The multigrid preconditioned conjugate gradient method

NASA Technical Reports Server (NTRS)

Tatebe, Osamu

1993-01-01

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

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.

Element-topology-independent preconditioners for parallel finite element computations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

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

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 Performance Comparison of the Parallel Preconditioners for Iterative Methods for Large Sparse Linear Systems Arising from Partial Differential Equations on Structured Grids

NASA Astrophysics Data System (ADS)

Ma, Sangback

In this paper we compare various parallel preconditioners such as Point-SSOR (Symmetric Successive OverRelaxation), ILU(0) (Incomplete LU) in the Wavefront ordering, ILU(0) in the Multi-color ordering, Multi-Color Block SOR (Successive OverRelaxation), SPAI (SParse Approximate Inverse) and pARMS (Parallel Algebraic Recursive Multilevel Solver) for solving large sparse linear systems arising from two-dimensional PDE (Partial Differential Equation)s on structured grids. Point-SSOR is well-known, and ILU(0) is one of the most popular preconditioner, but it is inherently serial. ILU(0) in the Wavefront ordering maximizes the parallelism in the natural order, but the lengths of the wave-fronts are often nonuniform. ILU(0) in the Multi-color ordering is a simple way of achieving a parallelism of the order N, where N is the order of the matrix, but its convergence rate often deteriorates as compared to that of natural ordering. We have chosen the Multi-Color Block SOR preconditioner combined with direct sparse matrix solver, since for the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with the Multi-Color ordering. By using block version we expect to minimize the interprocessor communications. SPAI computes the sparse approximate inverse directly by least squares method. Finally, ARMS is a preconditioner recursively exploiting the concept of independent sets and pARMS is the parallel version of ARMS. Experiments were conducted for the Finite Difference and Finite Element discretizations of five two-dimensional PDEs with large meshsizes up to a million on an IBM p595 machine with distributed memory. Our matrices are real positive, i. e., their real parts of the eigenvalues are positive. We have used GMRES(m) as our outer iterative method, so that the convergence of GMRES(m) for our test matrices are mathematically guaranteed. Interprocessor communications were done using MPI (Message Passing Interface) primitives. The results show that in general ILU(0) in the Multi-Color ordering ahd ILU(0) in the Wavefront ordering outperform the other methods but for symmetric and nearly symmetric 5-point matrices Multi-Color Block SOR gives the best performance, except for a few cases with a small number of processors.

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.

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.

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.

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

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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

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.

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.

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.

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.

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.

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

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.

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.

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

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

A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations.

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

Shadid, John Nicolas; Elman, Howard; Shuttleworth, Robert R.

2007-04-01

In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible Navier-Stokes equations based on preconditioned Krylov methods. These include physics-based methods, such as SIMPLE, and purely algebraic preconditioners based on the approximation of the Schur complement. All these techniques can be represented as approximate block factorization (ABF) type preconditioners. The goal is to decompose the application of the preconditioner into simplified sub-systems in which scalable multi-level type solvers can be applied. In this paper we develop a taxonomy of these ideas based on an adaptation of a generalized approximate factorization of themore » Navier-Stokes system first presented in [25]. This taxonomy illuminates the similarities and differences among these preconditioners and the central role played by efficient approximation of certain Schur complement operators. We then present a parallel computational study that examines the performance of these methods and compares them to an additive Schwarz domain decomposition (DD) algorithm. Results are presented for two and three-dimensional steady state problems for enclosed domains and inflow/outflow systems on both structured and unstructured meshes. The numerical experiments are performed using MPSalsa, a stabilized finite element code.« less

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.

Performance Models for the Spike Banded Linear System Solver

DOE PAGES

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

2011-01-01

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

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.

Algorithms for parallel and vector computations

NASA Technical Reports Server (NTRS)

Ortega, James M.

1995-01-01

This is a final report on work performed under NASA grant NAG-1-1112-FOP during the period March, 1990 through February 1995. Four major topics are covered: (1) solution of nonlinear poisson-type equations; (2) parallel reduced system conjugate gradient method; (3) orderings for conjugate gradient preconditioners, and (4) SOR as a preconditioner.

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

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.

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

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

NASA Astrophysics Data System (ADS)

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

2014-06-01

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

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

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.

Incomplete Sparse Approximate Inverses for Parallel Preconditioning

DOE PAGES

Anzt, Hartwig; Huckle, Thomas K.; Bräckle, Jürgen; ...

2017-10-28

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as anmore » attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.« less

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

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

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

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

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.

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.

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.

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.

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

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.

Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

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

Lin, Paul T.; Shadid, John N.; Sala, Marzio

In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system ismore » obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 10{sup 8} unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system.« less

Using Perturbed QR Factorizations To Solve Linear Least-Squares Problems

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

Avron, Haim; Ng, Esmond G.; Toledo, Sivan

2008-03-21

We propose and analyze a new tool to help solve sparse linear least-squares problems min{sub x} {parallel}Ax-b{parallel}{sub 2}. Our method is based on a sparse QR factorization of a low-rank perturbation {cflx A} of A. More precisely, we show that the R factor of {cflx A} is an effective preconditioner for the least-squares problem min{sub x} {parallel}Ax-b{parallel}{sub 2}, when solved using LSQR. We propose applications for the new technique. When A is rank deficient we can add rows to ensure that the preconditioner is well-conditioned without column pivoting. When A is sparse except for a few dense rows we canmore » drop these dense rows from A to obtain {cflx A}. Another application is solving an updated or downdated problem. If R is a good preconditioner for the original problem A, it is a good preconditioner for the updated/downdated problem {cflx A}. We can also solve what-if scenarios, where we want to find the solution if a column of the original matrix is changed/removed. We present a spectral theory that analyzes the generalized spectrum of the pencil (A*A,R*R) and analyze the applications.« 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.

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.

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.

Matrix-Free Polynomial-Based Nonlinear Least Squares Optimized Preconditioning and its Application to Discontinuous Galerkin Discretizations of the Euler Equations

DTIC Science & Technology

2015-06-01

cient parallel code for applying the operator. Our method constructs a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. We show...apply the underlying operator. Such a preconditioner can be very attractive in scenarios where one has a highly efficient parallel code for applying...repeatedly solve a large system of linear equations where one has an extremely fast parallel code for applying an underlying fixed linear operator

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.

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.

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

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.

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

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.

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.

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

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

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.

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.

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.

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.

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.

Parallel conjugate gradient algorithms for manipulator dynamic simulation

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheld, Robert E.

1989-01-01

Parallel conjugate gradient algorithms for the computation of multibody dynamics are developed for the specialized case of a robot manipulator. For an n-dimensional positive-definite linear system, the Classical Conjugate Gradient (CCG) algorithms are guaranteed to converge in n iterations, each with a computation cost of O(n); this leads to a total computational cost of O(n sq) on a serial processor. A conjugate gradient algorithms is presented that provide greater efficiency using a preconditioner, which reduces the number of iterations required, and by exploiting parallelism, which reduces the cost of each iteration. Two Preconditioned Conjugate Gradient (PCG) algorithms are proposed which respectively use a diagonal and a tridiagonal matrix, composed of the diagonal and tridiagonal elements of the mass matrix, as preconditioners. Parallel algorithms are developed to compute the preconditioners and their inversions in O(log sub 2 n) steps using n processors. A parallel algorithm is also presented which, on the same architecture, achieves the computational time of O(log sub 2 n) for each iteration. Simulation results for a seven degree-of-freedom manipulator are presented. Variants of the proposed algorithms are also developed which can be efficiently implemented on the Robot Mathematics Processor (RMP).

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.

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

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.

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.

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.

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.

PRECONDITIONED CONJUGATE-GRADIENT 2 (PCG2), a computer program for solving ground-water flow equations

USGS Publications Warehouse

Hill, Mary C.

1990-01-01

This report documents PCG2 : a numerical code to be used with the U.S. Geological Survey modular three-dimensional, finite-difference, ground-water flow model . PCG2 uses the preconditioned conjugate-gradient method to solve the equations produced by the model for hydraulic head. Linear or nonlinear flow conditions may be simulated. PCG2 includes two reconditioning options : modified incomplete Cholesky preconditioning, which is efficient on scalar computers; and polynomial preconditioning, which requires less computer storage and, with modifications that depend on the computer used, is most efficient on vector computers . Convergence of the solver is determined using both head-change and residual criteria. Nonlinear problems are solved using Picard iterations. This documentation provides a description of the preconditioned conjugate gradient method and the two preconditioners, detailed instructions for linking PCG2 to the modular model, sample data inputs, a brief description of PCG2, and a FORTRAN listing.

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.

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

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.

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.

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE PAGES

Li, Ruipeng; Saad, Yousef

2017-08-01

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

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

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

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

Li, Ruipeng; Saad, Yousef

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

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

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.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.

1990-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. D., Jr.

1992-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number od operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

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.

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

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

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

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.

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.

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.

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

Research in parallel computing

NASA Technical Reports Server (NTRS)

Ortega, James M.; Henderson, Charles

1994-01-01

This report summarizes work on parallel computations for NASA Grant NAG-1-1529 for the period 1 Jan. - 30 June 1994. Short summaries on highly parallel preconditioners, target-specific parallel reductions, and simulation of delta-cache protocols are provided.

Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes

NASA Technical Reports Server (NTRS)

Movriplis, Dimitri J.

1998-01-01

Unstructured multigrid techniques for relieving the stiffness associated with high-Reynolds number viscous flow simulations on extremely stretched grids are investigated. One approach consists of employing a semi-coarsening or directional-coarsening technique, based on the directions of strong coupling within the mesh, in order to construct more optimal coarse grid levels. An alternate approach is developed which employs directional implicit smoothing with regular fully coarsened multigrid levels. The directional implicit smoothing is obtained by constructing implicit lines in the unstructured mesh based on the directions of strong coupling. Both approaches yield large increases in convergence rates over the traditional explicit full-coarsening multigrid algorithm. However, maximum benefits are achieved by combining the two approaches in a coupled manner into a single algorithm. An order of magnitude increase in convergence rate over the traditional explicit full-coarsening algorithm is demonstrated, and convergence rates for high-Reynolds number viscous flows which are independent of the grid aspect ratio are obtained. Further acceleration is provided by incorporating low-Mach-number preconditioning techniques, and a Newton-GMRES strategy which employs the multigrid scheme as a preconditioner. The compounding effects of these various techniques on speed of convergence is documented through several example test cases.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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

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

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)

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

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.

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.

Optimal and fast E/B separation with a dual messenger field

NASA Astrophysics Data System (ADS)

Kodi Ramanah, Doogesh; Lavaux, Guilhem; Wandelt, Benjamin D.

2018-05-01

We adapt our recently proposed dual messenger algorithm for spin field reconstruction and showcase its efficiency and effectiveness in Wiener filtering polarized cosmic microwave background (CMB) maps. Unlike conventional preconditioned conjugate gradient (PCG) solvers, our preconditioner-free technique can deal with high-resolution joint temperature and polarization maps with inhomogeneous noise distributions and arbitrary mask geometries with relative ease. Various convergence diagnostics illustrate the high quality of the dual messenger reconstruction. In contrast, the PCG implementation fails to converge to a reasonable solution for the specific problem considered. The implementation of the dual messenger method is straightforward and guarantees numerical stability and convergence. We show how the algorithm can be modified to generate fluctuation maps, which, combined with the Wiener filter solution, yield unbiased constrained signal realizations, consistent with observed data. This algorithm presents a pathway to exact global analyses of high-resolution and high-sensitivity CMB data for a statistically optimal separation of E and B modes. It is therefore relevant for current and next-generation CMB experiments, in the quest for the elusive primordial B-mode signal.

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.

Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis

NASA Astrophysics Data System (ADS)

Jiao, Yujian; Wang, Li-Lian; Huang, Can

2016-01-01

The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general Jacobi-Gauss-Lobatto (JGL) points. We show that in the Caputo case, it suffices to compute F-PSDM of order μ ∈ (0 , 1) to compute that of any order k + μ with integer k ≥ 0, while in the modified RL case, it is only necessary to evaluate a fractional integral matrix of order μ ∈ (0 , 1). Secondly, we introduce suitable fractional JGL Birkhoff interpolation problems leading to new interpolation polynomial basis functions with remarkable properties: (i) the matrix generated from the new basis yields the exact inverse of F-PSDM at "interior" JGL points; (ii) the matrix of the highest fractional derivative in a collocation scheme under the new basis is diagonal; and (iii) the resulted linear system is well-conditioned in the Caputo case, while in the modified RL case, the eigenvalues of the coefficient matrix are highly concentrated. In both cases, the linear systems of the collocation schemes using the new basis can be solved by an iterative solver within a few iterations. Notably, the inverse can be computed in a very stable manner, so this offers optimal preconditioners for usual fractional collocation methods for fractional differential equations (FDEs). It is also noteworthy that the choice of certain special JGL points with parameters related to the order of the equations can ease the implementation. We highlight that the use of the Bateman's fractional integral formulas and fast transforms between Jacobi polynomials with different parameters, is essential for our algorithm development.

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

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

Analysis of the Hessian for Aerodynamic Optimization: Inviscid Flow

NASA Technical Reports Server (NTRS)

Arian, Eyal; Ta'asan, Shlomo

1996-01-01

In this paper we analyze inviscid aerodynamic shape optimization problems governed by the full potential and the Euler equations in two and three dimensions. The analysis indicates that minimization of pressure dependent cost functions results in Hessians whose eigenvalue distributions are identical for the full potential and the Euler equations. However the optimization problems in two and three dimensions are inherently different. While the two dimensional optimization problems are well-posed the three dimensional ones are ill-posed. Oscillations in the shape up to the smallest scale allowed by the design space can develop in the direction perpendicular to the flow, implying that a regularization is required. A natural choice of such a regularization is derived. The analysis also gives an estimate of the Hessian's condition number which implies that the problems at hand are ill-conditioned. Infinite dimensional approximations for the Hessians are constructed and preconditioners for gradient based methods are derived from these approximate Hessians.

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.

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.

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.

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

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.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

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

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.

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

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

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.

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.

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.

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.

Extending fields in a level set method by solving a biharmonic equation

NASA Astrophysics Data System (ADS)

Moroney, Timothy J.; Lusmore, Dylan R.; McCue, Scott W.; McElwain, D. L. Sean

2017-08-01

We present an approach for computing extensions of velocities or other fields in level set methods by solving a biharmonic equation. The approach differs from other commonly used approaches to velocity extension because it deals with the interface fully implicitly through the level set function. No explicit properties of the interface, such as its location or the velocity on the interface, are required in computing the extension. These features lead to a particularly simple implementation using either a sparse direct solver or a matrix-free conjugate gradient solver. Furthermore, we propose a fast Poisson preconditioner that can be used to accelerate the convergence of the latter. We demonstrate the biharmonic extension on a number of test problems that serve to illustrate its effectiveness at producing smooth and accurate extensions near interfaces. A further feature of the method is the natural way in which it deals with symmetry and periodicity, ensuring through its construction that the extension field also respects these symmetries.

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

DOE PAGES

Chacon, L.; Chen, G.

2016-04-19

Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. Anmore » asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.« less

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

NASA Astrophysics Data System (ADS)

Chacón, L.; Chen, G.

2016-07-01

We extend a recently proposed fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (ϕ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ ṡ A = 0 exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

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

Chacon, L.; Chen, G.

Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. Anmore » asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.« less

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.

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

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.

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.

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.

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

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

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.

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

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.

Preconditioned MoM Solutions for Complex Planar Arrays

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

Fasenfest, B J; Jackson, D; Champagne, N

2004-01-23

The numerical analysis of large arrays is a complex problem. There are several techniques currently under development in this area. One such technique is the FAIM (Faster Adaptive Integral Method). This method uses a modification of the standard AIM approach which takes into account the reusability properties of matrices that arise from identical array elements. If the array consists of planar conducting bodies, the array elements are meshed using standard subdomain basis functions, such as the RWG basis. These bases are then projected onto a regular grid of interpolating polynomials. This grid can then be used in a 2D ormore » 3D FFT to accelerate the matrix-vector product used in an iterative solver. The method has been proven to greatly reduce solve time by speeding the matrix-vector product computation. The FAIM approach also reduces fill time and memory requirements, since only the near element interactions need to be calculated exactly. The present work extends FAIM by modifying it to allow for layered material Green's Functions and dielectrics. In addition, a preconditioner is implemented to greatly reduce the number of iterations required for a solution. The general scheme of the FAIM method is reported in; this contribution is limited to presenting new results.« less

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.

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.

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

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

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

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.

The Magnetic Reconnection Code: an AMR-based fully implicit simulation suite

NASA Astrophysics Data System (ADS)

Germaschewski, K.; Bhattacharjee, A.; Ng, C.-S.

2006-12-01

Extended MHD models, which incorporate two-fluid effects, are promising candidates to enhance understanding of collisionless reconnection phenomena in laboratory, space and astrophysical plasma physics. In this paper, we introduce two simulation codes in the Magnetic Reconnection Code suite which integrate reduced and full extended MHD models. Numerical integration of these models comes with two challenges: Small-scale spatial structures, e.g. thin current sheets, develop and must be well resolved by the code. Adaptive mesh refinement (AMR) is employed to provide high resolution where needed while maintaining good performance. Secondly, the two-fluid effects in extended MHD give rise to dispersive waves, which lead to a very stringent CFL condition for explicit codes, while reconnection happens on a much slower time scale. We use a fully implicit Crank--Nicholson time stepping algorithm. Since no efficient preconditioners are available for our system of equations, we instead use a direct solver to handle the inner linear solves. This requires us to actually compute the Jacobian matrix, which is handled by a code generator that calculates the derivative symbolically and then outputs code to calculate it.

Curvilinear immersed-boundary method for simulating unsteady flows in shallow natural streams with arbitrarily complex obstacles

NASA Astrophysics Data System (ADS)

Kang, Seokkoo; Borazjani, Iman; Sotiropoulos, Fotis

2008-11-01

Unsteady 3D simulations of flows in natural streams is a challenging task due to the complexity of the bathymetry, the shallowness of the flow, and the presence of multiple nature- and man-made obstacles. This work is motivated by the need to develop a powerful numerical method for simulating such flows using coherent-structure-resolving turbulence models. We employ the curvilinear immersed boundary method of Ge and Sotiropoulos (Journal of Computational Physics, 2007) and address the critical issue of numerical efficiency in large aspect ratio computational domains and grids such as those encountered in long and shallow open channels. We show that the matrix-free Newton-Krylov method for solving the momentum equations coupled with an algebraic multigrid method with incomplete LU preconditioner for solving the Poisson equation yield a robust and efficient procedure for obtaining time-accurate solutions in such problems. We demonstrate the potential of the numerical approach by carrying out a direct numerical simulation of flow in a long and shallow meandering stream with multiple hydraulic structures.

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.

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.

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.

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.

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.

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.

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

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.

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

Parallel computing techniques for rotorcraft aerodynamics

NASA Astrophysics Data System (ADS)

Ekici, Kivanc

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

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.

Techniques and Software for Monolithic Preconditioning of Moderately-sized Geodynamic Stokes Flow Problems

NASA Astrophysics Data System (ADS)

Sanan, Patrick; May, Dave A.; Schenk, Olaf; Bollhöffer, Matthias

2017-04-01

Geodynamics simulations typically involve the repeated solution of saddle-point systems arising from the Stokes equations. These computations often dominate the time to solution. Direct solvers are known for their robustness and ``black box'' properties, yet exhibit superlinear memory requirements and time to solution. More complex multilevel-preconditioned iterative solvers have been very successful for large problems, yet their use can require more effort from the practitioner in terms of setting up a solver and choosing its parameters. We champion an intermediate approach, based on leveraging the power of modern incomplete factorization techniques for indefinite symmetric matrices. These provide an interesting alternative in situations in between the regimes where direct solvers are an obvious choice and those where complex, scalable, iterative solvers are an obvious choice. That is, much like their relatives for definite systems, ILU/ICC-preconditioned Krylov methods and ILU/ICC-smoothed multigrid methods, the approaches demonstrated here provide a useful addition to the solver toolkit. We present results with a simple, PETSc-based, open-source Q2-Q1 (Taylor-Hood) finite element discretization, in 2 and 3 dimensions, with the Stokes and Lamé (linear elasticity) saddle point systems. Attention is paid to cases in which full-operator incomplete factorization gives an improvement in time to solution over direct solution methods (which may not even be feasible due to memory limitations), without the complication of more complex (or at least, less-automatic) preconditioners or smoothers. As an important factor in the relevance of these tools is their availability in portable software, we also describe open-source PETSc interfaces to the factorization routines.

