed digital IF modulator using field programmable gate arrays (FPGAs). The architecture eliminates multipliers and sequential processing by storing the pre-computed modulated cosine and sine carriers in ROM look-up-tables (LUTs). The high-speed input data stream is parallel processed using the corresponding LUTs, which reduces the main processing speed, allowing the use of low cost FPGAs.

Omni-directional railguns

DOEpatents

Shahinpoor, Mohsen

1995-01-01

A device for electromagnetically accelerating projectiles. The invention features two parallel conducting circular plates, a plurality of electrode connections to both upper and lower plates, a support base, and a projectile magazine. A projectile is spring-loaded into a firing position concentrically located between the parallel plates. A voltage source is applied to the plates to cause current to flow in directions defined by selectable, discrete electrode connections on both upper and lower plates. Repulsive Lorentz forces are generated to eject the projectile in a 360 degree range of fire.

Towards the Teraflop CFD

NASA Technical Reports Server (NTRS)

Schreiber, Robert; Simon, Horst D.

1992-01-01

We are surveying current projects in the area of parallel supercomputers. The machines considered here will become commercially available in the 1990 - 1992 time frame. All are suitable for exploring the critical issues in applying parallel processors to large scale scientific computations, in particular CFD calculations. This chapter presents an overview of the surveyed machines, and a detailed analysis of the various architectural and technology approaches taken. Particular emphasis is placed on the feasibility of a Teraflops capability following the paths proposed by various developers.

Power-MOSFET Voltage Regulator

NASA Technical Reports Server (NTRS)

Miller, W. N.; Gray, O. E.

1982-01-01

Ninety-six parallel MOSFET devices with two-stage feedback circuit form a high-current dc voltage regulator that also acts as fully-on solid-state switch when fuel-cell out-put falls below regulated voltage. Ripple voltage is less than 20 mV, transient recovery time is less than 50 ms. Parallel MOSFET's act as high-current dc regulator and switch. Regulator can be used wherever large direct currents must be controlled. Can be applied to inverters, industrial furnaces photovoltaic solar generators, dc motors, and electric autos.

Theory of Dielectric Elastomers

DTIC Science & Technology

2010-10-25

partly in the air and partly in a dielectric liquid . The applied voltage causes the liquid to rise to a height h. The height results from the...balance of the Maxwell stress and the weight of the liquid . The Maxwell stress parallel to the electrodes in the air is 2/2Eaa   , where a is the...permittivity of the air. The Maxwell stress parallel to the electrodes in the liquid is 2/2Ell   , where l is the permittivity of the liquid

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.

Parallelization of a hydrological model using the message passing interface

USGS Publications Warehouse

Wu, Yiping; Li, Tiejian; Sun, Liqun; Chen, Ji

2013-01-01

With the increasing knowledge about the natural processes, hydrological models such as the Soil and Water Assessment Tool (SWAT) are becoming larger and more complex with increasing computation time. Additionally, other procedures such as model calibration, which may require thousands of model iterations, can increase running time and thus further reduce rapid modeling and analysis. Using the widely-applied SWAT as an example, this study demonstrates how to parallelize a serial hydrological model in a Windows® environment using a parallel programing technology—Message Passing Interface (MPI). With a case study, we derived the optimal values for the two parameters (the number of processes and the corresponding percentage of work to be distributed to the master process) of the parallel SWAT (P-SWAT) on an ordinary personal computer and a work station. Our study indicates that model execution time can be reduced by 42%–70% (or a speedup of 1.74–3.36) using multiple processes (two to five) with a proper task-distribution scheme (between the master and slave processes). Although the computation time cost becomes lower with an increasing number of processes (from two to five), this enhancement becomes less due to the accompanied increase in demand for message passing procedures between the master and all slave processes. Our case study demonstrates that the P-SWAT with a five-process run may reach the maximum speedup, and the performance can be quite stable (fairly independent of a project size). Overall, the P-SWAT can help reduce the computation time substantially for an individual model run, manual and automatic calibration procedures, and optimization of best management practices. In particular, the parallelization method we used and the scheme for deriving the optimal parameters in this study can be valuable and easily applied to other hydrological or environmental models.

Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

NASA Astrophysics Data System (ADS)

Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot

2016-01-01

Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which is not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate efficient scaling up to 1024, 4096 and 8192 compute cores which allowed the simulation of a single heart beat in 44.3, 87.8 and 235.3 minutes, respectively. The efficiency of the method allows fast simulation cycles without compromising anatomical or biophysical detail.

Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

PubMed Central

Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot

2016-01-01

Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate efficient scaling up to 1024, 4096 and 8192 compute cores which allowed the simulation of a single heart beat in 44.3, 87.8 and 235.3 minutes, respectively. The efficiency of the method allows fast simulation cycles without compromising anatomical or biophysical detail. PMID:26819483

Parallel algorithms for the molecular conformation problem

NASA Astrophysics Data System (ADS)

Rajan, Kumar

Given a set of objects, and some of the pairwise distances between them, the problem of identifying the positions of the objects in the Euclidean space is referred to as the molecular conformation problem. This problem is known to be computationally difficult. One of the most important applications of this problem is the determination of the structure of molecules. In the case of molecular structure determination, usually only the lower and upper bounds on some of the interatomic distances are available. The process of obtaining a tighter set of bounds between all pairs of atoms, using the available interatomic distance bounds is referred to as bound-smoothing . One method for bound-smoothing is to use the limits imposed by the triangle inequality. The distance bounds so obtained can often be tightened further by applying the tetrangle inequality---the limits imposed on the six pairwise distances among a set of four atoms (instead of three for the triangle inequalities). The tetrangle inequality is expressed by the Cayley-Menger determinants. The sequential tetrangle-inequality bound-smoothing algorithm considers a quadruple of atoms at a time, and tightens the bounds on each of its six distances. The sequential algorithm is computationally expensive, and its application is limited to molecules with up to a few hundred atoms. Here, we conduct an experimental study of tetrangle-inequality bound-smoothing and reduce the sequential time by identifying the most computationally expensive portions of the process. We also present a simple criterion to determine which of the quadruples of atoms are likely to be tightened the most by tetrangle-inequality bound-smoothing. This test could be used to enhance the applicability of this process to large molecules. We map the problem of parallelizing tetrangle-inequality bound-smoothing to that of generating disjoint packing designs of a certain kind. We map this, in turn, to a regular-graph coloring problem, and present a simple, parallel algorithm for tetrangle-inequality bound-smoothing. We implement the parallel algorithm on the Intel Paragon X/PS, and apply it to real-life molecules. Our results show that with this parallel algorithm, tetrangle inequality can be applied to large molecules in a reasonable amount of time. We extend the regular graph to represent more general packing designs, and present a coloring algorithm for this graph. This can be used to generate constant-weight binary codes in parallel. Once a tighter set of distance bounds is obtained, the molecular conformation problem is usually formulated as a non-linear optimization problem, and a global optimization algorithm is then used to solve the problem. Here we present a parallel, deterministic algorithm for the optimization problem based on Interval Analysis. We implement our algorithm, using dynamic load balancing, on a network of Sun Ultra-Sparc workstations. Our experience with this algorithm shows that its application is limited to small instances of the molecular conformation problem, where the number of measured, pairwise distances is close to the maximum value. However, since the interval method eliminates a substantial portion of the initial search space very quickly, it can be used to prune the search space before any of the more efficient, nondeterministic methods can be applied.

Slice-selective RF pulses for in vivo B1+ inhomogeneity mitigation at 7 tesla using parallel RF excitation with a 16-element coil.

PubMed

Setsompop, Kawin; Alagappan, Vijayanand; Gagoski, Borjan; Witzel, Thomas; Polimeni, Jonathan; Potthast, Andreas; Hebrank, Franz; Fontius, Ulrich; Schmitt, Franz; Wald, Lawrence L; Adalsteinsson, Elfar

2008-12-01

Slice-selective RF waveforms that mitigate severe B1+ inhomogeneity at 7 Tesla using parallel excitation were designed and validated in a water phantom and human studies on six subjects using a 16-element degenerate stripline array coil driven with a butler matrix to utilize the eight most favorable birdcage modes. The parallel RF waveform design applied magnitude least-squares (MLS) criteria with an optimized k-space excitation trajectory to significantly improve profile uniformity compared to conventional least-squares (LS) designs. Parallel excitation RF pulses designed to excite a uniform in-plane flip angle (FA) with slice selection in the z-direction were demonstrated and compared with conventional sinc-pulse excitation and RF shimming. In all cases, the parallel RF excitation significantly mitigated the effects of inhomogeneous B1+ on the excitation FA. The optimized parallel RF pulses for human B1+ mitigation were only 67% longer than a conventional sinc-based excitation, but significantly outperformed RF shimming. For example the standard deviations (SDs) of the in-plane FA (averaged over six human studies) were 16.7% for conventional sinc excitation, 13.3% for RF shimming, and 7.6% for parallel excitation. This work demonstrates that excitations with parallel RF systems can provide slice selection with spatially uniform FAs at high field strengths with only a small pulse-duration penalty. (c) 2008 Wiley-Liss, Inc.

Implementation of parallel transmit beamforming using orthogonal frequency division multiplexing--achievable resolution and interbeam interference.