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

TerraFERMA: Harnessing Advanced Computational Libraries in Earth Science

NASA Astrophysics Data System (ADS)

Wilson, C. R.; Spiegelman, M.; van Keken, P.

2012-12-01

Many important problems in Earth sciences can be described by non-linear coupled systems of partial differential equations. These "multi-physics" problems include thermo-chemical convection in Earth and planetary interiors, interactions of fluids and magmas with the Earth's mantle and crust and coupled flow of water and ice. These problems are of interest to a large community of researchers but are complicated to model and understand. Much of this complexity stems from the nature of multi-physics where small changes in the coupling between variables or constitutive relations can lead to radical changes in behavior, which in turn affect critical computational choices such as discretizations, solvers and preconditioners. To make progress in understanding such coupled systems requires a computational framework where multi-physics problems can be described at a high-level while maintaining the flexibility to easily modify the solution algorithm. Fortunately, recent advances in computational science provide a basis for implementing such a framework. Here we present the Transparent Finite Element Rapid Model Assembler (TerraFERMA), which leverages several advanced open-source libraries for core functionality. FEniCS (fenicsproject.org) provides a high level language for describing the weak forms of coupled systems of equations, and an automatic code generator that produces finite element assembly code. PETSc (www.mcs.anl.gov/petsc) provides a wide range of scalable linear and non-linear solvers that can be composed into effective multi-physics preconditioners. SPuD (amcg.ese.ic.ac.uk/Spud) is an application neutral options system that provides both human and machine-readable interfaces based on a single xml schema. Our software integrates these libraries and provides the user with a framework for exploring multi-physics problems. A single options file fully describes the problem, including all equations, coefficients and solver options. Custom compiled applications are generated from this file but share an infrastructure for services common to all models, e.g. diagnostics, checkpointing and global non-linear convergence monitoring. This maximizes code reusability, reliability and longevity ensuring that scientific results and the methods used to acquire them are transparent and reproducible. TerraFERMA has been tested against many published geodynamic benchmarks including 2D/3D thermal convection problems, the subduction zone benchmarks and benchmarks for magmatic solitary waves. It is currently being used in the investigation of reactive cracking phenomena with applications to carbon sequestration, but we will principally discuss its use in modeling the migration of fluids in subduction zones. Subduction zones require an understanding of the highly nonlinear interactions of fluids with solids and thus provide an excellent scientific driver for the development of multi-physics software.

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.

Numerical study of heat transfer and fluid flow for steady crystal growth in a vertical Bridgman device

NASA Astrophysics Data System (ADS)

Pohlman, Matthew Michael

The study of heat transfer and fluid flow in a vertical Bridgman device is motivated by current industrial difficulties in growing crystals with as few defects as possible. For example, Gallium Arsenide (GaAs) is of great interest to the semiconductor industry but remains an uneconomical alternative to silicon because of the manufacturing problems. This dissertation is a two dimensional study of the fluid in an idealized Bridgman device. The model nonlinear PDEs are discretized using second order finite differencing. Newton's method solves the resulting nonlinear discrete equations. The large sparse linear systems involving the Jacobian are solved iteratively using the Generalized Minimum Residual method (GMRES). By adapting fast direct solvers for elliptic equations with simple boundary conditions, a good preconditioner is developed which is essential for GMRES to converge quickly. Trends of the fluid flow and heat transfer for typical ranges of the physical parameters are determined. Also, the size of the terms in the mathematical model are found by numerical investigation, in order to find what terms are in balance as the physical parameters vary. The results suggest the plausibility of simpler asymptotic solutions.

A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm

DOE PAGES

Chen, G.; Chacón, L.

2015-08-11

For decades, the Vlasov–Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. We explore a fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space–time-centered, employing particle sub-cycling and orbit-averaging. This algorithm conserves total energy, local charge,more » canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. Finally, we demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D–3V.« less

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

PubMed

Coriani, Sonia; Høst, Stinne; Jansík, Branislav; Thøgersen, Lea; Olsen, Jeppe; Jørgensen, Poul; Reine, Simen; Pawłowski, Filip; Helgaker, Trygve; Sałek, Paweł

2007-04-21

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

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

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.

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.

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

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.

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.

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.

76 FR 27239 - Airworthiness Directives; Cessna Aircraft Company (Cessna) Model 172 Airplanes Modified by...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-05-11

... Airworthiness Directives; Cessna Aircraft Company (Cessna) Model 172 Airplanes Modified by Supplemental Type... months for Cessna Aircraft Company (Cessna) Model 172 Airplanes modified by Supplemental Type Certificate...

The Effects of Three Prereading Activities on Learning Disabled Students' Reading Comprehension.

ERIC Educational Resources Information Center

Sachs, Arlene

1983-01-01

Thirty-six learning disabled children (9-12 years old) participated in a modified Directed Reading Activity, a modified Concept Analysis Activity, and a Worksheet Activity (control). Results indicate that evaluative reading comprehension was more affected by both the modified Concept Analysis Activity and the modified Directed Reading Activity…

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.

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.

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.

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.

Next generation extended Lagrangian first principles molecular dynamics

NASA Astrophysics Data System (ADS)

Niklasson, Anders M. N.

2017-08-01

Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended Lagrangian framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.

Next generation extended Lagrangian first principles molecular dynamics.

PubMed

Niklasson, Anders M N

2017-08-07

Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended Lagrangian framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.

A directional entrapment modification on the polyethylene surface by the amphiphilic modifier of stearyl-alcohol poly(ethylene oxide) ether

NASA Astrophysics Data System (ADS)

Lu, Qiang; Chen, Yi; Huang, Juexin; Huang, Jian; Wang, Xiaolin; Yao, Jiaying

2018-05-01

A novel entrapment modification method involving directional implantation of the amphiphilic modifier of stearyl-alcohol poly(ethylene oxide) ether (AEO) into the high-density polyethylene (HDPE) surface is proposed. This modification technique allows the AEO modifier to be able to spontaneously attain and subsequently penetrate into the swollen HDPE surface with its hydrophobic stearyl segment, while its hydrophilic poly(ethylene oxide) (PEO) segment spontaneously points to water. The AEO modifier with a HLB number below 8.7 was proved appropriate for the directional entrapment, Nevertheless, AEOs with larger HLB numbers were also effective modifiers in the presence of salt additives. In addition, a larger and hydrophobic micelle, induced respectively by the AEO concentration above 1.3 × 10-2 mol/L and the entrapping temperature above the cloud point of AEO, could lead to a sharp contact angle decline of the modified surface. Finally, a hydrophilic HDPE surface with the modifier coverage of 38.9% was reached by the directional entrapment method, which is far larger than that of 19.2% by the traditional entrapment method.

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

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

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.

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

Investigation on direct electrochemical and electrocatalytic behavior of hemoglobin on palladium-graphene modified electrode.

PubMed

Chen, Wei; Niu, Xueliang; Li, Xiaoyan; Li, Xiaobao; Li, Guangjiu; He, Bolin; Li, Qiutong; Sun, Wei

2017-11-01

Palladium-graphene (Pd-GR) nanocomposite was acted as modifier for construction of the modified electrode with direct electrochemistry of hemoglobin (Hb) realized. By using Nafion as the immobilization film, Hb was fixed tightly on Pd-GR nanocomposite modified carbon ionic liquid electrode. Electrochemical behaviors of Hb modified electrode were checked by cyclic voltammetry and a pair of redox peaks originated from direct electron transfer of Hb was appeared. The Hb modified electrode had excellent electrocatalytic activity to the reduction of trichloroacetic acid and sodium nitrite in the concentration range from 0.6 to 13.0mmol·L -1 and from 0.04 to 0.5 mmol·L -1 . Therefore Pd-GR nanocomposite was proven to be a good candidate for the fabrication of third-generation electrochemical biosensor. Copyright © 2017 Elsevier B.V. All rights reserved.

Modified Anterolateral Portals in Elbow Arthroscopy: A Cadaveric Study on Safety.

PubMed

Thon, Stephen; Gold, Peter; Rush, Lane; O'Brien, Michael J; Savoie, Felix H

2017-11-01

To evaluate the proximity to the radial nerve on cadaveric specimens of 2 modified anterolateral portals used for elbow arthroscopy. Ten fresh cadaveric elbow specimens were prepared. Four-millimeter Steinman pins were inserted into 3 anterolateral portal sites in relation to the lateral epicondyle: (1) the standard distal anterolateral portal, (2) a modified direct anterolateral portal, and (3) a modified proximal anterolateral portal. These were defined as follows: direct portals 2 cm directly anterior to the lateral epicondyle, and proximal portals 2 cm proximal and 2 cm directly anterior to the lateral epicondyle. Each elbow was then dissected to reveal the course of the radial nerve. Digital photographs were taken of each specimen, and the distance from the Steinman pin to the radial nerve was measured. The modified proximal anterolateral and direct anterolateral portals were found to be a statistically significant distance from the radial nerve compare to the distal portal site (P = .011 and P = .0011, respectively). No significant difference was found in the proximity of the radial nerve between the modified proximal and direct anterolateral portals (P = .25). Inadequate imaging was found at a single portal site for the proximal site; 9 specimens were used for analysis of this portal with 10 complete specimens for the other 2 sites. In cadaveric analysis, both the modified proximal and direct lateral portals provide adequate distance from the radial nerve and may be safe for clinical use. In this study, the distal anterolateral portal was in close proximity of the radial nerve and may result in iatrogenic injury in the clinical setting. This is a cadaveric analysis of 2 modified portal locations at the anterolateral elbow for use in elbow arthroscopy. Further clinical studies are needed prior to determining their absolute safety in comparison to previously identified portal sites. Copyright © 2017 Arthroscopy Association of North America. Published by Elsevier Inc. All rights reserved.

Direct state tomography using continuous variable measuring device

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

Zhu, Xuanmin, E-mail: zhuxuanmin@xidian.edu.cn; Wei, Qun

Compared with the conventional quantum state tomography (QST), the efficiency of the direct state tomography (DST) using weak value is very low. However, DST is easily manipulated in experiments. We modify the direct state tomography by using coupling-deformed observables. The modified direct state measurement is valid for arbitrarily large measurement strength. The optimal measurement strengths are obtained to attain the highest efficiency. The efficiency of DST is significantly improved in the modified strategy, and the reconstructed state has no inherent bias. The state reconstruction strategy investigated in this paper might be useful in actual experiments.

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.

Conformity of modified O-ring test and maximal pinch strength for cross tape application direction.

PubMed

Lee, Jung-Hoon; Choi, Hyun-Su

2018-06-01

Although cross tape has recently been used by clinicians for various musculoskeletal conditions, scientific studies on the direction of cross tape application are lacking. The present study aimed to investigate whether the direction of cross tape application affected the outcomes of the modified O-ring test and maximal pinch strength using a pinch gauge and the conformity between these 2 tests when cross tape was applied to the forearm muscles of individuals with no upper extremity pain and no restriction of joint range of motion.This study used a single-blinding crossover design. The subjects comprised 39 adults (16 men and 23 women). Cross tape was applied to the dominant hand so that the 4 rows were at an angle of 45° to the right or left of the direction of the flexor digitorum superficialis muscle fibers, and then the subjects underwent a modified O-ring test and a test of maximal pinch strength using a pinch gauge. Both tests were performed in both directions, and the order of the directions and tests was randomized. SPSS 18.0 was used for statistical analysis. Cohen's kappa coefficient was used to analyze the conformity of the results from the 2 tests. The statistical significance level was P < .05. A positive response in the modified O-ring test and maximal pinch strength were both affected by cross tape direction. The modified O-ring test and maximal pinch strength using pinch gauge results were in agreement (P < .00), and the kappa coefficient was significant at 1.00. The direction of cross tape application that produced a positive response in the modified O-ring test also produced greater maximal pinch strength. Thus, we propose that when applying cross tape to muscles, the direction of the 4 lines of the cross tape should be 45° relative to the direction of the muscle fibers, toward the side that produces a positive response in the modified O-ring test or produces the greatest maximal pinch strength using a pinch gauge.

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.

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.

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.

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.

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 \

Second derivative time integration methods for discontinuous Galerkin solutions of unsteady compressible flows

NASA Astrophysics Data System (ADS)

Nigro, A.; De Bartolo, C.; Crivellini, A.; Bassi, F.

2017-12-01

In this paper we investigate the possibility of using the high-order accurate A (α) -stable Second Derivative (SD) schemes proposed by Enright for the implicit time integration of the Discontinuous Galerkin (DG) space-discretized Navier-Stokes equations. These multistep schemes are A-stable up to fourth-order, but their use results in a system matrix difficult to compute. Furthermore, the evaluation of the nonlinear function is computationally very demanding. We propose here a Matrix-Free (MF) implementation of Enright schemes that allows to obtain a method without the costs of forming, storing and factorizing the system matrix, which is much less computationally expensive than its matrix-explicit counterpart, and which performs competitively with other implicit schemes, such as the Modified Extended Backward Differentiation Formulae (MEBDF). The algorithm makes use of the preconditioned GMRES algorithm for solving the linear system of equations. The preconditioner is based on the ILU(0) factorization of an approximated but computationally cheaper form of the system matrix, and it has been reused for several time steps to improve the efficiency of the MF Newton-Krylov solver. We additionally employ a polynomial extrapolation technique to compute an accurate initial guess to the implicit nonlinear system. The stability properties of SD schemes have been analyzed by solving a linear model problem. For the analysis on the Navier-Stokes equations, two-dimensional inviscid and viscous test cases, both with a known analytical solution, are solved to assess the accuracy properties of the proposed time integration method for nonlinear autonomous and non-autonomous systems, respectively. The performance of the SD algorithm is compared with the ones obtained by using an MF-MEBDF solver, in order to evaluate its effectiveness, identifying its limitations and suggesting possible further improvements.

Lecture Notes on Multigrid Methods

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

Vassilevski, P S

The Lecture Notes are primarily based on a sequence of lectures given by the author while been a Fulbright scholar at 'St. Kliment Ohridski' University of Sofia, Sofia, Bulgaria during the winter semester of 2009-2010 academic year. The notes are somewhat expanded version of the actual one semester class he taught there. The material covered is slightly modified and adapted version of similar topics covered in the author's monograph 'Multilevel Block-Factorization Preconditioners' published in 2008 by Springer. The author tried to keep the notes as self-contained as possible. That is why the lecture notes begin with some basic introductory matrix-vectormore » linear algebra, numerical PDEs (finite element) facts emphasizing the relations between functions in finite dimensional spaces and their coefficient vectors and respective norms. Then, some additional facts on the implementation of finite elements based on relation tables using the popular compressed sparse row (CSR) format are given. Also, typical condition number estimates of stiffness and mass matrices, the global matrix assembly from local element matrices are given as well. Finally, some basic introductory facts about stationary iterative methods, such as Gauss-Seidel and its symmetrized version are presented. The introductory material ends up with the smoothing property of the classical iterative methods and the main definition of two-grid iterative methods. From here on, the second part of the notes begins which deals with the various aspects of the principal TG and the numerous versions of the MG cycles. At the end, in part III, we briefly introduce algebraic versions of MG referred to as AMG, focusing on classes of AMG specialized for finite element matrices.« less

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.

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

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

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

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.

Application of N-doped graphene modified carbon ionic liquid electrode for direct electrochemistry of hemoglobin.

PubMed

Sun, Wei; Dong, Lifeng; Deng, Ying; Yu, Jianhua; Wang, Wencheng; Zhu, Qianqian

2014-06-01

Nitrogen-doped graphene (NG) was synthesized and used for the investigation on direct electrochemistry of hemoglobin (Hb) with a carbon ionic liquid electrode as the substrate electrode. Due to specific characteristics of NG such as excellent electrocatalytic property and large surface area, direct electron transfer of Hb was realized with enhanced electrochemical responses appearing. Electrochemical behaviors of Hb on the NG modified electrode were carefully investigated with the electrochemical parameters calculated. The Hb modified electrode exhibited excellent electrocatalytic reduction activity toward different substrates, such as trichloroacetic acid and H2O2, with wider dynamic range and lower detection limit. These findings show that NG can be used for the preparation of chemically modified electrodes with improved performance and has potential applications in electrochemical sensing. Copyright © 2014 Elsevier B.V. All rights reserved.

Low-temperature metal-oxide thin-film transistors formed by directly photopatternable and combustible solution synthesis.

PubMed

Rim, You Seung; Lim, Hyun Soo; Kim, Hyun Jae

2013-05-01

We investigated the formation of ultraviolet (UV)-assisted directly patternable solution-processed oxide semiconductor films and successfully fabricated thin-film transistors (TFTs) based on these films. An InGaZnO (IGZO) solution that was modified chemically with benzoylacetone (BzAc), whose chelate rings decomposed via a π-π* transition as result of UV irradiation, was used for the direct patterning. A TFT was fabricated using the directly patterned IGZO film, and it had better electrical characteristics than those of conventional photoresist (PR)-patterned TFTs. In addition, the nitric acid (HNO3) and acetylacetone (AcAc) modified In2O3 (NAc-In2O3) solution exhibited both strong UV absorption and high exothermic reaction. This method not only resulted in the formation of a low-energy path because of the combustion of the chemically modified metal-oxide solution but also allowed for photoreaction-induced direct patterning at low temperatures.

MEASUREMENT OF BI-DIRECTIONAL AMMONIA FLUXES OVER SOYBEAN USING MODIFIED BOWEN-RATIO TECHNIQUE

EPA Science Inventory

Measurements of bi-directional ammonia exchange over a fertilized soybean canopy are presented for an 8-week period during the summer of 2002. The modified Bowne-ratio approach was used to determine fluxes from vertical NH3 and temperature gradients in combination with eddy covar...

EFFECT OF SOIL MODIFYING FACTORS ON THE BIOAVAILABILITY AND TOXICITY OF METAL CONTAMINATED SOILS

EPA Science Inventory

Heavy metal and organic chemical contamination of soils is a worldwide problem posing a risk to humans and more directly, soil organisms. Metal toxicity is often not directly related to the total concentration of metals present due to a number of modifying factors that depend,...

Artificial specific binders directly recovered from chemically modified nucleic acid libraries.

PubMed

Kasahara, Yuuya; Kuwahara, Masayasu

2012-01-01

Specific binders comprised of nucleic acids, that is, RNA/DNA aptamers, are attractive functional biopolymers owing to their potential broad application in medicine, food hygiene, environmental analysis, and biological research. Despite the large number of reports on selection of natural DNA/RNA aptamers, there are not many examples of direct screening of chemically modified nucleic acid aptamers. This is because of (i) the inferior efficiency and accuracy of polymerase reactions involving transcription/reverse-transcription of modified nucleotides compared with those of natural nucleotides, (ii) technical difficulties and additional time and effort required when using modified nucleic acid libraries, and (iii) ambiguous efficacies of chemical modifications in binding properties until recently; in contrast, the effects of chemical modifications on biostability are well studied using various nucleotide analogs. Although reports on the direct screening of a modified nucleic acid library remain in the minority, chemical modifications would be essential when further functional expansion of nucleic acid aptamers, in particular for medical and biological uses, is considered. This paper focuses on enzymatic production of chemically modified nucleic acids and their application to random screenings. In addition, recent advances and possible future research are also described.

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2014-10-01

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen et al., 2011). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation to Maxwell's equations, which avoids radiative noise issues by ordering out the light wave. An implicit, orbit-averaged, time-space-centered finite difference scheme is employed in both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. We have developed a simple preconditioner that targets electrostatic waves and skin currents, and allows us to employ time steps O(√{mi /me } c /veT) larger than the explicit CFL. Several 1D numerical experiments demonstrate the accuracy, performance, and conservation properties of the algorithm. In particular, the scheme is shown to be second-order accurate, and CPU speedups of more than three orders of magnitude vs. an explicit Vlasov-Maxwell solver are demonstrated in the "cold" plasma regime (where kλD ≪ 1).

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.

Direct Connection between the RII Chain and the Nonautonomous Discrete Modified KdV Lattice

NASA Astrophysics Data System (ADS)

Maeda, Kazuki; Tsujimoto, Satoshi

2013-11-01

The spectral transformation technique for symmetric RII polynomials is developed. Use of this technique reveals that the nonautonomous discrete modified KdV (nd-mKdV) lattice is directly connected with the RII chain. Hankel determinant solutions to the semi-infinite nd-mKdV lattice are also presented.

Modified Direct-Type Septal Extension Grafts: Their Stability and Usefulness in Asian Rhinoplasty.

PubMed

Han, So-Eun; Han, Kihwan; Choi, Jaehoon; Yun, Tae Bin

2017-03-01

In Asian rhinoplasty, many autogenous cartilage grafts are required for correction of the nasal tip and columella, but the amount has limitations. A modified direct-type septal extension graft, in continuity with the entire caudal border of the septal cartilage with an edge-to-edge coaptation, can effectively and concomitantly correct the nasal tip and columella deformities using a limited amount of septal cartilage graft. The purpose of this study was to evaluate long-term cosmetic outcomes and stability from the modified direct extension grafts. Fifty-seven patients with a follow-up of more than 1 year were enrolled in the study. A total of 11 measurement items were evaluated from basal and right lateral views by photogrammetry using standardized clinical photographic techniques. The overall mean follow-up period was 20.4 months. When comparing the preoperative and postoperative values, the nasal tip projection, nasal bridge length, nasal tip angle, height of nose, and the columellar labial angle increased significantly; additionally, the soft nose width index, width between ac-ac index, nostril axis inclination, columellar length (Rt-Lt), and the alar length (Rt-Lt) decreased significantly. No resorption, buckling, or displacement of the graft was observed during the follow-up period. The modified direct extension graft demonstrated a marked aesthetic improvement in the nasal tip and columella, and it provided long-term stability. Therefore, the modified direct extension graft is useful for correction of the nasal tip and columella in Asian rhinoplasty.

24 CFR 1000.306 - How can the IHBG formula be modified?

Code of Federal Regulations, 2010 CFR

2010-04-01

... formula be modified? (a) The IHBG formula can be modified upon development of a set of measurable and verifiable data directly related to Indian and Alaska Native housing need. Any data set developed shall be...

24 CFR 1000.306 - How can the IHBG formula be modified?

Code of Federal Regulations, 2011 CFR

2011-04-01

... formula be modified? (a) The IHBG formula can be modified upon development of a set of measurable and verifiable data directly related to Indian and Alaska Native housing need. Any data set developed shall be...

24 CFR 1000.306 - How can the IHBG formula be modified?

Code of Federal Regulations, 2012 CFR

2012-04-01

... formula be modified? (a) The IHBG formula can be modified upon development of a set of measurable and verifiable data directly related to Indian and Alaska Native housing need. Any data set developed shall be...

24 CFR 1000.306 - How can the IHBG formula be modified?

Code of Federal Regulations, 2013 CFR

2013-04-01

... formula be modified? (a) The IHBG formula can be modified upon development of a set of measurable and verifiable data directly related to Indian and Alaska Native housing need. Any data set developed shall be...

24 CFR 1000.306 - How can the IHBG formula be modified?

Code of Federal Regulations, 2014 CFR

2014-04-01

... formula be modified? (a) The IHBG formula can be modified upon development of a set of measurable and verifiable data directly related to Indian and Alaska Native housing need. Any data set developed shall be...

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.

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.

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.

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.

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.

Partner-based adherence intervention for second-line antiretroviral therapy (ACTG A5234): a multinational randomised trial.

PubMed

Gross, Robert; Zheng, Lu; La Rosa, Alberto; Sun, Xin; Rosenkranz, Susan L; Cardoso, Sandra Wagner; Ssali, Francis; Camp, Rob; Godfrey, Catherine; Cohn, Susan E; Robbins, Gregory K; Chisada, Anthony; Wallis, Carole L; Reynolds, Nancy R; Lu, Darlene; Safren, Steven A; Hosey, Lara; Severe, Patrice; Collier, Ann C

2015-01-01

Adherence is key to the success of antiretroviral therapy. Enhanced partner support might benefit patients with previous treatment failure. We aimed to assess whether an enhanced partner-based support intervention with modified directly observed therapy would improve outcomes with second-line therapy in HIV-infected patients for whom first-line therapy had failed. We did a multicentre, international, randomised clinical trial at nine sites in Botswana, Brazil, Haiti, Peru, South Africa, Uganda, Zambia, and Zimbabwe. Participants aged 18 years or older for whom first-line therapy had failed, with HIV RNA concentrations greater than 1000 copies per mL and with a willing partner, were randomly assigned (1:1), via computer-generated randomisation, to receive partner-based modified directly observed therapy or standard of care. Randomisation was stratified by screening HIV RNA concentration (≤10 000 copies per mL vs >10 000 copies per mL). Participants and site investigators were not masked to group assignment. Primary outcome was confirmed virological failure (viral load >400 copies per mL) by week 48. Analysis was by intention to treat. This trial is registered with ClinicalTrials.gov, number NCT00608569. Between April 23, 2009, and Sept 29, 2011, we randomly assigned 259 participants to the modified directly observed therapy group (n=129) or the standard-of-care group (n=130). 34 (26%) participants in the modified directly observed therapy group achieved the primary endpoint of virological failure by week 48 compared with 23 (18%) participants in the standard-of-care group. The Kaplan-Meier estimated cumulative probability of virological failure by week 48 was 25·1% (95% CI 17·7-32·4) in the modified directly observed therapy group and 17·3% (10·8-23·7) in the standard-of-care group, for a weighted difference in standard of care versus modified directly observed therapy of -6·6% (95% CI -16·5% to 3·2%; p=0·19). 36 (14%) participants reported at least one grade 3 or higher adverse event or laboratory abnormality (n=21 in the modified directly observed therapy group and n=15 in the standard-of-care group). Partner-based training with modified directly observed therapy had no effect on virological suppression. The intervention does not therefore seem to be a promising strategy to increase adherence. Intensive follow-up with clinic staff might be a viable approach in this setting. AIDS Clinical Trials Group and the National Institute of Allergy and Infectious Diseases, US National Institutes of Health. Copyright © 2015 Elsevier Ltd. All rights reserved.

Novel use of residue from direct coal liquefaction process

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

Jianli Yang; Zhaixia Wang; Zhenyu Liu

2009-09-15

Direct coal liquefaction residue (DCLR) is, commonly, designed to be used as a feed stock for gasification or combustion. Use of DCLR as a value added product is very important for improving overall economy of direct coal liquefaction processes. This study shows that the DCLR may be used as a pavement asphalt modifier. The modification ability is similar to that of Trinidad Lake Asphalt (TLA), a superior commercial modifier. Asphalts modified by two DCLRs meet the specifications of ASTM D5710 and BSI BS-3690 designated for the TLA-modified asphalts. The required addition amount for the DCLRs tested is less than thatmore » for TLA due possibly to the high content of asphaltene in DCLRs. Different compatibility was observed for the asphalts with the same penetration grade but from the different origin. Different components in the DCLR play different roles in the modification. Positive synergetic effects among the fractions were observed, which may due to the formation of the stable colloid structure. Unlike polymer-type modifier, the structure of asphalt-type modifier has a similarity with petroleum asphalts which favors the formation of a stable dispersed polar fluid (DPF) colloid structure and improves the performance of pavement asphalt. 12 refs., 1 fig., 6 tabs.« less

Direct runoff assessment using modified SME method in catchments in the Upper Vistula River Basin

NASA Astrophysics Data System (ADS)

Wałęga, A.; Rutkowska, A.; Grzebinoga, M.

2017-04-01

Correct determination of direct runoff is crucial for proper and safe dimensioning of hydroengineering structures. It is commonly assessed using SCS-CN method developed in the United States. However, due to deficiencies of this method, many improvements and modifications have been proposed. In this paper, a modified Sahu-Mishra-Eldo (SME) method was introduced and tested for three catchments located in the upper Vistula basin. Modification of SME method involved a determination of maximum potential retention S based on CN parameter derived from SCS-CN method. The modified SME method yielded direct runoff values very similar to those observed in the investigated catchments. Moreover, it generated significantly smaller errors in the direct runoff estimation as compared with SCS-CN and SME methods in the analyzed catchments. This approach may be used for estimating the runoff in uncontrolled catchments.

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

Direct Detection of Drug-Resistant Hepatitis B Virus in Serum Using a Dendron-Modified Microarray

PubMed Central

Kim, Doo Hyun; Kang, Hong Seok; Hur, Seong-Suk; Sim, Seobo; Ahn, Sung Hyun; Park, Yong Kwang; Park, Eun-Sook; Lee, Ah Ram; Park, Soree; Kwon, So Young; Lee, Jeong-Hoon

2018-01-01

Background/Aims Direct sequencing is the gold standard for the detection of drug-resistance mutations in hepatitis B virus (HBV); however, this procedure is time-consuming, labor-intensive, and difficult to adapt to high-throughput screening. In this study, we aimed to develop a dendron-modified DNA microarray for the detection of genotypic resistance mutations and evaluate its efficiency. Methods The specificity, sensitivity, and selectivity of dendron-modified slides for the detection of representative drug-resistance mutations were evaluated and compared to those of conventional slides. The diagnostic accuracy was validated using sera obtained from 13 patients who developed viral breakthrough during lamivudine, adefovir, or entecavir therapy and compared with the accuracy of restriction fragment mass polymorphism and direct sequencing data. Results The dendron-modified slides significantly outperformed the conventional microarray slides and were able to detect HBV DNA at a very low level (1 copy/μL). Notably, HBV mutants could be detected in the chronic hepatitis B patient sera without virus purification. The validation of our data revealed that this technique is fully compatible with sequencing data of drug-resistant HBV. Conclusions We developed a novel diagnostic technique for the simultaneous detection of several drug-resistance mutations using a dendron-modified DNA microarray. This technique can be directly applied to sera from chronic hepatitis B patients who show resistance to several nucleos(t)ide analogues. PMID:29271185

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

Comparative Studies on Dyeability with Direct, Acid and Reactive Dyes after Chemical Modification of Jute with Mixed Amino Acids Obtained from Extract of Waste Soya Bean Seeds

NASA Astrophysics Data System (ADS)

Bhaumik, Nilendu Sekhar; Konar, Adwaita; Roy, Alok Nath; Samanta, Ashis Kumar

2017-12-01

Jute fabric was treated with mixed natural amino acids obtained from waste soya bean seed extract for chemical modification of jute for its cataionization and to enhance its dyeability with anionic dyes (like direct, reactive and acid dye) as well enabling soya modified jute for salt free dyeing with anionic reactive dyes maintaining its eco-friendliness. Colour interaction parameters including surface colour strength were assessed and compared for both bleached and soya-modified jute fabric for reactive dyeing and compared with direct and acid dye. Improvement in K/S value (surface colour strength) was observed for soya-modified jute even in absence of salt applied in dye bath for reactive dyes as well as for direct and acid dyes. In addition, reactive dye also shows good dyeability even in acid bath in salt free conditions. Colour fastness to wash was evaluated for bleached and soya-modified jute fabric after dyeing with direct, acid and reactive dyes are reported. Treatment of jute with soya-extracted mixed natural amino acids showed anchoring of some amino/aldemine groups on jute cellulosic polymer evidenced from Fourier Transform Infra-Red (FTIR) Spectroscopy. This amino or aldemine group incorporation in bleached jute causes its cationization and hence when dyed in acid bath for reactive dye (instead of conventional alkali bath) showed dye uptake for reactive dyes. Study of surface morphology by Scanning Electron Microscopy (SEM) of said soya-modified jute as compared to bleached jute was studied and reported.

Intercomparison of two BRDF models in the estimation of the directional emissivity in MIR channel from MSG1-SEVIRI data.

PubMed

Jiang, Geng-Ming; Li, Zhao-Liang

2008-11-10

This work intercompared two Bi-directional Reflectance Distribution Function (BRDF) models, the modified Minnaert's model and the RossThick-LiSparse-R model, in the estimation of the directional emissivity in Middle Infra-Red (MIR) channel from the data acquired by the Spinning Enhanced Visible and Infra-Red Imager (SEVIRI) onboard the first Meteosat Second Generation (MSG1). The bi-directional reflectances in SEVIRI channel 4 (3.9 microm) were estimated from the combined MIR and Thermal Infra-Red (TIR) data and then were used to estimate the directional emissivity in this channel with aid of the BRDF models. The results show that: (1) Both models can relatively well describe the non-Lambertian reflective behavior of land surfaces in SEVIRI channel 4; (2) The RossThick-LiSparse-R model is better than the modified Minnaert's model in modeling the bi-directional reflectances, and the directional emissivities modeled by the modified Minnaert's model are always lower than the ones obtained by the RossThick-LiSparse-R model with averaged emissivity differences of approximately 0.01 and approximately 0.04 over the vegetated and bare areas, respectively. The use of the RossThick-LiSparse-R model in the estimation of the directional emissivity in MIR channel is recommended.

Effect of intake swirl on the performance of single cylinder direct injection diesel engine

NASA Astrophysics Data System (ADS)

Sharma, Vinod Kumar; Mohan, Man; Mouli, Chandra

2017-11-01

In the present work, the effect of inlet manifold geometry and swirl intensity on the direct injection (DI) diesel engine performance was investigated experimentally. Modifications in inlet manifold geometry have been suggested to achieve optimized swirl for the better mixing of fuel with air. The intake swirl intensities of modified cylinder head were measured in swirl test rig at different valve lifts. Later, the overall performance of 435 CC DI diesel engine was measured using modified cylinder head. In addition, the performance of engine was compared for both modified and old cylinder head. For same operating conditions, the brake power and brake specific fuel consumption was improved by 6% and 7% respectively with modified cylinder head compared to old cylinder head. The maximum brake power of 9 HP was achieved for modified cylinder head. The results revealed that the intake swirl has great influence on engine performance.

Using the Multiplicative Schwarz Alternating Algorithm (MSAA) for Solving the Large Linear System of Equations Related to Global Gravity Field Recovery up to Degree and Order 120

NASA Astrophysics Data System (ADS)

Safari, A.; Sharifi, M. A.; Amjadiparvar, B.

2010-05-01

The GRACE mission has substantiated the low-low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high-low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair is the mostly used observable for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. In this paper, mathematical formulae for LOS acceleration difference observations have been derived and the corresponding linear system of equations has been set up for spherical harmonic up to degree and order 120. The total number of unknowns is 14641. Such a linear equation system can be solved with iterative solvers or direct solvers. However, the runtime of direct methods or that of iterative solvers without a suitable preconditioner increases tremendously. This is the reason why we need a more sophisticated method to solve the linear system of problems with a large number of unknowns. Multiplicative variant of the Schwarz alternating algorithm is a domain decomposition method, which allows it to split the normal matrix of the system into several smaller overlaped submatrices. In each iteration step the multiplicative variant of the Schwarz alternating algorithm solves linear systems with the matrices obtained from the splitting successively. It reduces both runtime and memory requirements drastically. In this paper we propose the Multiplicative Schwarz Alternating Algorithm (MSAA) for solving the large linear system of gravity field recovery. The proposed algorithm has been tested on the International Association of Geodesy (IAG)-simulated data of the GRACE mission. The achieved results indicate the validity and efficiency of the proposed algorithm in solving the linear system of equations from accuracy and runtime points of view. Keywords: Gravity field recovery, Multiplicative Schwarz Alternating Algorithm, Low-Low Satellite-to-Satellite Tracking

76 FR 39256 - Airworthiness Directives; Dassault Aviation Model FALCON 7X Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2011-07-06

... include modifying the applicable wiring and layout, a general visual inspection for absence of marks of... March 3, 2010. (2) Modify the applicable wiring and layout, in accordance with the Accomplishment... modifying the applicable wiring and layout, in accordance with Dassault Mandatory Service Bulletin 7X- 006...

Nested Conjugate Gradient Algorithm with Nested Preconditioning for Non-linear Image Restoration.

PubMed

Skariah, Deepak G; Arigovindan, Muthuvel

2017-06-19

We develop a novel optimization algorithm, which we call Nested Non-Linear Conjugate Gradient algorithm (NNCG), for image restoration based on quadratic data fitting and smooth non-quadratic regularization. The algorithm is constructed as a nesting of two conjugate gradient (CG) iterations. The outer iteration is constructed as a preconditioned non-linear CG algorithm; the preconditioning is performed by the inner CG iteration that is linear. The inner CG iteration, which performs preconditioning for outer CG iteration, itself is accelerated by an another FFT based non-iterative preconditioner. We prove that the method converges to a stationary point for both convex and non-convex regularization functionals. We demonstrate experimentally that proposed method outperforms the well-known majorization-minimization method used for convex regularization, and a non-convex inertial-proximal method for non-convex regularization functional.

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.

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.

A scalable parallel black oil simulator on distributed memory parallel computers

NASA Astrophysics Data System (ADS)

Wang, Kun; Liu, Hui; Chen, Zhangxin

2015-11-01

This paper presents our work on developing a parallel black oil simulator for distributed memory computers based on our in-house parallel platform. The parallel simulator is designed to overcome the performance issues of common simulators that are implemented for personal computers and workstations. The finite difference method is applied to discretize the black oil model. In addition, some advanced techniques are employed to strengthen the robustness and parallel scalability of the simulator, including an inexact Newton method, matrix decoupling methods, and algebraic multigrid methods. A new multi-stage preconditioner is proposed to accelerate the solution of linear systems from the Newton methods. Numerical experiments show that our simulator is scalable and efficient, and is capable of simulating extremely large-scale black oil problems with tens of millions of grid blocks using thousands of MPI processes on parallel computers.

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.

Multi-dimensional, fully implicit, exactly conserving electromagnetic particle-in-cell simulations in curvilinear geometry

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacon, Luis

2015-11-01

We discuss a new, conservative, fully implicit 2D3V Vlasov-Darwin particle-in-cell algorithm in curvilinear geometry for non-radiative, electromagnetic kinetic plasma simulations. Unlike standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. Here, we extend these algorithms to curvilinear geometry. The algorithm retains its exact conservation properties in curvilinear grids. The nonlinear iteration is effectively accelerated with a fluid preconditioner for weakly to modestly magnetized plasmas, which allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. In this presentation, we will introduce the main algorithmic components of the approach, and demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 1D (slow shock) and 2D (island coalescense).

Improved Convergence and Robustness of USM3D Solutions on Mixed Element Grids (Invited)

NASA Technical Reports Server (NTRS)

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

2015-01-01

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 Scheme (HANIS), has been developed and implemented. It 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 (RANS) equations and a nonlinear control of the solution update. Two variants of the new methodology 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 baseline solver technology.

Algorithm 937: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems.

PubMed

Choi, Sou-Cheng T; Saunders, Michael A

2014-02-01

We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite pre-conditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP.

Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations

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

Cai, Yunfeng, E-mail: yfcai@math.pku.edu.cn; Department of Computer Science, University of California, Davis 95616; Bai, Zhaojun, E-mail: bai@cs.ucdavis.edu

2013-12-15

The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for ab initio electronic structure calculations. We propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative diagonalization of such eigenvalue problems. In partition-of-unity finite-element (PUFE) pseudopotential density-functional calculations, employing a nonorthogonal basis, we show that the hybrid preconditioned block steepest descent method is a cost-effective eigensolver, outperforming current state-of-the-art global preconditioning schemes, and comparably efficient for the ill-conditioned generalized eigenvalue problems produced by PUFE as the locally optimal blockmore » preconditioned conjugate-gradient method for the well-conditioned standard eigenvalue problems produced by planewave methods.« less

A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods

NASA Astrophysics Data System (ADS)

Parand, K.; Nikarya, M.

2017-11-01

In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.

Determining the Transference Number of H[superscript +](aq) by a Modified Moving Boundary Method: A Directed Study for the Undergraduate Physical Chemistry Laboratory

ERIC Educational Resources Information Center

Dabke, Rajeev B.; Gebeyehu, Zewdu; Padelford, Jonathan

2012-01-01

A directed study for the undergraduate physical chemistry laboratory for determining the transference number of H[superscript +](aq) using a modified moving boundary method is presented. The laboratory study combines Faraday's laws of electrolysis with mole ratios and the perfect gas equation. The volume of hydrogen gas produced at the cathode is…

Electrocatalytic oxidation of 2-mercaptoethanol using modified glassy carbon electrode by MWCNT in combination with unsymmetrical manganese (II) Schiff base complexes

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

Mohebbi, Sajjad, E-mail: smohebbi@uok.ac.ir; Eslami, Saadat

2015-06-15

Highlights: • High electocatalytic efficiency and stability of modified hybrid electrode GC/MWCNTs/MnSaloph. • Direct reflection of catalytic activity of manganese complexes on electrocatalytic oxidation of 2-ME. • Decreasing overpotential and increasing catalytic peak current toward oxidation of 2-ME. • Deposition of range of novel substituted N{sub 2}O{sub 2} Saloph complexes of manganese(II) on GCE/MWCNT. • Enhancement of electrocatalytic oxidation activity upon electron donating substitutions on the Saloph. - Abstract: The performance of modified hybrid glassy carbon electrode with composite of carbon nanotubes and manganese complexes for the electrocatalytic oxidation of 2-mercaptoethanol is developed. GC electrode was modified using MWCNT andmore » new N{sub 2}O{sub 2} unsymmetrical tetradentate Schiff base complexes of manganese namely Manganese Saloph complexes 1-5, with general formula Mn[(5-x-4-y-Sal)(5-x′-4-y′-Sal) Ph], where x, x′ = H, Br, NO{sub 2} and y, y′ = H, MeO. Direct immobilization of CNT on the surface of GCE is performed by abrasive immobilization, and then modified by manganese(II) complexes via direct deposition method. These novel modified electrodes clearly demonstrate the necessity of modifying bare carbon electrodes to endow them with the desired behavior and were identified by HRTEM. Also complexes were characterized by elemental analyses, MS, UV–vis and IR spectroscopy. Modified hybrid GC/MWCNT/MnSaloph electrode exhibits strong and stable electrocatalytic activity towards the electrooxidation of 2-mercaptoethanol molecules in comparison with bare glassy carbon electrode with advantages of very low over potential and high catalytic current. Such ability promotes the thiol’s electron transfer reaction. Also, electron withdrawing substituent on the Saloph was enhanced electrocatalytic oxidation activity.« less

Healthcare Resource Uses and Out-of-Pocket Expenses Associated with Pulmonary TB Treatment in Thailand.