PubMed

Demi, Libertario; Viti, Jacopo; Kusters, Lieneke; Guidi, Francesco; Tortoli, Piero; Mischi, Massimo

2013-11-01

The speed of sound in the human body limits the achievable data acquisition rate of pulsed ultrasound scanners. To overcome this limitation, parallel beamforming techniques are used in ultrasound 2-D and 3-D imaging systems. Different parallel beamforming approaches have been proposed. They may be grouped into two major categories: parallel beamforming in reception and parallel beamforming in transmission. The first category is not optimal for harmonic imaging; the second category may be more easily applied to harmonic imaging. However, inter-beam interference represents an issue. To overcome these shortcomings and exploit the benefit of combining harmonic imaging and high data acquisition rate, a new approach has been recently presented which relies on orthogonal frequency division multiplexing (OFDM) to perform parallel beamforming in transmission. In this paper, parallel transmit beamforming using OFDM is implemented for the first time on an ultrasound scanner. An advanced open platform for ultrasound research is used to investigate the axial resolution and interbeam interference achievable with parallel transmit beamforming using OFDM. Both fundamental and second-harmonic imaging modalities have been considered. Results show that, for fundamental imaging, axial resolution in the order of 2 mm can be achieved in combination with interbeam interference in the order of -30 dB. For second-harmonic imaging, axial resolution in the order of 1 mm can be achieved in combination with interbeam interference in the order of -35 dB.

ORCA Project: Research on high-performance parallel computer programming environments. Final report, 1 Apr-31 Mar 90

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

Snyder, L.; Notkin, D.; Adams, L.

1990-03-31

This task relates to research on programming massively parallel computers. Previous work on the Ensamble concept of programming was extended and investigation into nonshared memory models of parallel computation was undertaken. Previous work on the Ensamble concept defined a set of programming abstractions and was used to organize the programming task into three distinct levels; Composition of machine instruction, composition of processes, and composition of phases. It was applied to shared memory models of computations. During the present research period, these concepts were extended to nonshared memory models. During the present research period, one Ph D. thesis was completed, onemore » book chapter, and six conference proceedings were published.« less

Enabling Requirements-Based Programming for Highly-Dependable Complex Parallel and Distributed Systems

NASA Technical Reports Server (NTRS)

Hinchey, Michael G.; Rash, James L.; Rouff, Christopher A.

2005-01-01

The manual application of formal methods in system specification has produced successes, but in the end, despite any claims and assertions by practitioners, there is no provable relationship between a manually derived system specification or formal model and the customer's original requirements. Complex parallel and distributed system present the worst case implications for today s dearth of viable approaches for achieving system dependability. No avenue other than formal methods constitutes a serious contender for resolving the problem, and so recognition of requirements-based programming has come at a critical juncture. We describe a new, NASA-developed automated requirement-based programming method that can be applied to certain classes of systems, including complex parallel and distributed systems, to achieve a high degree of dependability.

Shared Memory Parallelization of an Implicit ADI-type CFD Code

NASA Technical Reports Server (NTRS)

Hauser, Th.; Huang, P. G.

1999-01-01

A parallelization study designed for ADI-type algorithms is presented using the OpenMP specification for shared-memory multiprocessor programming. Details of optimizations specifically addressed to cache-based computer architectures are described and performance measurements for the single and multiprocessor implementation are summarized. The paper demonstrates that optimization of memory access on a cache-based computer architecture controls the performance of the computational algorithm. A hybrid MPI/OpenMP approach is proposed for clusters of shared memory machines to further enhance the parallel performance. The method is applied to develop a new LES/DNS code, named LESTool. A preliminary DNS calculation of a fully developed channel flow at a Reynolds number of 180, Re(sub tau) = 180, has shown good agreement with existing data.

Application of lean manufacturing concepts to drug discovery: rapid analogue library synthesis.

PubMed

Weller, Harold N; Nirschl, David S; Petrillo, Edward W; Poss, Michael A; Andres, Charles J; Cavallaro, Cullen L; Echols, Martin M; Grant-Young, Katherine A; Houston, John G; Miller, Arthur V; Swann, R Thomas

2006-01-01

The application of parallel synthesis to lead optimization programs in drug discovery has been an ongoing challenge since the first reports of library synthesis. A number of approaches to the application of parallel array synthesis to lead optimization have been attempted over the years, ranging from widespread deployment by (and support of) individual medicinal chemists to centralization as a service by an expert core team. This manuscript describes our experience with the latter approach, which was undertaken as part of a larger initiative to optimize drug discovery. In particular, we highlight how concepts taken from the manufacturing sector can be applied to drug discovery and parallel synthesis to improve the timeliness and thus the impact of arrays on drug discovery.