PubMed

Tanvejsilp, Pimwara; Loeb, Mark; Dushoff, Jonathan; Xie, Feng

2017-08-22

In Thailand, pharmaceutical care has been recently introduced to a tertiary hospital as an approach to improve adherence to tuberculosis (TB) treatment in addition to home visit and modified directly observed therapy (DOT). However, the economic impact of pharmaceutical care is not known. The aim of this study was to estimate healthcare resource uses and costs associated with pharmaceutical care compared with home visit and modified DOT in pulmonary TB patients in Thailand from a healthcare sector perspective inclusive of out-of-pocket expenditures. We conducted a retrospective study using data abstracted from the hospital billing database associated with pulmonary TB patients who began treatment between 2010 and 2013 in three hospitals in Thailand. We used generalized linear models to compare the costs by accounting for baseline characteristics. All costs were converted to international dollars (Intl$) RESULTS: The mean direct healthcare costs to the public payer were $519.96 (95%confidence interval [CI] 437.31-625.58) associated with pharmaceutical care, $1020.39 (95% CI 911.13-1154.11) for home visit, and $887.79 (95% CI 824.28-955.91) for modified DOT. The mean costs to patients were $175.45 (95% CI 130.26-230.48) for those receiving pharmaceutical care, $53.77 (95% CI 33.25-79.44) for home visit, and $49.33 (95% CI 34.03-69.30) for modified DOT. After adjustment for baseline characteristics, pharmaceutical care was associated with lower total direct costs compared with home visit (-$354.95; 95% CI -285.67 to -424.23) and modified DOT (-$264.61; 95% CI -198.76 to -330.46). After adjustment for baseline characteristics, pharmaceutical care was associated with lower direct costs compared with home visit and modified DOT.

[Genetically modified plants and food safety. State of the art and discussion in the European Union].

PubMed

Schauzu, M

2004-09-01

Placing genetically modified (GM) plants and derived products on the European Union's (EU) market has been regulated by a Community Directive since 1990. This directive was complemented by a regulation specific for genetically modified and other novel foods in 1997. Specific labelling requirements have been applicable for GM foods since 1998. The law requires a pre-market safety assessment for which criteria have been elaborated and continuously adapted in accordance with the state of the art by national and international bodies and organisations. Consequently, only genetically modified products that have been demonstrated to be as safe as their conventional counterparts can be commercialized. However, the poor acceptance of genetically modified foods has led to a de facto moratorium since 1998. It is based on the lack of a qualified majority of EU member states necessary for authorization to place genetically modified plants and derived foods on the market. New Community Regulations are intended to end this moratorium by providing a harmonized and transparent safety assessment, a centralised authorization procedure, extended labelling provisions and a traceability system for genetically modified organisms (GMO) and derived food and feed.

75 FR 22514 - Airworthiness Directives; The Boeing Company Model 747-200B Series Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2010-04-29

... airplanes that were modified by Boeing to the stretched upper deck (SUD) configuration require inspection... airplanes that were modified by Boeing to the stretched upper deck (SUD) configuration require inspecting... modified to the stretched upper deck (SUD) configuration by Boeing require inspection for cracking of the...

Numerical Methods for Forward and Inverse Problems in Discontinuous Media

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

Chartier, Timothy P.

The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise tomore » medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.« less

Application of three-dimensional reduced graphene oxide-gold composite modified electrode for direct electrochemistry and electrocatalysis of myoglobin.

PubMed

Shi, Fan; Xi, Jingwen; Hou, Fei; Han, Lin; Li, Guangjiu; Gong, Shixing; Chen, Chanxing; Sun, Wei

2016-01-01

In this paper a three-dimensional (3D) reduced graphene oxide (RGO) and gold (Au) composite was synthesized by electrodeposition and used for the electrode modification with carbon ionic liquid electrode (CILE) as the substrate electrode. Myoglobin (Mb) was further immobilized on the surface of 3D RGO-Au/CILE to obtain an electrochemical sensing platform. Direct electrochemistry of Mb on the modified electrode was investigated with a pair of well-defined redox waves appeared on cyclic voltammogram, indicating the realization of direct electron transfer of Mb with the modified electrode. The results can be ascribed to the presence of highly conductive 3D RGO-Au composite on the electrode surface that accelerate the electron transfer rate between the electroactive center of Mb and the electrode. The Mb modified electrode showed excellent electrocatalytic activity to the reduction of trichloroacetic acid in the concentration range from 0.2 to 36.0 mmol/L with the detection limit of 0.06 mmol/L (3σ). Copyright © 2015 Elsevier B.V. All rights reserved.

Identification of prostate cancer modifier pathways using parental strain expression mapping

PubMed Central

Xu, Qing; Majumder, Pradip K.; Ross, Kenneth; Shim, Yeonju; Golub, Todd R.; Loda, Massimo; Sellers, William R.

2007-01-01

Inherited genetic risk factors play an important role in cancer. However, other than the Mendelian fashion cancer susceptibility genes found in familial cancer syndromes, little is known about risk modifiers that control individual susceptibility. Here we developed a strategy, parental strain expression mapping, that utilizes the homogeneity of inbred mice and genome-wide mRNA expression analyses to directly identify candidate germ-line modifier genes and pathways underlying phenotypic differences among murine strains exposed to transgenic activation of AKT1. We identified multiple candidate modifier pathways and, specifically, the glycolysis pathway as a candidate negative modulator of AKT1-induced proliferation. In keeping with the findings in the murine models, in multiple human prostate expression data set, we found that enrichment of glycolysis pathways in normal tissues was associated with decreased rates of cancer recurrence after prostatectomy. Together, these data suggest that parental strain expression mapping can directly identify germ-line modifier pathways of relevance to human disease. PMID:17978178

The Effects of a Modified Direct Instruction Procedure on Time Telling for a Third Grade Student with Learning Disabilities with a Brief Comparison of Interesting and Boring Formats

ERIC Educational Resources Information Center

Wieber, Adrianne Essex; Evoy, Katie; McLaughlin, T. F.; Derby, K. Mark; Kellogg, Ethyl; Williams, Randy Lee; Peterson, Stephanie Marie; Rinaldi, Lisa

2017-01-01

We designed and implemented a modified eight-week Direct Instruction (DI) program intended to teach a third grade student with learning disabilities to tell time. The first objective was to determine whether or not the appearance (interesting or boring) of the worksheet affected performance. These data suggested the use of large-scale clocks and…

Enhanced electrocaloric analysis and energy-storage performance of lanthanum modified lead titanate ceramics for potential solid-state refrigeration applications.

PubMed

Zhang, Tian-Fu; Huang, Xian-Xiong; Tang, Xin-Gui; Jiang, Yan-Ping; Liu, Qiu-Xiang; Lu, Biao; Lu, Sheng-Guo

2018-01-10

The unique properties and great variety of relaxer ferroelectrics make them highly attractive in energy-storage and solid-state refrigeration technologies. In this work, lanthanum modified lead titanate ceramics are prepared and studied. The giant electrocaloric effect in lanthanum modified lead titanate ceramics is revealed for the first time. Large refrigeration efficiency (27.4) and high adiabatic temperature change (1.67 K) are achieved by indirect analysis. Direct measurements of electrocaloric effect show that reversible adiabatic temperature change is also about 1.67 K, which exceeds many electrocaloric effect values in current direct measured electrocaloric studies. Both theoretical calculated and direct measured electrocaloric effects are in good agreements in high temperatures. Temperature and electric field related energy storage properties are also analyzed, maximum energy-storage density and energy-storage efficiency are about 0.31 J/cm 3 and 91.2%, respectively.

75 FR 66700 - Airworthiness Directives; Cessna Aircraft Company (Cessna) Model 402C Airplanes Modified by...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-10-29

... Company (Cessna) Model 402C Airplanes Modified by Supplemental Type Certificate (STC) SA927NW and Model... Company (Cessna) Model 402C airplanes modified by Supplemental Type Certificate (STC) SA927NW and Model... products of the same type design. Proposed AD Requirements This proposed AD would require accomplishing the...

Comparison of five parasitological techniques for laboratory diagnosis of Balantidium coli cysts.

PubMed

Barbosa, Alynne da Silva; Bastos, Otilio Machado Pereira; Uchôa, Claudia Maria Antunes; Pissinatti, Alcides; Bastos, Augusto César Machado Pereira; Souza, Igo Vieira de; Dib, Laís Verdan; Azevedo, Eduarda Peixoto; Siqueira, Mayara Perlingeiro de; Cardozo, Matheus Lessa; Amendoeira, Maria Regina Reis

2016-01-01

Balantidium coli is a protozoon that can cause dysentery in humans, pigs and nonhuman primates, with zoonotic potential. In the literature, there is still little information on the effectiveness of different laboratory techniques for diagnosing this disease. This study compared and evaluated the performance of the Lutz, modified Ritchie, Faust, modified Sheather and direct examination techniques for detecting cysts of this protozoon. Between 2012 and 2014, 1905 fecal samples were collected from captive animals in the state of Rio de Janeiro. Of these, 790 were obtained from the rectum of pigs and 1115 from enclosures occupied by nonhuman primates. B. coli cysts were most evident through direct examination (22.4% of the samples) and the Lutz technique (21%). Fair agreement (Kappa = 0.41; p < 0.05) was observed only between direct examination and Lutz. The flotation techniques (Faust and modified Sheather) did not show good recovery of cysts. A statistically significant difference (p < 0.05) in the frequency of cysts between pigs and nonhuman primates could only be observed through direct examination and the Lutz technique. The most efficient method for diagnosing this parasitosis was seen to an association between direct examination and the spontaneous sedimentation technique.

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

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.

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

Characterizing the inverses of block tridiagonal, block Toeplitz matrices

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

Boffi, Nicholas M.; Hill, Judith C.; Reuter, Matthew G.

2014-12-04

We consider the inversion of block tridiagonal, block Toeplitz matrices and comment on the behaviour of these inverses as one moves away from the diagonal. Using matrix M bius transformations, we first present an O(1) representation (with respect to the number of block rows and block columns) for the inverse matrix and subsequently use this representation to characterize the inverse matrix. There are four symmetry-distinct cases where the blocks of the inverse matrix (i) decay to zero on both sides of the diagonal, (ii) oscillate on both sides, (iii) decay on one side and oscillate on the other and (iv)more » decay on one side and grow on the other. This characterization exposes the necessary conditions for the inverse matrix to be numerically banded and may also aid in the design of preconditioners and fast algorithms. Finally, we present numerical examples of these matrix types.« less

Design of a Variational Multiscale Method for Turbulent Compressible Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo Tibor; Murman, Scott M.

2013-01-01

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

A multi-dimensional nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell (PIC) algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; CoCoMans Team

2014-10-01

For decades, the Vlasov-Darwin model has been recognized to be attractive for PIC simulations (to avoid radiative noise issues) in non-radiative electromagnetic regimes. However, the Darwin model results in elliptic field equations that renders explicit time integration unconditionally unstable. Improving on linearly implicit schemes, fully implicit PIC algorithms for both electrostatic and electromagnetic regimes, with exact discrete energy and charge conservation properties, have been recently developed in 1D. This study builds on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the particle-field equations in multiple dimensions. The algorithm conserves energy, charge, and canonical-momentum exactly, even with grid packing. A simple fluid preconditioner allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. We demonstrate the accuracy and efficiency properties of the of the algorithm with various numerical experiments in 2D3V.

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.

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.

Unsymmetric ordering using a constrained Markowitz scheme

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

Amestoy, Patrick R.; Xiaoye S.; Pralet, Stephane

2005-01-18

We present a family of ordering algorithms that can be used as a preprocessing step prior to performing sparse LU factorization. The ordering algorithms simultaneously achieve the objectives of selecting numerically good pivots and preserving the sparsity. We describe the algorithmic properties and challenges in their implementation. By mixing the two objectives we show that we can reduce the amount of fill-in in the factors and reduce the number of numerical problems during factorization. On a set of large unsymmetric real problems, we obtained the median reductions of 12% in the factorization time, of 13% in the size of themore » LU factors, of 20% in the number of operations performed during the factorization phase, and of 11% in the memory needed by the multifrontal solver MA41-UNS. A byproduct of this ordering strategy is an incomplete LU-factored matrix that can be used as a preconditioner in an iterative solver.« less

Monolithic multigrid methods for two-dimensional resistive magnetohydrodynamics

DOE PAGES

Adler, James H.; Benson, Thomas R.; Cyr, Eric C.; ...

2016-01-06

Magnetohydrodynamic (MHD) representations are used to model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. The resulting linear systems that arise from discretization and linearization of the nonlinear problem are generally difficult to solve. In this paper, we investigate multigrid preconditioners for this system. We consider two well-known multigrid relaxation methods for incompressible fluid dynamics: Braess--Sarazin relaxation and Vanka relaxation. We first extend these to the context of steady-state one-fluid viscoresistive MHD. Then we compare the two relaxationmore » procedures within a multigrid-preconditioned GMRES method employed within Newton's method. To isolate the effects of the different relaxation methods, we use structured grids, inf-sup stable finite elements, and geometric interpolation. Furthermore, we present convergence and timing results for a two-dimensional, steady-state test problem.« less

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.

An interior-point method-based solver for simulation of aircraft parts riveting

NASA Astrophysics Data System (ADS)

Stefanova, Maria; Yakunin, Sergey; Petukhova, Margarita; Lupuleac, Sergey; Kokkolaras, Michael

2018-05-01

The particularities of the aircraft parts riveting process simulation necessitate the solution of a large amount of contact problems. A primal-dual interior-point method-based solver is proposed for solving such problems efficiently. The proposed method features a worst case polynomial complexity bound ? on the number of iterations, where n is the dimension of the problem and ε is a threshold related to desired accuracy. In practice, the convergence is often faster than this worst case bound, which makes the method applicable to large-scale problems. The computational challenge is solving the system of linear equations because the associated matrix is ill conditioned. To that end, the authors introduce a preconditioner and a strategy for determining effective initial guesses based on the physics of the problem. Numerical results are compared with ones obtained using the Goldfarb-Idnani algorithm. The results demonstrate the efficiency of the proposed method.

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).

Algorithm 937: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems

PubMed Central

Choi, Sou-Cheng T.; Saunders, Michael A.

2014-01-01

We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite pre-conditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP. PMID:25328255

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations

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

Chen, G., E-mail: gchen@lanl.gov; Chacón, L.; Leibs, C.A.

2014-02-01

A recent proof-of-principle study proposes an energy- and charge-conserving, nonlinearly implicit electrostatic particle-in-cell (PIC) algorithm in one dimension [9]. The algorithm in the reference employs an unpreconditioned Jacobian-free Newton–Krylov method, which ensures nonlinear convergence at every timestep (resolving the dynamical timescale of interest). Kinetic enslavement, which is one key component of the algorithm, not only enables fully implicit PIC as a practical approach, but also allows preconditioning the kinetic solver with a fluid approximation. This study proposes such a preconditioner, in which the linearized moment equations are closed with moments computed from particles. Effective acceleration of the linear GMRES solvemore » is demonstrated, on both uniform and non-uniform meshes. The algorithm performance is largely insensitive to the electron–ion mass ratio. Numerical experiments are performed on a 1D multi-scale ion acoustic wave test problem.« less

Higher Order Bases in a 2D Hybrid BEM/FEM Formulation

NASA Technical Reports Server (NTRS)

Fink, Patrick W.; Wilton, Donald R.

2002-01-01

The advantages of using higher order, interpolatory basis functions are examined in the analysis of transverse electric (TE) plane wave scattering by homogeneous, dielectric cylinders. A boundary-element/finite-element (BEM/FEM) hybrid formulation is employed in which the interior dielectric region is modeled with the vector Helmholtz equation, and a radiation boundary condition is supplied by an Electric Field Integral Equation (EFIE). An efficient method of handling the singular self-term arising in the EFIE is presented. The iterative solution of the partially dense system of equations is obtained using the Quasi-Minimal Residual (QMR) algorithm with an Incomplete LU Threshold (ILUT) preconditioner. Numerical results are shown for the case of an incident wave impinging upon a square dielectric cylinder. The convergence of the solution is shown versus the number of unknowns as a function of the completeness order of the basis functions.

The sensitivity of direct faecal examination, direct faecal flotation, modified centrifugal faecal flotation and centrifugal sedimentation/flotation in the diagnosis of canine spirocercosis.

PubMed

Christie, J; Schwan, E V; Bodenstein, L L; Sommerville, J E M; van der Merwe, L L

2011-06-01

Several faecal examination techniques have shown variable sensitivity in demonstrating Spirocerca lupi (S. lupi) eggs. The objective of this study was to determine which faecal examination technique, including a novel modified centrifugal flotation technique, was most sensitive to diagnose spirocercosis. Ten coproscopic examinations were performed on faeces collected from 33 dogs confirmed endoscopically to have spirocercosis. The tests included a direct faecal examination, a faecal sedimentation/flotation test, 4 direct faecal flotations and 4 modified faecal centrifugal flotations. These latter 2 flotation tests utilised 4 different faecal flotation solutions: NaNO3 (SG 1.22), MgSO4 (SG 1.29), ZnSO4 (SG 1.30) and sugar (SG 1.27). The sensitivity of the tests ranged between 42% and 67%, with the NaNO3 solution showing the highest sensitivity in both the direct and modified-centrifugal flotations. The modified NaNO3 centrifugal method ranked 1st with the highest mean egg count (45.24 +/- 83), and was superior (i.e. higher egg count) and significantly different (P < 0.05) compared with the routine saturated sugar, ZnSO4 and MgSO4 flotation methods. The routine NaNO3 flotation method was also superior and significantly different (P < 0.05) compared with the routine ZnSO4 and MgSO4 flotation methods. Fifteen per cent (n = 5) of dogs had neoplastic oesophageal nodules and a further 18% (n = 6) had both neoplastic and non-neoplastic nodules. S. lupi eggs were demonstrated in 40% of dogs with neoplastic nodules only and 72.9% of the dogs with non-neoplastic nodules. The mean egg count in the non-neoplastic group (61) was statistically greater (P = 0.02) than that of the neoplastic group (1). The results show that faecal examination using a NaNO3 solution is the most sensitive in the diagnosis of spirocercosis. The modified centrifugal flotation faecal method using this solution has the highest egg count. The study also found that dogs with neoplastic nodules shed significantly fewer eggs than dogs with non-neoplastic nodules.

Methanol electro-oxidation on platinum modified tungsten carbides in direct methanol fuel cells: a DFT study.

PubMed

Sheng, Tian; Lin, Xiao; Chen, Zhao-Yang; Hu, P; Sun, Shi-Gang; Chu, You-Qun; Ma, Chun-An; Lin, Wen-Feng

2015-10-14

In exploration of low-cost electrocatalysts for direct methanol fuel cells (DMFCs), Pt modified tungsten carbide (WC) materials are found to be great potential candidates for decreasing Pt usage whilst exhibiting satisfactory reactivity. In this work, the mechanisms, onset potentials and activity for electrooxidation of methanol were studied on a series of Pt-modified WC catalysts where the bare W-terminated WC(0001) substrate was employed. In the surface energy calculations of a series of Pt-modified WC models, we found that the feasible structures are mono- and bi-layer Pt-modified WCs. The tri-layer Pt-modified WC model is not thermodynamically stable where the top layer Pt atoms tend to accumulate and form particles or clusters rather than being dispersed as a layer. We further calculated the mechanisms of methanol oxidation on the feasible models via methanol dehydrogenation to CO involving C-H and O-H bonds dissociating subsequently, and further CO oxidation with the C-O bond association. The onset potentials for the oxidation reactions over the Pt-modified WC catalysts were determined thermodynamically by water dissociation to surface OH* species. The activities of these Pt-modified WC catalysts were estimated from the calculated kinetic data. It has been found that the bi-layer Pt-modified WC catalysts may provide a good reactivity and an onset oxidation potential comparable to pure Pt and serve as promising electrocatalysts for DMFCs with a significant decrease in Pt usage.

Layer-by-Layer Assembly of Glucose Oxidase on Carbon Nanotube Modified Electrodes.

PubMed

Suroviec, Alice H

2017-01-01

The use of enzymatically modified electrodes for the detection of glucose or other non-electrochemically active analytes is becoming increasingly common. Direct heterogeneous electron transfer to glucose oxidase has been shown to be kinetically difficult, which is why electron transfer mediators or indirect detection is usually used for monitoring glucose with electrochemical sensors. It has been found, however, that electrodes modified with single or multi-walled carbon nanotubes (CNTs) demonstrate fast heterogeneous electron transfer kinetics as compared to that found for traditional electrodes. Incorporating CNTs into the assembly of electrochemical glucose sensors, therefore, affords the possibility of facile electron transfer to glucose oxidase, and a more direct determination of glucose. This chapter describes the methods used to use CNTs in a layer-by-layer structure along with glucose oxidase to produce an enzymatically modified electrode with high turnover rates, increased stability and shelf-life.

Modified fundamental Airy wave.

PubMed

Seshadri, S R

2014-01-01

The propagation characteristics of the fundamental Airy wave are obtained; the intensity distribution is the same as that for a point electric dipole situated at the origin and oriented normal to the propagation direction. The propagation characteristics of the modified fundamental Airy wave are determined. These characteristics are the same as those for the fundamental Gaussian wave provided that an equivalent waist is identified for the Airy wave. In general, the waves are localized spatially with the peak in the propagation direction.

Directed evolution: an approach to engineer enzymes.

PubMed

Kaur, Jasjeet; Sharma, Rohit

2006-01-01

Directed evolution is being used increasingly in industrial and academic laboratories to modify and improve commercially important enzymes. Laboratory evolution is thought to make its biggest contribution in explorations of non-natural functions, by allowing us to distinguish the properties nurtured by evolution. In this review we report the significant advances achieved with respect to the methods of biocatalyst improvement and some critical properties and applications of the modified enzymes. The application of directed evolution has been elaborately demonstrated for protein solubility, stability and catalytic efficiency. Modification of certain enzymes for their application in enantioselective catalysis has also been elucidated. By providing a simple and reliable route to enzyme improvement, directed evolution has emerged as a key technology for enzyme engineering and biocatalysis.

Cytocompatibility of Direct Laser Interference-patterned Titanium Surfaces for Implants.

PubMed

Hartjen, Philip; Nada, Ola; Silva, Thiago Gundelwein; Precht, Clarissa; Henningsen, Anders; Holthaus, Marzellus GROßE; Gulow, Nikolai; Friedrich, Reinhard E; Hanken, Henning; Heiland, Max; Zwahr, Christoph; Smeets, Ralf; Jung, Ole

2017-01-01

In an effort to generate titanium surfaces for implants with improved osseointegration, we used direct laser interference patterning (DLIP) to modify the surface of pure titanium grade 4 of four different structures. We assessed in vitro cytoxicity and cell attachment, as well as the viability and proliferation of cells cultured directly on the surfaces. Attachment of the cells to the modified surfaces was comparably good compared to that of cells on grit-blasted and acid-etched reference titanium surfaces. In concordance with this, viability and proliferation of the cells directly cultured on the specimens were similar on all the titanium surfaces, regardless of the laser modification, indicating good cytocompatibility. Copyright© 2017, International Institute of Anticancer Research (Dr. George J. Delinasios), All rights reserved.

Predicting photosynthesis and transpiration responses to ozone: decoupling modeled photosynthesis and stomatal conductance

NASA Astrophysics Data System (ADS)

Lombardozzi, D.; Levis, S.; Bonan, G.; Sparks, J. P.

2012-08-01

Plants exchange greenhouse gases carbon dioxide and water with the atmosphere through the processes of photosynthesis and transpiration, making them essential in climate regulation. Carbon dioxide and water exchange are typically coupled through the control of stomatal conductance, and the parameterization in many models often predict conductance based on photosynthesis values. Some environmental conditions, like exposure to high ozone (O3) concentrations, alter photosynthesis independent of stomatal conductance, so models that couple these processes cannot accurately predict both. The goals of this study were to test direct and indirect photosynthesis and stomatal conductance modifications based on O3 damage to tulip poplar (Liriodendron tulipifera) in a coupled Farquhar/Ball-Berry model. The same modifications were then tested in the Community Land Model (CLM) to determine the impacts on gross primary productivity (GPP) and transpiration at a constant O3 concentration of 100 parts per billion (ppb). Modifying the Vcmax parameter and directly modifying stomatal conductance best predicts photosynthesis and stomatal conductance responses to chronic O3 over a range of environmental conditions. On a global scale, directly modifying conductance reduces the effect of O3 on both transpiration and GPP compared to indirectly modifying conductance, particularly in the tropics. The results of this study suggest that independently modifying stomatal conductance can improve the ability of models to predict hydrologic cycling, and therefore improve future climate predictions.

Modified electrical survey for effective leakage detection at concrete hydraulic facilities

NASA Astrophysics Data System (ADS)

Lee, Bomi; Oh, Seokhoon

2018-02-01

Three original electrode arrays for the effective leakage detection of concrete hydraulic facilities through electrical resistivity surveys are proposed: 'cross-potential', 'direct-potential' and modified tomography-like arrays. The main differences with respect to the commonly used arrays are that the current line-sources are separated from potential pole lines and floated upon the water. The potential pole lines are located directly next to the facility in order to obtain intuitive data and useful interpretations of the internal conditions of the hydraulic facility. This modified configuration of the array clearly displays the horizontal variation of the electrical field around the damaged zones of the concrete hydraulic facility, and any anomalous regions that might be found between potential poles placed across the facilities. In order to facilitate the interpretation of these modified electrical surveys, a new and creative way of presenting the measurements is also proposed and an inversion approach is provided for the modified tomography-like array. A numerical modeling and two field tests were performed to verify these new arrays and interpretation methods. The cross and direct potential array implied an ability to detect small variations of the potential field near the measurement poles. The proposed array showed the overall potential distribution across the hydraulic facility which may be used to assist in the search of trouble zones within the structure, in combination with the traditional electrical resistivity array.

Atmospheric pressure matrix-assisted laser desorption/ionization mass spectrometry of friction modifier additives analyzed directly from base oil solutions.

PubMed

Widder, Lukas; Brennerb, Josef; Huttera, Herbert

2014-01-01

To develop new products and to apply measures of quality control quick and simple accessibility of additive composition in automo- tive lubrication is important. The aim of this study was to investigate the possibility of analyzing organic friction modifier additives by means of atmospheric pressure matrix-assisted laser desorption/ionization mass spectrometry [AP-MALDI-MS] from lubricant solu- tions without the use of additional separation techniques. Analyses of selected friction modifier ethoxylated tallow amines and oleic acid amide were compared using two ionization methods, positive-ion electrospray ionization (ESI) and AP-MALDI, using a LTQ Orbitrap mass spectrometer. Pure additives were characterized from solvent solutions, as well as from synthetic and mineral base oil mixtures. Detected ions of pure additive samples consisted mainly of [M + H]+, but also alkaLi metal adducts [M + Na]+ and [M + K]+ could be seen. Characterizations of blends of both friction modifiers from the base oil mixtures were carried out as well and showed significant inten- sities for several additive peaks. Thus, this work shows a method to directly analyze friction modifier additives used in the automotive industry from an oil blend via the use of AP-MALDI without any further separation steps. The method presented will further simplify the acquisition of data on lubricant composition and additives. Furthermore, it allows the perspective of analyzing additive reaction products directly from formulated oil blends.

Peroxynitrite modified DNA presents better epitopes for anti-DNA autoantibodies in diabetes type 1 patients.

PubMed

Tripathi, Prashant; Moinuddin; Dixit, Kiran; Mir, Abdul Rouf; Habib, Safia; Alam, Khursheed; Ali, Asif

2014-07-01

Peroxynitrite (ONOO(-)), formed by the reaction between nitric oxide (NO) and superoxide (O2(-)), has been implicated in the etiology of numerous disease processes. Peroxynitrite interacts with DNA via direct oxidative reactions or via indirect radical-mediated mechanism. It can inflict both oxidative and nitrosative damages on DNA bases, generating abasic sites, resulting in the single strand breaks. Plasmid pUC 18 isolated from Escherichiacoli was modified with peroxynitrite, generated by quenched flow process. Modifications incurred in plasmid DNA were characterized by ultraviolet and fluorescence spectroscopy, circular dichroism, HPLC and melting temperature studies. Binding characteristics and specificity of antibodies from diabetes patients were analyzed by direct binding and inhibition ELISA. Peroxynitrite modification of pUC 18 plasmid resulted in the formation of strand breaks and base modification. The major compound formed when peroxynitrite reacted with DNA was 8-nitroguanine, a specific marker for peroxynitrite induced DNA damage in inflamed tissues. The concentration of 8-nitroguanine was found to be 3.8 μM. Sera from diabetes type 1 patients from different age groups were studied for their binding to native and peroxynitrite modified plasmid. Direct binding and competitive-inhibition ELISA results showed higher recognition of peroxynitrite modified plasmid, as compared to the native form, by auto-antibodies present in diabetes patients. The preferential recognition of modified plasmid by diabetes autoantibodies was further reiterated by gel shift assay. Experimentally induced anti-peroxynitrite-modified plasmid IgG was used as a probe to detect nitrosative lesions in the DNA isolated from diabetes patients. Copyright © 2014 Elsevier Inc. All rights reserved.

Kerogen extraction from subterranean oil shale resources

DOEpatents

Looney, Mark Dean; Lestz, Robert Steven; Hollis, Kirk; Taylor, Craig; Kinkead, Scott; Wigand, Marcus

2010-09-07

The present invention is directed to methods for extracting a kerogen-based product from subsurface (oil) shale formations, wherein such methods rely on fracturing and/or rubblizing portions of said formations so as to enhance their fluid permeability, and wherein such methods further rely on chemically modifying the shale-bound kerogen so as to render it mobile. The present invention is also directed at systems for implementing at least some of the foregoing methods. Additionally, the present invention is also directed to methods of fracturing and/or rubblizing subsurface shale formations and to methods of chemically modifying kerogen in situ so as to render it mobile.

Kerogen extraction from subterranean oil shale resources

DOEpatents

Looney, Mark Dean [Houston, TX; Lestz, Robert Steven [Missouri City, TX; Hollis, Kirk [Los Alamos, NM; Taylor, Craig [Los Alamos, NM; Kinkead, Scott [Los Alamos, NM; Wigand, Marcus [Los Alamos, NM

2009-03-10

The present invention is directed to methods for extracting a kerogen-based product from subsurface (oil) shale formations, wherein such methods rely on fracturing and/or rubblizing portions of said formations so as to enhance their fluid permeability, and wherein such methods further rely on chemically modifying the shale-bound kerogen so as to render it mobile. The present invention is also directed at systems for implementing at least some of the foregoing methods. Additionally, the present invention is also directed to methods of fracturing and/or rubblizing subsurface shale formations and to methods of chemically modifying kerogen in situ so as to render it mobile.

Cryopreservation of human blood for alkaline and Fpg-modified comet assay.

PubMed

Pu, Xinzhu; Wang, Zemin; Klaunig, James E

2016-01-01

The Comet assay is a reproducible and sensitive assay for the detection of DNA damage in eukaryotic cells and tissues. Incorporation of lesion specific, oxidative DNA damage repair enzymes (for example, Fpg, OGG1 and EndoIII) in the standard alkaline Comet assay procedure allows for the detection and measurement of oxidative DNA damage. The Comet assay using white blood cells (WBC) has proven useful in monitoring DNA damage from environmental agents in humans. However, it is often impractical to performance Comet assay immediately after blood sampling. Thus, storage of blood sample is required. In this study, we developed and tested a simple storage method for very small amount of whole blood for standard and Fpg-modified modified Comet assay. Whole blood was stored in RPMI 1640 media containing 10% FBS, 10% DMSO and 1 mM deferoxamine at a sample to media ratio of 1:50. Samples were stored at -20 °C and -80 °C for 1, 7, 14 and 28 days. Isolated lymphocytes from the same subjects were also stored under the same conditions for comparison. Direct DNA strand breakage and oxidative DNA damage in WBC and lymphocytes were analyzed using standard and Fpg-modified alkaline Comet assay and compared with freshly analyzed samples. No significant changes in either direct DNA strand breakage or oxidative DNA damage was seen in WBC and lymphocytes stored at -20 °C for 1 and 7 days compared to fresh samples. However, significant increases in both direct and oxidative DNA damage were seen in samples stored at -20 °C for 14 and 28 days. No changes in direct and oxidative DNA damage were observed in WBC and lymphocytes stored at -80 °C for up to 28 days. These results identified the proper storage conditions for storing whole blood or isolated lymphocytes to evaluate direct and oxidative DNA damage using standard and Fpg-modified alkaline Comet assay.

Cystic fibrosis gene modifier SLC26A9 modulates airway response to CFTR-directed therapeutics.

PubMed

Strug, Lisa J; Gonska, Tanja; He, Gengming; Keenan, Katherine; Ip, Wan; Boëlle, Pierre-Yves; Lin, Fan; Panjwani, Naim; Gong, Jiafen; Li, Weili; Soave, David; Xiao, Bowei; Tullis, Elizabeth; Rabin, Harvey; Parkins, Michael D; Price, April; Zuberbuhler, Peter C; Corvol, Harriet; Ratjen, Felix; Sun, Lei; Bear, Christine E; Rommens, Johanna M

2016-10-15

Cystic fibrosis is realizing the promise of personalized medicine. Recent advances in drug development that target the causal CFTR directly result in lung function improvement, but variability in response is demanding better prediction of outcomes to improve management decisions. The genetic modifier SLC26A9 contributes to disease severity in the CF pancreas and intestine at birth and here we assess its relationship with disease severity and therapeutic response in the airways. SLC26A9 association with lung disease was assessed in individuals from the Canadian and French CF Gene Modifier consortia with CFTR-gating mutations and in those homozygous for the common Phe508del mutation. Variability in response to a CFTR-directed therapy attributed to SLC26A9 genotype was assessed in Canadian patients with gating mutations. A primary airway model system determined if SLC26A9 shows modification of Phe508del CFTR function upon treatment with a CFTR corrector. In those with gating mutations that retain cell surface-localized CFTR we show that SLC26A9 modifies lung function while this is not the case in individuals homozygous for Phe508del where cell surface expression is lacking. Treatment response to ivacaftor, which aims to improve CFTR-channel opening probability in patients with gating mutations, shows substantial variability in response, 28% of which can be explained by rs7512462 in SLC26A9 (P = 0.0006). When homozygous Phe508del primary bronchial cells are treated to restore surface CFTR, SLC26A9 likewise modifies treatment response (P = 0.02). Our findings indicate that SLC26A9 airway modification requires CFTR at the cell surface, and that a common variant in SLC26A9 may predict response to CFTR-directed therapeutics.

77 FR 50954 - Airworthiness Directives; Cessna Aircraft Company

Federal Register 2010, 2011, 2012, 2013, 2014

2012-08-23

... Company (Cessna) Model 402C airplanes modified by Sierra Industries, Ltd. Supplemental Type Certificate... Airworthiness Directives; Cessna Aircraft Company AGENCY: Federal Aviation Administration (FAA), DOT. ACTION... earlier proposed airworthiness directive (AD) for all Cessna Aircraft Company (Cessna) Model 402C...

Construction and testing of crumb rubber modified hot mix asphalt pavement.

DOT National Transportation Integrated Search

1999-12-01

This research project was structured toward addressing that portion of ISTEA which directs the individual states to conduct studies on the recyclability of crumb rubber modified : (CRM) hot mix asphalt (HMA) and the technical performance of CRMHMA pa...

A Modified Direct-Reading Azimuth Protractor

ERIC Educational Resources Information Center

Larson, William C.; Pugliese, Joseph M.

1977-01-01

Describes the construction of a direct-reading azimuth protractor (DRAP) used for mapping fracture and joint-surface orientations in underground mines where magnetic disturbances affect typical geologic pocket transit. (SL)

Direct electrochemistry and electrocatalysis of glucose oxidase immobilized on reduced graphene oxide and silver nanoparticles nanocomposite modified electrode.

PubMed

Palanisamy, Selvakumar; Karuppiah, Chelladurai; Chen, Shen-Ming

2014-02-01

The direct electrochemistry of glucose oxidase (GOx) was successfully realized on electrochemically reduced graphene oxide and silver nanoparticles (RGO/Ag) nanocomposite modified electrode. The fabricated nanocomposite was characterized by field emission scanning electron microscope and energy dispersive spectroscopy. The GOx immobilized nanocomposite modified electrode showed a pair of well-defined redox peaks with a formal potential (E°) of -0.422 V, indicating that the bioactivity of GOx was retained. The heterogeneous electron transfer rate constant (Ks) of GOx at the nanocomposite was calculated to be 5.27 s(-1), revealing a fast direct electron transfer of GOx. The GOx immobilized RGO/Ag nanocomposite electrode exhibited a good electrocatalytic activity toward glucose over a linear concentration range from 0.5 to 12.5 mM with a detection limit of 0.16 mM. Besides, the fabricated biosensor showed an acceptable sensitivity and selectivity for glucose. Copyright © 2013 Elsevier B.V. All rights reserved.

Niche construction, sources of selection and trait coevolution.

PubMed

Laland, Kevin; Odling-Smee, John; Endler, John

2017-10-06

Organisms modify and choose components of their local environments. This 'niche construction' can alter ecological processes, modify natural selection and contribute to inheritance through ecological legacies. Here, we propose that niche construction initiates and modifies the selection directly affecting the constructor, and on other species, in an orderly, directed and sustained manner. By dependably generating specific environmental states, niche construction co-directs adaptive evolution by imposing a consistent statistical bias on selection. We illustrate how niche construction can generate this evolutionary bias by comparing it with artificial selection. We suggest that it occupies the middle ground between artificial and natural selection. We show how the perspective leads to testable predictions related to: (i) reduced variance in measures of responses to natural selection in the wild; (ii) multiple trait coevolution, including the evolution of sequences of traits and patterns of parallel evolution; and (iii) a positive association between niche construction and biodiversity. More generally, we submit that evolutionary biology would benefit from greater attention to the diverse properties of all sources of selection.

Low-temperature direct heterogeneous bonding of polyether ether ketone and platinum.

PubMed

Fu, Weixin; Shigetou, Akitsu; Shoji, Shuichi; Mizuno, Jun

2017-10-01

Direct heterogeneous bonding between polyether ether ketone (PEEK) and Pt was realized at the temperatures lower than 150°C. In order to create sufficient bondability to diverse materials, the surface was modified by vacuum ultraviolet (VUV) irradiation, which formed hydrate bridges. For comparison, direct bonding between surfaces atomically cleaned via Ar fast atom bombardment (FAB) was conducted in a vacuum. The VUV irradiation was found to be effective for creating an ultrathin hydrate bridge layer from the residual water molecules in the chamber. Tight bonds were formed through dehydration of the hydrate bridges by heating at 150°C, which also contributed to enhancing interdiffusion across the interface. The VUV-modified surfaces showed bondability as good as that of the FAB-treated surfaces, and the VUV-modified samples had shear strengths at the same level as those of FAB-treated surfaces. This technology will be of practical use in the packaging of lightweight, flexible biomedical devices. Copyright © 2017 Elsevier B.V. All rights reserved.

Aircraft noise synthesis system: Version 4 user instructions

NASA Technical Reports Server (NTRS)

Mccurdy, David A.; Sullivan, Brenda M.; Grandle, Robert E.

1987-01-01

A modified version of the Aircraft Noise Synthesis System with improved directivity and tonal content modeling has been developed. The synthesis system is used to provide test stimuli for studies of community annoyance to aircraft flyover noise. The computer-based system generates realistic, time-varying audio simulations of aircraft flyover noise at a specified observer location on the ground. The synthesis takes into account the time-varying aircraft position relative to the observer; specified reference spectra consisting of broadband, narrowband, and pure tone components; directivity patterns; Doppler shift; atmospheric effects; and ground effects. These parameters can be specified and controlled in such a way as to generate stimuli in which certain noise characteristics such as duration or tonal content are independently varied while the remaining characteristics such as broadband content are held constant. The modified version of the system provides improved modeling of noise directivity patterns and an increased number of pure tone components. User instructions for the modified version of the synthesis system are provided.

Sensitivity of the activated partial thromboplastin time, the dilute Russell's viper venom time, and the kaolin clotting time for the detection of the lupus anticoagulant: a direct comparison using plasma dilutions.

PubMed

Martin, B A; Branch, D W; Rodgers, G M

1996-01-01

Increasing dilutions of lupus anticoagulant (LA) plasmas from twelve patients were used to directly compare the sensitivity of four tests for LA. The tests evaluated were the modified Bell and Alton activated partial thromboplastin time (APTT), an APTT using a commercially prepared partial thromboplastin (Platelin LS APTT), a modified dilute Russell's viper venom time (DRVVT), and a modified kaolin clotting time (KCT). LAs were detected in all twelve plasmas by each of three tests and eleven of twelve plasmas in a fourth test when undiluted patient plasma was used. Repeating the tests after diluting the LA plasmas with normal platelet-free plasma (PFP) showed that the KCT was the most sensitive test for LA, detecting eleven of twelve LAs at a dilution of 10% patient plasma and ten of twelve LAs at a dilution of 5% patient plasma. The modified Bell and Alton APTT and the modified DRVVT had similar sensitivities at a patient plasma concentration of 10%, detecting seven of twelve and eight of twelve LAs, respectively. The Platelin LS APTT detected only four of twelve LAs at a patient plasma concentration of 10%. Our results indicate that the modified KCT is a sensitive method for the detection of LAs. The modified Bell and Alton APTT and the DRVVT were less sensitive.

Mechanical analysis of non-uniform bi-directional functionally graded intelligent micro-beams using modified couple stress theory

NASA Astrophysics Data System (ADS)

Bakhshi Khaniki, Hossein; Rajasekaran, Sundaramoorthy

2018-05-01

This study develops a comprehensive investigation on mechanical behavior of non-uniform bi-directional functionally graded beam sensors in the framework of modified couple stress theory. Material variation is modelled through both length and thickness directions using power-law, sigmoid and exponential functions. Moreover, beam is assumed with linear, exponential and parabolic cross-section variation through the length using power-law and sigmoid varying functions. Using these assumptions, a general model for microbeams is presented and formulated by employing Hamilton’s principle. Governing equations are solved using a mixed finite element method with Lagrangian interpolation technique, Gaussian quadrature method and Wilson’s Lagrangian multiplier method. It is shown that by using bi-directional functionally graded materials in nonuniform microbeams, mechanical behavior of such structures could be affected noticeably and scale parameter has a significant effect in changing the rigidity of nonuniform bi-directional functionally graded beams.

PiggyBac-mediated Cancer Immunotherapy Using EBV-specific Cytotoxic T-cells Expressing HER2-specific Chimeric Antigen Receptor

PubMed Central

Nakazawa, Yozo; Huye, Leslie E; Salsman, Vita S; Leen, Ann M; Ahmed, Nabil; Rollins, Lisa; Dotti, Gianpietro; Gottschalk, Stephen M; Wilson, Matthew H; Rooney, Cliona M

2011-01-01

Epstein-Barr virus (EBV)-specific cytotoxic T lymphocytes (CTLs) can be modified to function as heterologous tumor directed effector cells that survive longer in vivo than tumor directed T cells without virus specificity, due to chronic stimulation by viral antigens expressed during persistent infection in seropositive individuals. We evaluated the nonviral piggyBac (PB) transposon system as a platform for modifying EBV-CTLs to express a functional human epidermal growth factor receptor 2-specific chimeric antigen receptor (HER2-CAR) thereby directing virus-specific, gene modified CTLs towards HER2-positive cancer cells. Peripheral blood mononuclear cells (PBMCs) were nucleofected with transposons encoding a HER2-CAR and a truncated CD19 molecule for selection followed by specific activation and expansion of EBV-CTLs. HER2-CAR was expressed in ~40% of T cells after CD19 selection with retention of immunophenotype, polyclonality, and function. HER2-CAR-modified EBV-CTLs (HER2-CTLs) killed HER2-positive brain tumor cell lines in vitro, exhibited transient and reversible increases in HER2-CAR expression following antigen-specific stimulation, and stably expressed HER2-CAR beyond 120 days. Adoptive transfer of PB-modified HER2-CTLs resulted in tumor regression in a murine xenograft model. Our results demonstrate that PB can be used to redirect virus-specific CTLs to tumor targets, which should prolong tumor-specific T cell survival in vivo producing more efficacious immunotherapy. PMID:21772253

PiggyBac-mediated cancer immunotherapy using EBV-specific cytotoxic T-cells expressing HER2-specific chimeric antigen receptor.

PubMed

Nakazawa, Yozo; Huye, Leslie E; Salsman, Vita S; Leen, Ann M; Ahmed, Nabil; Rollins, Lisa; Dotti, Gianpietro; Gottschalk, Stephen M; Wilson, Matthew H; Rooney, Cliona M

2011-12-01

Epstein-Barr virus (EBV)-specific cytotoxic T lymphocytes (CTLs) can be modified to function as heterologous tumor directed effector cells that survive longer in vivo than tumor directed T cells without virus specificity, due to chronic stimulation by viral antigens expressed during persistent infection in seropositive individuals. We evaluated the nonviral piggyBac (PB) transposon system as a platform for modifying EBV-CTLs to express a functional human epidermal growth factor receptor 2-specific chimeric antigen receptor (HER2-CAR) thereby directing virus-specific, gene modified CTLs towards HER2-positive cancer cells. Peripheral blood mononuclear cells (PBMCs) were nucleofected with transposons encoding a HER2-CAR and a truncated CD19 molecule for selection followed by specific activation and expansion of EBV-CTLs. HER2-CAR was expressed in ~40% of T cells after CD19 selection with retention of immunophenotype, polyclonality, and function. HER2-CAR-modified EBV-CTLs (HER2-CTLs) killed HER2-positive brain tumor cell lines in vitro, exhibited transient and reversible increases in HER2-CAR expression following antigen-specific stimulation, and stably expressed HER2-CAR beyond 120 days. Adoptive transfer of PB-modified HER2-CTLs resulted in tumor regression in a murine xenograft model. Our results demonstrate that PB can be used to redirect virus-specific CTLs to tumor targets, which should prolong tumor-specific T cell survival in vivo producing more efficacious immunotherapy.

Domain wall fermion QCD with the exact one flavor algorithm

DOE PAGES

Jung, C.; Kelly, C.; Mawhinney, R. D.; ...

2018-03-13

Lattice QCD calculations including the effects of one or more nondegenerate sea quark flavors are conventionally performed using the rational hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant ofmore » $${\\mathcal{D}}^{\\dagger{}}\\mathcal{D}$$, where $$\\mathcal{D}$$ is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of $${\\mathcal{D}}^{\\dagger{}}\\mathcal{D}$$—in particular, no square root is necessary—enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors—such as the strange or charm—computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the $$\\mathrm{{\\Delta}}I=1/2$$ $$K{\\rightarrow}{\\pi}{\\pi}$$ matrix elements on lattice ensembles with $G$-parity boundary conditions, since $G$-parity is associated with a doubling of the number of quark flavors described by $$\\mathcal{D}$$ , and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD Collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to reuse the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our $2+1$ flavor $G$-parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2.« less

Domain wall fermion QCD with the exact one flavor algorithm

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

Jung, C.; Kelly, C.; Mawhinney, R. D.

Lattice QCD calculations including the effects of one or more nondegenerate sea quark flavors are conventionally performed using the rational hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant ofmore » $${\\mathcal{D}}^{\\dagger{}}\\mathcal{D}$$, where $$\\mathcal{D}$$ is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of $${\\mathcal{D}}^{\\dagger{}}\\mathcal{D}$$—in particular, no square root is necessary—enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors—such as the strange or charm—computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the $$\\mathrm{{\\Delta}}I=1/2$$ $$K{\\rightarrow}{\\pi}{\\pi}$$ matrix elements on lattice ensembles with $G$-parity boundary conditions, since $G$-parity is associated with a doubling of the number of quark flavors described by $$\\mathcal{D}$$ , and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD Collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to reuse the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our $2+1$ flavor $G$-parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2.« less

Differential geometry based solvation model I: Eulerian formulation

NASA Astrophysics Data System (ADS)

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-11-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

Differential geometry based solvation model I: Eulerian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature. PMID:20938489

Three-dimensional forward modeling and inversion of marine CSEM data in anisotropic conductivity structures

NASA Astrophysics Data System (ADS)

Han, B.; Li, Y.

2016-12-01

We present a three-dimensional (3D) forward and inverse modeling code for marine controlled-source electromagnetic (CSEM) surveys in anisotropic media. The forward solution is based on a primary/secondary field approach, in which secondary fields are solved using a staggered finite-volume (FV) method and primary fields are solved for 1D isotropic background models analytically. It is shown that it is rather straightforward to extend the isotopic 3D FV algorithm to a triaxial anisotropic one, while additional coefficients are required to account for full tensor conductivity. To solve the linear system resulting from FV discretization of Maxwell' s equations, both iterative Krylov solvers (e.g. BiCGSTAB) and direct solvers (e.g. MUMPS) have been implemented, makes the code flexible for different computing platforms and different problems. For iterative soloutions, the linear system in terms of electromagnetic potentials (A-Phi) is used to precondition the original linear system, transforming the discretized Curl-Curl equations to discretized Laplace-like equations, thus much more favorable numerical properties can be obtained. Numerical experiments suggest that this A-Phi preconditioner can dramatically improve the convergence rate of an iterative solver and high accuracy can be achieved without divergence correction even for low frequencies. To efficiently calculate the sensitivities, i.e. the derivatives of CSEM data with respect to tensor conductivity, the adjoint method is employed. For inverse modeling, triaxial anisotropy is taken into account. Since the number of model parameters to be resolved of triaxial anisotropic medias is twice or thrice that of isotropic medias, the data-space version of the Gauss-Newton (GN) minimization method is preferred due to its lower computational cost compared with the traditional model-space GN method. We demonstrate the effectiveness of the code with synthetic examples.

Domain wall fermion QCD with the exact one flavor algorithm

NASA Astrophysics Data System (ADS)

Jung, C.; Kelly, C.; Mawhinney, R. D.; Murphy, D. J.

2018-03-01

Lattice QCD calculations including the effects of one or more nondegenerate sea quark flavors are conventionally performed using the rational hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant of D†D , where D is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of D†D —in particular, no square root is necessary—enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors—such as the strange or charm—computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the Δ I =1 /2 K →π π matrix elements on lattice ensembles with G -parity boundary conditions, since G -parity is associated with a doubling of the number of quark flavors described by D , and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD Collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to reuse the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our 2 +1 flavor G -parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2.

Technical note: Avoiding the direct inversion of the numerator relationship matrix for genotyped animals in single-step genomic best linear unbiased prediction solved with the preconditioned conjugate gradient.

PubMed

Masuda, Y; Misztal, I; Legarra, A; Tsuruta, S; Lourenco, D A L; Fragomeni, B O; Aguilar, I

2017-01-01

This paper evaluates an efficient implementation to multiply the inverse of a numerator relationship matrix for genotyped animals () by a vector (). The computation is required for solving mixed model equations in single-step genomic BLUP (ssGBLUP) with the preconditioned conjugate gradient (PCG). The inverse can be decomposed into sparse matrices that are blocks of the sparse inverse of a numerator relationship matrix () including genotyped animals and their ancestors. The elements of were rapidly calculated with the Henderson's rule and stored as sparse matrices in memory. Implementation of was by a series of sparse matrix-vector multiplications. Diagonal elements of , which were required as preconditioners in PCG, were approximated with a Monte Carlo method using 1,000 samples. The efficient implementation of was compared with explicit inversion of with 3 data sets including about 15,000, 81,000, and 570,000 genotyped animals selected from populations with 213,000, 8.2 million, and 10.7 million pedigree animals, respectively. The explicit inversion required 1.8 GB, 49 GB, and 2,415 GB (estimated) of memory, respectively, and 42 s, 56 min, and 13.5 d (estimated), respectively, for the computations. The efficient implementation required <1 MB, 2.9 GB, and 2.3 GB of memory, respectively, and <1 sec, 3 min, and 5 min, respectively, for setting up. Only <1 sec was required for the multiplication in each PCG iteration for any data sets. When the equations in ssGBLUP are solved with the PCG algorithm, is no longer a limiting factor in the computations.

Safe Heavens: Military Strategy and Space Sanctuary Thought

DTIC Science & Technology

1997-06-01

November 1957, his service proposed two ASAT solutions: a modified Nike Zeus antiballistic missile and a “homing satellite” carrying a destructive charge.18...May 1962, Secretary of Defense (SECDEF) McNamara ordered the Army to modify the Nike Zeus antiballistic missile for a future ASAT role. The modified...would never become operational. President Carter’s 1978 Presidential Directive on Space Policy stated: The United States finds itself under increasing

77 FR 69742 - Airworthiness Directives; Cessna Aircraft Company Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2012-11-21

... Company (Cessna) Model 402C airplanes modified by Supplemental Type Certificate (STC) SA927NW and Model... Airworthiness Directives; Cessna Aircraft Company Airplanes AGENCY: Federal Aviation Administration (FAA), DOT... new airworthiness directive (AD): 2012-23-01 Cessna Aircraft Company: Amendment 39-17257; Docket No...

Direct analysis of in-gel proteins by carbon nanotubes-modified paper spray ambient mass spectrometry.

PubMed

Han, Feifei; Yang, Yuhan; Ouyang, Jin; Na, Na

2015-02-07

The in situ and direct extraction, desorption and ionization of in-gel intact proteins after electrophoresis has been achieved by carbon nanotubes (CNTs)-modified paper spray mass spectrometry at ambient conditions. Characteristics of CNTs (including larger surface area, smaller pore diameter and enhanced conductivity) were endowed to the porous filter paper substrate by uniformly dispersing the CNTs on the filter paper. Upon applying electric potential to the CNTs-modified paper, the in-gel proteins were extracted from the gel and subsequently migrated to the tip of the filter paper by electrophoresis-like behavior for paper spray ionization, which was monitored by extracted ion chronograms. The characterizations of modified filter papers and CNTs nanoparticles further confirmed the role of CNTs in in-gel protein extraction, protein migration as well as spray ionization at the paper tip. Under optimized conditions, a mixture of cytochrome c, lysozyme and myoglobin was successfully separated by native electrophoresis and subsequently analysed by the present method, showing a limit of detection of 10 ng per gel band. The present strategy offers a new pathway for the direct detection of in-gel intact proteins at ambient conditions without any pre-treatment (e.g. digestion, chemical extraction and desalting), which exhibits potential applications in top-down proteomics.

DETERMINING BERYLLIUM IN DRINKING WATER BY GRAPHITE FURNACE ATOMIC ABSORPTION SPECTROSCOPY

EPA Science Inventory

A direct graphite furnace atomic absorption spectroscopy method for the analysis of beryllium in drinking water has been derived from a method for determining beryllium in urine. Ammonium phosphomolybdate and ascorbic acid were employed as matrix modifiers. The matrix modifiers s...

High performance membrane-electrode assembly based on a surface-modified membrane

NASA Astrophysics Data System (ADS)

Han, Sangil; Lee, Jang Woo; Kwak, Chan; Chai, Geun Seok; Son, In Hyuk; Jang, Moon Yup; An, Sung Guk; Cho, Sung Yong; Kim, Jun Young; Kim, Hyung Wook; Serov, Alexey Alexandrovych; Yoo, Youngtai; Nam, Kie Hyun

A surface-modified membrane is prepared using a sputtering technique that deposits gold directly on a Nafion ® 115 membrane surface that is roughened with silicon carbide paper. The surface-modified membranes are characterized by means of a scanning electron microscope (SEM), differential scanning calorimetry (DSC), and water contact-angle analysis. A single direct methanol fuel cell (DMFC) with a surface-modified membrane exhibits enhanced performance (160 mW cm -2), while a bare Nafion ® 115 cell yields 113 mW cm -2 at 0.4 V and an operating temperature of 70 °C. From FE-SEM images and CO ad stripping voltammograms, it is also found that the gold layer is composed of clusters of porous nodule-like particles, which indicates that an anode with nodule-like gold leads to the preferential oxidation of carbon monoxide. These results suggest that the topology of gold in the interfacial area and its electrocatalytic nature may be the critical factors that affect DMFC performance.

Submerged combustion melting processes for producing glass and similar materials, and systems for carrying out such processes

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

Charbonneau, Mark William

Processes of controlling submerged combustion melters, and systems for carrying out the methods. One process includes feeding vitrifiable material into a melter vessel, the melter vessel including a fluid-cooled refractory panel in its floor, ceiling, and/or sidewall, and heating the vitrifiable material with a burner directing combustion products into the melting zone under a level of the molten material in the zone. Burners impart turbulence to the molten material in the melting zone. The fluid-cooled refractory panel is cooled, forming a modified panel having a frozen or highly viscous material layer on a surface of the panel facing the moltenmore » material, and a sensor senses temperature of the modified panel using a protected thermocouple positioned in the modified panel shielded from direct contact with turbulent molten material. Processes include controlling the melter using the temperature of the modified panel. Other processes and systems are presented.« less

Involvement of a eukaryotic-like ubiquitin-related modifier in the proteasome pathway of the archaeon Sulfolobus acidocaldarius

NASA Astrophysics Data System (ADS)

Anjum, Rana S.; Bray, Sian M.; Blackwood, John K.; Kilkenny, Mairi L.; Coelho, Matthew A.; Foster, Benjamin M.; Li, Shurong; Howard, Julie A.; Pellegrini, Luca; Albers, Sonja-Verena; Deery, Michael J.; Robinson, Nicholas P.

2015-09-01

In eukaryotes, the covalent attachment of ubiquitin chains directs substrates to the proteasome for degradation. Recently, ubiquitin-like modifications have also been described in the archaeal domain of life. It has subsequently been hypothesized that ubiquitin-like proteasomal degradation might also operate in these microbes, since all archaeal species utilize homologues of the eukaryotic proteasome. Here we perform a structural and biochemical analysis of a ubiquitin-like modification pathway in the archaeon Sulfolobus acidocaldarius. We reveal that this modifier is homologous to the eukaryotic ubiquitin-related modifier Urm1, considered to be a close evolutionary relative of the progenitor of all ubiquitin-like proteins. Furthermore we demonstrate that urmylated substrates are recognized and processed by the archaeal proteasome, by virtue of a direct interaction with the modifier. Thus, the regulation of protein stability by Urm1 and the proteasome in archaea is likely representative of an ancient pathway from which eukaryotic ubiquitin-mediated proteolysis has evolved.

Lateral-access Class II restoration using resin-modified glass-ionomer or silver-cermet cement.

PubMed

Croll, T P

1995-02-01

Direct-access preparation of a carious proximal surface is perhaps the most conservative approach to restoration. Physical properties and handling characteristics of silver amalgam and of resin composite and lack of fluoride ion release make these materials unsuitable for direct buccal- or lingual-access proximal restoration. Insufficient strengths and radiolucency of self-hardening glass-ionomer cements preclude their use for Class II restorations. However, glass-ionomer silver-cermet cement and some resin-modified glass-ionomer materials are proving useful for non-stress-bearing Class II restorations and may have applications in preventive dentistry. This article describes lateral-access Class II restoration with modified glass-ionomer cements. Emphasis is placed on careful handling of materials, maintenance of an ideal operative field, and conservation of tooth structure.

Analysis of fuel using the Direct LSC method determination of bio-originated fuel in the presence of quenching

DOE PAGES

Doll, Charles G.; Wright, Cherylyn W.; Morley, Shannon M.; ...

2017-02-01

In this paper, a modified version of the Direct LSC method to correct for quenching effect was investigated for the determination of bio-originated fuel content in fuel samples produced from multiple biological starting materials. The modified method was found to be accurate in determining the percent bio-originated fuel to within 5% of the actual value for samples with quenching effects ≤43%. Finally, analysis of highly quenched samples was possible when diluted with the exception of one sample with a 100% quenching effect.

Analysis of fuel using the Direct LSC method determination of bio-originated fuel in the presence of quenching

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

Doll, Charles G.; Wright, Cherylyn W.; Morley, Shannon M.

A modified version of the Direct LSC method to correct for quenching effect was investigated for the determination of bio-originated fuel content in fuel samples produced from multiple biological starting materials. The modified method was found to be accurate in determining the percent bio-originated fuel to within 5% of the actual value for samples with quenching effects ≤43%. Analysis of highly quenched samples was possible when diluted with the exception of one sample with a 100% quenching effect.

Measurements of farfield sound generation from a flow-excited cavity

NASA Technical Reports Server (NTRS)

Block, P. J. W.; Heller, H.

1975-01-01

Results of 1/3-octave-band spectral measurements of internal pressures and the external acoustic field of a tangentially blown rectangular cavity are compared. Proposed mechanisms for sound generation are reviewed, and spectra and directivity plots of cavity noise are presented. Directivity plots show a slightly modified monopole pattern. Frequencies of cavity response are calculated using existing predictions and are compared with those obtained experimentally. The effect of modifying the upstream boundary layer on the noise was investigated, and its effectiveness was found to be a function of cavity geometry and flow velocity.

Analysis of fuel using the Direct LSC method determination of bio-originated fuel in the presence of quenching

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

Doll, Charles G.; Wright, Cherylyn W.; Morley, Shannon M.

In this paper, a modified version of the Direct LSC method to correct for quenching effect was investigated for the determination of bio-originated fuel content in fuel samples produced from multiple biological starting materials. The modified method was found to be accurate in determining the percent bio-originated fuel to within 5% of the actual value for samples with quenching effects ≤43%. Finally, analysis of highly quenched samples was possible when diluted with the exception of one sample with a 100% quenching effect.

75 FR 76630 - Direct Investment Surveys: BE-577, Quarterly Survey of U.S. Direct Investment Abroad-Direct...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-12-09

... between U.S.-owned foreign business enterprises and their U.S. parents. Through this rule, BEA will modify... other investment, for which statistics are collected by the Treasury Department through the Treasury... statistics for income and direct investment position--will drop out of the sample and will be estimated based...

Absolute quantitation of NAPQI-modified rat serum albumin by LC-MS/MS: monitoring acetaminophen covalent binding in vivo.

PubMed

LeBlanc, André; Shiao, Tze Chieh; Roy, René; Sleno, Lekha

2014-09-15

Acetaminophen is known to cause hepatoxicity via the formation of a reactive metabolite, N-acetyl p-benzoquinone imine (NAPQI), as a result of covalent binding to liver proteins. Serum albumin (SA) is known to be covalently modified by NAPQI and is present at high concentrations in the bloodstream and is therefore a potential biomarker to assess the levels of protein modification by NAPQI. A newly developed method for the absolute quantitation of serum albumin containing NAPQI covalently bound to its active site cysteine (Cys34) is described. This optimized assay represents the first absolute quantitation of a modified protein, with very low stoichiometric abundance, using a protein-level standard combined with isotope dilution. The LC-MS/MS assay is based on a protein standard modified with a custom-designed reagent, yielding a surrogate peptide (following digestion) that is a positional isomer to the target peptide modified by NAPQI. To illustrate the potential of this approach, the method was applied to quantify NAPQI-modified SA in plasma from rats dosed with acetaminophen. The resulting method is highly sensitive (capable of quantifying down to 0.0006% of total RSA in its NAPQI-modified form) and yields excellent precision and accuracy statistics. A time-course pharmacokinetic study was performed to test the usefulness of this method for following acetaminophen-induced covalent binding at four dosing levels (75-600 mg/kg IP), showing the viability of this approach to directly monitor in vivo samples. This approach can reliably quantify NAPQI-modified albumin, allowing direct monitoring of acetaminophen-related covalent binding.

Negative ion spectrometry for detecting nitrated explosives

NASA Technical Reports Server (NTRS)

Boettger, H. G.; Yinon, J.

1975-01-01

Ionization procedure is modified to produce mainly negative ions by electron capture. Peaks of negative ions are monitored conventionally. Nitrated organic materials could be identified directly from sample sniff inlet stream by suitably modified mass spectrometer because of unique electronegativity which nitro group imparts to organic material.

Solving Differential Equations Using Modified Picard Iteration

ERIC Educational Resources Information Center

Robin, W. A.

2010-01-01

Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

Safe Heavens. Military Strategy and Space Sanctuary Thought,

DTIC Science & Technology

1998-06-01

service proposed two ASAT solutions: a modified Nike Zeus antiballistic missile (ABM) and a "homing satellite" carrying a destructive charge.9...McNamara ordered the Army to modify the Nike Zeus ABM for a future ASAT role. The modified system, Program 505, was based at Kwajalein Atoll in...operational. President Carter’s 1978 Presidential Directive on Space Policy stated that "the United States finds itself under increasing pressure to

Direct electron transfer of Phanerochaete chrysosporium cellobiose dehydrogenase at platinum and palladium nanoparticles decorated carbon nanotubes modified electrodes.

PubMed

Bozorgzadeh, Somayyeh; Hamidi, Hassan; Ortiz, Roberto; Ludwig, Roland; Gorton, Lo

2015-10-07

In the present work, platinum and palladium nanoparticles (PtNPs and PdNPs) were decorated on the surface of multi-walled carbon nanotubes (MWCNTs) by a simple thermal decomposition method. The prepared nanohybrids, PtNPs-MWCNTs and PdNPs-MWCNTs, were cast on the surface of spectrographic graphite electrodes and then Phanerochaete chrysosporium cellobiose dehydrogenase (PcCDH) was adsorbed on the modified layer. Direct electron transfer between PcCDH and the nanostructured modified electrodes was studied using flow injection amperometry and cyclic voltammetry. The maximum current responses (Imax) and the apparent Michaelis-Menten constants (K) for the different PcCDH modified electrodes were calculated by fitting the data to the Michaelis-Menten equation and compared. The sensitivity towards lactose was 3.07 and 3.28 μA mM(-1) at the PcCDH/PtNPs-MWCNTs/SPGE and PcCDH/PdNPs-MWCNTs/SPGE electrodes, respectively, which were higher than those measured at the PcCDH/MWCNTs/SPGE (2.60 μA mM(-1)) and PcCDH/SPGE (0.92 μA mM(-1)). The modified electrodes were additionally tested as bioanodes for biofuel cell applications.

AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation

PubMed Central

Koehl, Patrice; Delarue, Marc

2010-01-01

The Poisson–Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson–Boltzmann–Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available. PMID:20151727

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.

AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.

PubMed

Koehl, Patrice; Delarue, Marc

2010-02-14

The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available.

Urine Anion Gap to Predict Urine Ammonium and Related Outcomes in Kidney Disease.

PubMed

Raphael, Kalani L; Gilligan, Sarah; Ix, Joachim H

2018-02-07

Low urine ammonium excretion is associated with ESRD in CKD. Few laboratories measure urine ammonium, limiting clinical application. We determined correlations between urine ammonium, the standard urine anion gap, and a modified urine anion gap that includes sulfate and phosphate and compared risks of ESRD or death between these ammonium estimates and directly measured ammonium. We measured ammonium, sodium, potassium, chloride, phosphate, and sulfate from baseline 24-hour urine collections in 1044 African-American Study of Kidney Disease and Hypertension participants. We evaluated the cross-sectional correlations between urine ammonium, the standard urine anion gap (sodium + potassium - chloride), and a modified urine anion gap that includes urine phosphate and sulfate in the calculation. Multivariable-adjusted Cox models determined the associations of the standard urine anion gap and the modified urine anion gap with the composite end point of death or ESRD; these results were compared with results using urine ammonium as the predictor of interest. The standard urine anion gap had a weak and direct correlation with urine ammonium ( r =0.18), whereas the modified urine anion gap had a modest inverse relationship with urine ammonium ( r =-0.58). Compared with the highest tertile of urine ammonium, those in the lowest urine ammonium tertile had higher risk of ESRD or death (hazard ratio, 1.46; 95% confidence interval, 1.13 to 1.87) after adjusting for demographics, GFR, proteinuria, and other confounders. In comparison, participants in the corresponding standard urine anion gap tertile did not have higher risk of ESRD or death (hazard ratio, 0.82; 95% confidence interval, 0.64 to 1.07), whereas the risk for those in the corresponding modified urine anion gap tertile (hazard ratio, 1.32; 95% confidence interval, 1.03 to 1.68) approximated that of directly measured urine ammonium. Urine anion gap is a poor surrogate of urine ammonium in CKD unless phosphate and sulfate are included in the calculation. Because the modified urine anion gap merely estimates urine ammonium and requires five measurements, direct measurements of urine ammonium are preferable in CKD. Copyright © 2018 by the American Society of Nephrology.

Improving the readability and processability of a pediatric informed consent document: effects on parents' understanding.

PubMed

Tait, Alan R; Voepel-Lewis, Terri; Malviya, Shobha; Philipson, Sandra J

2005-04-01

To examine whether a consent document modified to conform with the federal guidelines for readability and processability would result in greater parental understanding compared with a standard form. Randomized clinical study. The preoperative waiting area of a larger tertiary care children's hospital. A total of 305 parents of children scheduled for minor elective surgical procedures. Parents were randomized to receive information about a clinical study in 1 of 4 ways: (1) standard consent form alone, (2) standard consent form with verbal disclosure, (3) modified form alone (standard form modified to meet the federal guidelines for readability and processability), and (4) modified form with verbal disclosure. Parents were interviewed to determine their understanding of 11 elements of consent, including study purpose, protocol, risks, benefits to child (direct), benefit to others (indirect), freedom to withdraw, alternatives, duration of study, voluntariness, confidentiality, and whom to contact. Their responses were scored by 2 independent assessors. Understanding of the protocol, study duration, risks, and direct benefits, together with overall understanding, was greater among parents who received the modified form (P<.001). Additionally, parents reported that the modified form had greater clarity (P = .009) and improved layout compared with the standard form (P<.001). When parents were shown both forms, 81.2% preferred the modified version. Results suggest that a consent form written according to federal guidelines for readability and processability can improve parent understanding and thus will be important in enhancing the informed consent process.

University of Idaho's low-speed flex fuel direct-injected 797cc two-stroke rear drive snowmobile.

DOT National Transportation Integrated Search

2012-06-01

The University of Idahos entry into the 2012 SAE Clean Snowmobile Challenge uses a Ski-Doo XP chassis with a low-speed 797 cc direct-injection two-stroke powered snowmobile modified for flex fuel use on blended ethanol fuel. A battery-less direct ...

78 FR 47233 - Airworthiness Directives; The Boeing Company Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2013-08-05

...-0670; Directorate Identifier 2013-NM-081-AD] RIN 2120-AA64 Airworthiness Directives; The Boeing Company...). SUMMARY: We propose to adopt a new airworthiness directive (AD) for certain The Boeing Company Model 737-600, -700, -800, -900, and -900ER airplanes modified by particular supplemental type certificates (STC...

Development of an Ethanol Blend Two-Stroke Direct-Injection Snowmobile for Use in the Clean Snowmobile Challenge and National Parks

DOT National Transportation Integrated Search

2010-09-01

The University of Idaho's entry into the 2010 SAE Clean Snowmobile Challenge (CSC) was a direct-injection (DI) two-stroke powered snowmobile modified to use blended ethanol fuel. The modulated and battery-less direct-injection system used to decrease...

Computer-Communications Networks and Teletraffic.

ERIC Educational Resources Information Center

Switzer, I.

Bi-directional cable TV (CATV) systems that are being installed today may not be well suited for computer communications. Older CATV systems are being modified to bi-directional transmission and most new systems are being built with bi-directional capability included. The extreme bandwidth requirement for carrying 20 or more TV channels on a…

77 FR 33129 - Airworthiness Directives; The Boeing Company Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2012-06-05

... modify the fuel quantity indication system (FQIS) wiring or fuel tank systems to prevent development of..., 2012 (77 FR 12506). That NPRM proposed to require modifying the fuel quantity indication system wiring or fuel tank systems to prevent development of an ignition source inside the center fuel tank. That...

21 CFR 172.892 - Food starch-modified.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 21 Food and Drugs 3 2013-04-01 2013-04-01 false Food starch-modified. 172.892 Section 172.892 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) FOOD FOR HUMAN CONSUMPTION (CONTINUED) FOOD ADDITIVES PERMITTED FOR DIRECT ADDITION TO FOOD FOR HUMAN CONSUMPTION...

21 CFR 172.892 - Food starch-modified.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 21 Food and Drugs 3 2012-04-01 2012-04-01 false Food starch-modified. 172.892 Section 172.892 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) FOOD FOR HUMAN CONSUMPTION (CONTINUED) FOOD ADDITIVES PERMITTED FOR DIRECT ADDITION TO FOOD FOR HUMAN CONSUMPTION...

21 CFR 172.892 - Food starch-modified.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 21 Food and Drugs 3 2014-04-01 2014-04-01 false Food starch-modified. 172.892 Section 172.892 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) FOOD ADDITIVES PERMITTED FOR DIRECT ADDITION TO FOOD FOR HUMAN CONSUMPTION Multipurpose Additives § 172.892 Food...

78 FR 54383 - Airworthiness Directives; Eurocopter Deutschland GmbH Helicopters

Federal Register 2010, 2011, 2012, 2013, 2014

2013-09-04

... the main transmission filter housing upper part and modifying the main transmission housing upper part... filter area was not manufactured in accordance with applicable design specifications. The actions of this... a corrugated washer in the filter housing of the housing upper part and modifying each affected main...

Statistical evaluation of fatty acid profile and cholesterol content in fish (common carp) lipids obtained by different sample preparation procedures.

PubMed

Spiric, Aurelija; Trbovic, Dejana; Vranic, Danijela; Djinovic, Jasna; Petronijevic, Radivoj; Matekalo-Sverak, Vesna

2010-07-05

Studies performed on lipid extraction from animal and fish tissues do not provide information on its influence on fatty acid composition of the extracted lipids as well as on cholesterol content. Data presented in this paper indicate the impact of extraction procedures on fatty acid profile of fish lipids extracted by the modified Soxhlet and ASE (accelerated solvent extraction) procedure. Cholesterol was also determined by direct saponification method, too. Student's paired t-test used for comparison of the total fat content in carp fish population obtained by two extraction methods shows that differences between values of the total fat content determined by ASE and modified Soxhlet method are not statistically significant. Values obtained by three different methods (direct saponification, ASE and modified Soxhlet method), used for determination of cholesterol content in carp, were compared by one-way analysis of variance (ANOVA). The obtained results show that modified Soxhlet method gives results which differ significantly from the results obtained by direct saponification and ASE method. However the results obtained by direct saponification and ASE method do not differ significantly from each other. The highest quantities for cholesterol (37.65 to 65.44 mg/100 g) in the analyzed fish muscle were obtained by applying direct saponification method, as less destructive one, followed by ASE (34.16 to 52.60 mg/100 g) and modified Soxhlet extraction method (10.73 to 30.83 mg/100 g). Modified Soxhlet method for extraction of fish lipids gives higher values for n-6 fatty acids than ASE method (t(paired)=3.22 t(c)=2.36), while there is no statistically significant difference in the n-3 content levels between the methods (t(paired)=1.31). The UNSFA/SFA ratio obtained by using modified Soxhlet method is also higher than the ratio obtained using ASE method (t(paired)=4.88 t(c)=2.36). Results of Principal Component Analysis (PCA) showed that the highest positive impact to the second principal component (PC2) is recorded by C18:3 n-3, and C20:3 n-6, being present in a higher amount in the samples treated by the modified Soxhlet extraction, while C22:5 n-3, C20:3 n-3, C22:1 and C20:4, C16 and C18 negatively influence the score values of the PC2, showing significantly increased level in the samples treated by ASE method. Hotelling's paired T-square test used on the first three principal components for confirmation of differences in individual fatty acid content obtained by ASE and Soxhlet method in carp muscle showed statistically significant difference between these two data sets (T(2)=161.308, p<0.001). Copyright 2010 Elsevier B.V. All rights reserved.

Modified social force model based on information transmission toward crowd evacuation simulation

NASA Astrophysics Data System (ADS)

Han, Yanbin; Liu, Hong

2017-03-01

In this paper, the information transmission mechanism is introduced into the social force model to simulate pedestrian behavior in an emergency, especially when most pedestrians are unfamiliar with the evacuation environment. This modified model includes a collision avoidance strategy and an information transmission model that considers information loss. The former is used to avoid collision among pedestrians in a simulation, whereas the latter mainly describes how pedestrians obtain and choose directions appropriate to them. Simulation results show that pedestrians can obtain the correct moving direction through information transmission mechanism and that the modified model can simulate actual pedestrian behavior during an emergency evacuation. Moreover, we have drawn four conclusions to improve evacuation based on the simulation results; and these conclusions greatly contribute in optimizing a number of efficient emergency evacuation schemes for large public places.

A modified NARMAX model-based self-tuner with fault tolerance for unknown nonlinear stochastic hybrid systems with an input-output direct feed-through term.

PubMed

Tsai, Jason S-H; Hsu, Wen-Teng; Lin, Long-Guei; Guo, Shu-Mei; Tann, Joseph W

2014-01-01

A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input-output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Self-assembling siloxane bilayer directly on SiO2 surface of micro-cantilevers for long-term highly repeatable sensing to trace explosives.

PubMed

Chen, Ying; Xu, Pengcheng; Li, Xinxin

2010-07-02

This paper presents a novel sensing layer modification technique for static micro-cantilever sensors that detect trace explosives by measuring specific adsorption-induced surface stress. For the first time, a method of directly modifying a siloxane sensing bilayer on an SiO(2) surface is proposed to replace the conventional self-assembled monolayers (SAMs) of thiols on Au to avoid the trouble from long-term unstable Au-S bonds. For modifying the long-term reliable sensing bilayer on the piezoresistor-integrated micro-cantilevers, a siloxane-head bottom layer is self-assembled directly on the SiO(2) cantilever surface, which is followed by grafting another explosive-sensing-group functionalized molecule layer on top of the siloxane layer. The siloxane-modified sensor has experimentally exhibited a highly resoluble response to 0.1 ppb TNT vapor. More importantly, the repeated detection results after 140 days show no obvious attenuation in sensing signal. Also observed experimentally, the specific adsorption of the siloxane sensing bilayer to TNT molecules causes a tensile surface stress on the cantilever. Herein the measured tensile surface stress is in contrast to the compressive surface stress normally measured from conventional cantilever sensors where the sensitive thiol-SAMs are modified on an Au surface. The reason for this newly observed phenomenon is discussed and preliminarily analyzed.

Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion

NASA Astrophysics Data System (ADS)

Philip, B.; Wang, Z.; Berrill, M. A.; Birke, M.; Pernice, M.

2014-04-01

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling 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.

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.

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

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.

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

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

Desiccant outdoor air preconditioners maximize heat recovery ventilation potentials

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

Meckler, M.

1995-12-31

Microorganisms are well protected indoors by the moisture surrounding them if the relative humidity is above 70%. They can cause many acute diseases, infections, and allergies. Humidity also has an effect on air cleanliness and causes the building structure and its contents to deteriorate. Therefore, controlling humidity is a very important factor to human health and comfort and the structural longevity of a building. To date, a great deal of research has been done, and is continuing, in the use of both solid and liquid desiccants. This paper introduces a desiccant-assisted system that combines dehumidification and mechanical refrigeration by meansmore » of a desiccant preconditioning module that can serve two or more conventional air-conditioning units. It will be demonstrated that the proposed system, also having indirect evaporative cooling within the preconditioning module, can reduce energy consumption and provide significant cost savings, independent humidity and temperature control, and, therefore, improved indoor air quality and enhanced occupant comfort.« less

Pseudospectral collocation methods for fourth order differential equations

NASA Technical Reports Server (NTRS)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

Analysis of fuel using the Direct LSC method determination of bio-originated fuel in the presence of quenching.

PubMed

Doll, Charles G; Wright, Cherylyn W; Morley, Shannon M; Wright, Bob W

2017-04-01

A modified version of the Direct LSC method to correct for quenching effect was investigated for the determination of bio-originated fuel content in fuel samples produced from multiple biological starting materials. The modified method was found to be accurate in determining the percent bio-originated fuel to within 5% of the actual value for samples with quenching effects ≤43%. Analysis of highly quenched samples was possible when diluted with the exception of one sample with a 100% quenching effect. Copyright © 2017. Published by Elsevier Ltd.

Research on the Mechanism of In-Plane Vibration on Friction Reduction

PubMed Central

Wang, Peng; Ni, Hongjian; Wang, Ruihe; Liu, Weili; Lu, Shuangfang

2017-01-01

A modified model for predicting the friction force between drill-string and borehole wall under in-plane vibrations was developed. It was found that the frictional coefficient in sliding direction decreased significantly after applying in-plane vibration on the bottom specimen. The friction reduction is due to the direction change of friction force, elastic deformation of surface asperities and the change of frictional coefficient. Normal load, surface topography, vibration direction, velocity ratio and interfacial shear factor are the main influence factors of friction force in sliding direction. Lower driving force can be realized for a pair of determinate rubbing surfaces under constant normal load by setting the driving direction along the minimum arithmetic average attack angle direction, and applying intense longitudinal vibration on the rubbing pair. The modified model can significantly improve the accuracy in predicting frictional coefficient under vibrating conditions, especially under the condition of lower velocity ratio. The results provide a theoretical gist for friction reduction technology by vibrating drill-string, and provide a reference for determination of frictional coefficient during petroleum drilling process, which has great significance for realizing digitized and intelligent drilling. PMID:28862679

76 FR 53326 - Airworthiness Directives; Eurocopter France (ECF) Model EC120B Helicopters

Federal Register 2010, 2011, 2012, 2013, 2014

2011-08-26

... also requires modifying the emergency switch electrical wiring and performing tests to ensure correct... the RFM after modifying the emergency switch electrical wiring and performing tests to ensure correct... likely to exist or develop on other helicopters of the same type design. Differences Between This AD and...

Characterizing Stressors and Modifiable Health Risk Factors among Homeless Smokers: An Exploratory Pilot Study

ERIC Educational Resources Information Center

Kendzor, Darla E.; Reitzel, Lorraine R.; Businelle, Michael S.

2015-01-01

This pilot study was conducted to explore the associations between stressors related to homelessness and modifiable health risk factors (poor diet, insufficient physical activity, and overweight/obesity) and to provide direction for future research. Participants (N = 57) were homeless adults enrolled in a smoking cessation program. Analyses were…

76 FR 33988 - Airworthiness Directives; The Boeing Company Model 737-100, -200, -200C, -300, -400, and -500...

Federal Register 2010, 2011, 2012, 2013, 2014

2011-06-10

..., performing certain bonding resistance measurements, and modifying relay module assemblies. This AD also... resistance measurements, and modifying relay module assemblies. That NPRM also proposed to require revising... determined that air safety and the public interest require adopting the AD with the changes described...

77 FR 23385 - Airworthiness Directives; Fokker Services B.V. Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2012-04-19

... modifying the crossfeed valve control and power supply, the crossfeed indication logic and power supply, and... supply, of the crossfeed indication logic and power supply and of the fuel fire shut-off valve indication... this AD, modify the crossfeed valve control and power supply, the crossfeed indication logic and power...

Enzyme use in kibble diets formulated with wheat bran for dogs: effects on processing and digestibility.

PubMed

Sá, F C; Vasconcellos, R S; Brunetto, M A; Filho, F O R; Gomes, M O S; Carciofi, A C

2013-05-01

Recently, there is an interest in technologies that favour the use of coproducts for animal nutrition. The effect of adding two enzyme mixtures in diets for dogs formulated with wheat bran (WB) was evaluated. Two foods with similar compositions were formulated: negative control (NC; without WB) and test diet (25% of WB). The test diet was divided into four treatments: without enzyme (positive control), enzyme mixture 1 (ENZ1; added before extrusion β-glucanase, xylanase, cellulase, glucoamylase, phytase); enzyme mixture 2 (ENZ2; added before extrusion the ENZ1 more α-amylase); enzyme mixture 2 added after the extrusion (ENZ2ex). ENZ1 and ENZ2 were used to evaluate the enzyme effect on extruder pre-conditioner (processing additive) and ENZ2ex to evaluate the effect of enzyme supplementation for the animal. Digestibility was measured through total collection of faeces and urine. The experiment followed a randomized block design with five treatments (diets) and six dogs per diet, totalling 30 dogs (7.0 ± 1.2 years old and 11.0 ± 2.2 kg of body weight). Data were submitted to analysis of variance and means compared by Tukey's test and orthogonal contrasts (p < 0.05). Reducing sugars showed an important reduction after extrusion, suggesting the formation of carbohydrate complexes. The apparent total tract digestibility (ATTD) of dry matter, organic matter, crude protein, acid-hydrolysed fat and energy was higher in NC than in diets with WB (p < 0.001), without effects of enzyme additions. WB diets resulted in higher faecal production and concentration of short-chain fatty acids (SCFA) and reduced pH and ammonia concentration (p < 0.01), with no effect of enzyme addition. The enzyme addition did not result in improved digestibility of a diet high in non-starch polysaccharides; however, only ATTD was measured and nutrient fermentation in the large intestine may have interfered with the results obtained. WB modified fermentation product formation in the colon of dogs. Journal of Animal Physiology and Animal Nutrition © 2013 Blackwell Verlag GmbH.

Mechanisms and Modifiers of Methylmercury-Induced Neurotoxicity

PubMed Central

Fretham, Stephanie JB; Caito, Samuel; Martinez-Finley, Ebany J; Aschner, Michael

2016-01-01

The neurotoxic consequences of methylmercury (MeHg) exposure have long been known, however a complete understanding of the mechanisms underlying this toxicity is elusive. Recent epidemiological and experimental studies have provided many mechanistic insights, particularly into the contribution of genetic and environmental factors that interact with MeHg to modify toxicity. This review will outline cellular processes directly and indirectly affected by MeHg, including oxidative stress, cellular signaling and gene expression, and discuss genetic, environmental and nutritional factors capable of modifying MeHg toxicity. PMID:27795823

A Comparison of the OSHA Modified NIOSH Physical and Chemical Analytical Method (P and CAM) 304 and the Dust Trak Photometric Aerosol Sampler for 0-Chlorobenzylidine Malonitrile

DTIC Science & Technology

2013-04-02

photometric particle counting instrument, DustTrak, to the established OSHA modified NIOSH P&CAM 304 method to determine correlation between the two...study compared the non-specific, rapid photometric particle counting instrument, DustTrak, to the established OSHA modified NIOSH P&CAM 304 method...mask confidence training (27) . This study will compare a direct reading, non-specific photometric particle count instrument (DustTrak TSI Model

Genetic Modification of Human Pancreatic Progenitor Cells Through Modified mRNA.

PubMed

Lu, Song; Chow, Christie C; Zhou, Junwei; Leung, Po Sing; Tsui, Stephen K; Lui, Kathy O

2016-01-01

In this chapter, we describe a highly efficient genetic modification strategy for human pancreatic progenitor cells using modified mRNA-encoding GFP and Neurogenin-3. The properties of modified mRNA offer an invaluable platform to drive protein expression, which has broad applicability in pathway regulation, directed differentiation, and lineage specification. This approach can also be used to regulate expression of other pivotal transcription factors during pancreas development and might have potential therapeutic values in regenerative medicine.

Genetic modifiers of muscular dystrophy act on sarcolemmal resealing and recovery from injury

PubMed Central

Quattrocelli, Mattia; Capote, Joanna; Ohiri, Joyce C.; Warner, James L.; Vo, Andy H.; Hadhazy, Michele; Demonbreun, Alexis R.; Spencer, Melissa J.; McNally, Elizabeth M.

2017-01-01

Genetic disruption of the dystrophin complex produces muscular dystrophy characterized by a fragile muscle plasma membrane leading to excessive muscle degeneration. Two genetic modifiers of Duchenne Muscular Dystrophy implicate the transforming growth factor β (TGFβ) pathway, osteopontin encoded by the SPP1 gene and latent TGFβ binding protein 4 (LTBP4). We now evaluated the functional effect of these modifiers in the context of muscle injury and repair to elucidate their mechanisms of action. We found that excess osteopontin exacerbated sarcolemmal injury, and correspondingly, that loss of osteopontin reduced injury extent both in isolated myofibers and in muscle in vivo. We found that ablation of osteopontin was associated with reduced expression of TGFβ and TGFβ-associated pathways. We identified that increased TGFβ resulted in reduced expression of Anxa1 and Anxa6, genes encoding key components of the muscle sarcolemma resealing process. Genetic manipulation of Ltbp4 in dystrophic muscle also directly modulated sarcolemmal resealing, and Ltbp4 alleles acted in concert with Anxa6, a distinct modifier of muscular dystrophy. These data provide a model in which a feed forward loop of TGFβ and osteopontin directly impacts the capacity of muscle to recover from injury, and identifies an intersection of genetic modifiers on muscular dystrophy. PMID:29065150

Genetic modifiers of muscular dystrophy act on sarcolemmal resealing and recovery from injury.

PubMed

Quattrocelli, Mattia; Capote, Joanna; Ohiri, Joyce C; Warner, James L; Vo, Andy H; Earley, Judy U; Hadhazy, Michele; Demonbreun, Alexis R; Spencer, Melissa J; McNally, Elizabeth M

2017-10-01

Genetic disruption of the dystrophin complex produces muscular dystrophy characterized by a fragile muscle plasma membrane leading to excessive muscle degeneration. Two genetic modifiers of Duchenne Muscular Dystrophy implicate the transforming growth factor β (TGFβ) pathway, osteopontin encoded by the SPP1 gene and latent TGFβ binding protein 4 (LTBP4). We now evaluated the functional effect of these modifiers in the context of muscle injury and repair to elucidate their mechanisms of action. We found that excess osteopontin exacerbated sarcolemmal injury, and correspondingly, that loss of osteopontin reduced injury extent both in isolated myofibers and in muscle in vivo. We found that ablation of osteopontin was associated with reduced expression of TGFβ and TGFβ-associated pathways. We identified that increased TGFβ resulted in reduced expression of Anxa1 and Anxa6, genes encoding key components of the muscle sarcolemma resealing process. Genetic manipulation of Ltbp4 in dystrophic muscle also directly modulated sarcolemmal resealing, and Ltbp4 alleles acted in concert with Anxa6, a distinct modifier of muscular dystrophy. These data provide a model in which a feed forward loop of TGFβ and osteopontin directly impacts the capacity of muscle to recover from injury, and identifies an intersection of genetic modifiers on muscular dystrophy.

Optimal modified tracking performance for MIMO networked control systems with communication constraints.

PubMed

Wu, Jie; Zhou, Zhu-Jun; Zhan, Xi-Sheng; Yan, Huai-Cheng; Ge, Ming-Feng

2017-05-01

This paper investigates the optimal modified tracking performance of multi-input multi-output (MIMO) networked control systems (NCSs) with packet dropouts and bandwidth constraints. Some explicit expressions are obtained by using co-prime factorization and the spectral decomposition technique. The obtained results show that the optimal modified tracking performance is related to the intrinsic properties of a given plant such as non-minimum phase (NMP) zeros, unstable poles, and their directions. Furthermore, the modified factor, packet dropouts probability and bandwidth also impact the optimal modified tracking performance of the NCSs. The optimal modified tracking performance with channel input power constraint is obtained by searching through all stabilizing two-parameter compensator. Finally, some typical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Direct and mediated electrochemistry of peroxidase and its electrocatalysis on a variety of screen-printed carbon electrodes: amperometric hydrogen peroxide and phenols biosensor.

PubMed

Chekin, Fereshteh; Gorton, Lo; Tapsobea, Issa

2015-01-01

This study compares the behaviour of direct and mediated electrochemistry of horseradish peroxidase (HRP) immobilised on screen-printed carbon electrodes (SPCEs), screen-printed carbon electrodes modified with carboxyl-functionalised multi-wall carbon nanotubes (MWCNT-SPCEs) and screen-printed carbon electrodes modified with carboxyl-functionalised single-wall carbon nanotubes (SWCNT-SPCEs). The techniques of cyclic voltammetry and amperometry in the flow mode were used to characterise the properties of the HRP immobilised on screen-printed electrodes. From measurements of the mediated and mediatorless currents of hydrogen peroxide reduction at the HRP-modified electrodes, it was concluded that the fraction of enzyme molecules in direct electron transfer (DET) contact with the electrode varies substantially for the different electrodes. It was observed that the screen-printed carbon electrodes modified with carbon nanotubes (MWCNT-SPCEs and SWCNT-SPCEs) demonstrated a substantially higher percentage (≈100 %) of HRP molecules in DET contact than the screen-printed carbon electrodes (≈60 %). The HRP-modified electrodes were used for determination of hydrogen peroxide in mediatorless mode. The SWCNT-SPCE gave the lowest detection limit (0.40 ± 0.09 μM) followed by MWCNT-SPCE (0.48 ± 0.07 μM) and SPCE (0.98 ± 0.2 μM). These modified electrodes were additionally developed for amperometric determination of phenolic compounds. It was found that the SWCNT-SPCE gave a detection limit for catechol of 110.2 ± 3.6 nM, dopamine of 640.2 ± 9.2 nM, octopamine of 3341 ± 15 nM, pyrogallol of 50.10 ± 2.9 nM and 3,4-dihydroxy-L-phenylalanine of 980.7 ± 8.7 nM using 50 μM H2O2 in the flow carrier.

Perceptual learning modifies untrained pursuit eye movements.

PubMed

Szpiro, Sarit F A; Spering, Miriam; Carrasco, Marisa

2014-07-07

Perceptual learning improves detection and discrimination of relevant visual information in mature humans, revealing sensory plasticity. Whether visual perceptual learning affects motor responses is unknown. Here we implemented a protocol that enabled us to address this question. We tested a perceptual response (motion direction estimation, in which observers overestimate motion direction away from a reference) and a motor response (voluntary smooth pursuit eye movements). Perceptual training led to greater overestimation and, remarkably, it modified untrained smooth pursuit. In contrast, pursuit training did not affect overestimation in either pursuit or perception, even though observers in both training groups were exposed to the same stimuli for the same time period. A second experiment revealed that estimation training also improved discrimination, indicating that overestimation may optimize perceptual sensitivity. Hence, active perceptual training is necessary to alter perceptual responses, and an acquired change in perception suffices to modify pursuit, a motor response. © 2014 ARVO.

Perceptual learning modifies untrained pursuit eye movements

PubMed Central

Szpiro, Sarit F. A.; Spering, Miriam; Carrasco, Marisa

2014-01-01

Perceptual learning improves detection and discrimination of relevant visual information in mature humans, revealing sensory plasticity. Whether visual perceptual learning affects motor responses is unknown. Here we implemented a protocol that enabled us to address this question. We tested a perceptual response (motion direction estimation, in which observers overestimate motion direction away from a reference) and a motor response (voluntary smooth pursuit eye movements). Perceptual training led to greater overestimation and, remarkably, it modified untrained smooth pursuit. In contrast, pursuit training did not affect overestimation in either pursuit or perception, even though observers in both training groups were exposed to the same stimuli for the same time period. A second experiment revealed that estimation training also improved discrimination, indicating that overestimation may optimize perceptual sensitivity. Hence, active perceptual training is necessary to alter perceptual responses, and an acquired change in perception suffices to modify pursuit, a motor response. PMID:25002412

Direct determination of creatinine based on poly(ethyleneimine)/phosphotungstic acid multilayer modified electrode.

PubMed

Han, Ping; Xu, Shimei; Feng, Shun; Hao, Yanjun; Wang, Jide

2016-05-01

In this work, the direct determination of creatinine was achieved using a poly(ethyleneimine)/phosphotungstic acid multilayer modified electrode with the assistance of Copper(II) ions by cyclic voltammetry. The quantity of creatinine were determined by measuring the redox peak current of Cu(II)-creatinine complex/Cu(I)-creatinine complex. Factors affecting the response current of creatinine at the modified electrode were optimized. A linear relationship between the response current and the concentration of creatinine ranging from 0.125 to 62.5μM was obtained with a detection limit of 0.06μM. The proposed method was applied to determine creatinine in human urine, and satisfied results were gotten which was validated in accordance with high performance liquid chromatography. The proposed electrode provided a promising alternative in routine sensing for creatinine without enzymatic assistance. Copyright © 2016 Elsevier B.V. All rights reserved.

System and Method for Scan Range Gating

NASA Technical Reports Server (NTRS)

Lindemann, Scott (Inventor); Zuk, David M. (Inventor)

2017-01-01

A system for scanning light to define a range gated signal includes a pulsed coherent light source that directs light into the atmosphere, a light gathering instrument that receives the light modified by atmospheric backscatter and transfers the light onto an image plane, a scanner that scans collimated light from the image plane to form a range gated signal from the light modified by atmospheric backscatter, a control circuit that coordinates timing of a scan rate of the scanner and a pulse rate of the pulsed coherent light source so that the range gated signal is formed according to a desired range gate, an optical device onto which an image of the range gated signal is scanned, and an interferometer to which the image of the range gated signal is directed by the optical device. The interferometer is configured to modify the image according to a desired analysis.

Assessment of healthy behaviors for metabolic syndrome among Korean adults: a modified information-motivation-behavioral skills with psychological distress.

PubMed

Lee, Guna; Yang, Sook Ja; Chee, Yeon Kyung

2016-06-18

Since the worldwide incidence of metabolic syndrome (Mets) has rapidly increased, healthy behaviors such as weight control, engaging in physical activity, and healthy diet have been crucial in the management of Mets. The purpose of this study was to examine healthy behaviors practice and factors that affect the practice in relation to Mets on the basis of a modified Information-Motivation-Behavioral skills model (IMB) with psychological distress, which is a well-known factor affecting healthy behaviors among individuals with Mets. Study participants were 267 community dwelling adults (M age: 54.0 ± 8.1 years) with Mets who were attending public health centers located in Seoul, South Korea. A structured questionnaire was administered in the areas of information, motivation, behavioral skills, and practice of Mets healthy behaviors and levels of psychological distress from May 2014 to September 2014. Structural equation modeling was used to test the modified IMB model. The modified IMB model had a good fit with the data, indicating that motivation and behavioral skills directly influenced the practice of Mets healthy behaviors, whereas information and psychological distress directly influenced motivation and influenced the practice of healthy behaviors through behavioral skills. These components of the modified IMB model explained 29.8 % of the variance in healthy behaviors for Mets. Findings suggested that strengthening motivation and behavioral skills for healthy behaviors can directly enhance healthy behavior practice. Providing information about Mets related healthy behaviors and strategies for psychological distress management can be used as the first line evidence based intervention to systemically enhance motivation and behavioral skills among individuals with Mets.

Nonequal iteration directional filters permit selective clearance of ripples in passband circuits

NASA Technical Reports Server (NTRS)

Kurpis, G. P.

1970-01-01

Modified directional filter is comprised of alternate pairs of dielectric and air gap filter sections with unequal electrical lengths. Filter provides more flexibility in choosing dielectric material thickness and permits switching from specially ground to standard thicknesses.

Testing of Strategies for the Acceleration of the Cost Optimization

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

Ponciroli, Roberto; Vilim, Richard B.

The general problem addressed in the Nuclear-Renewable Hybrid Energy System (N-R HES) project is finding the optimum economical dispatch (ED) and capacity planning solutions for the hybrid energy systems. In the present test-problem configuration, the N-R HES unit is composed of three electrical power-generating components, i.e. the Balance of Plant (BOP), the Secondary Energy Source (SES), and the Energy Storage (ES). In addition, there is an Industrial Process (IP), which is devoted to hydrogen generation. At this preliminary stage, the goal is to find the power outputs of each one of the N-R HES unit components (BOP, SES, ES) andmore » the IP hydrogen production level that maximizes the unit profit by simultaneously satisfying individual component operational constraints. The optimization problem is meant to be solved in the Risk Analysis Virtual Environment (RAVEN) framework. The dynamic response of the N-R HES unit components is simulated by using dedicated object-oriented models written in the Modelica modeling language. Though this code coupling provides for very accurate predictions, the ensuing optimization problem is characterized by a very large number of solution variables. To ease the computational burden and to improve the path to a converged solution, a method to better estimate the initial guess for the optimization problem solution was developed. The proposed approach led to the definition of a suitable Monte Carlo-based optimization algorithm (called the preconditioner), which provides an initial guess for the optimal N-R HES power dispatch and the optimal installed capacity for each one of the unit components. The preconditioner samples a set of stochastic power scenarios for each one of the N-R HES unit components, and then for each of them the corresponding value of a suitably defined cost function is evaluated. After having simulated a sufficient number of power histories, the configuration which ensures the highest profit is selected as the optimal one. The component physical dynamics are represented through suitable ramp constraints, which considerably simplify the numerical solving. In order to test the capabilities of the proposed approach, in the present report, the dispatch problem only is tackled, i.e. a reference unit configuration is assumed, and each one of the N-R HES unit components is assumed to have a fixed installed capacity. As for the next steps, the main improvement will concern the operation strategy of the ES facility. In particular, in order to describe a more realistic battery commitment strategy, the ES operation will be regulated according to the electricity price forecasts.« less

75 FR 1678 - Self-Regulatory Organizations; International Securities Exchange, LLC; Notice of Filing and Order...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-01-12

... Accelerated Approval to a Proposed Rule Change Relating to the Amounts That Direct Edge ECN, in Its Capacity... Substance of the Proposed Rule Change The Exchange proposes to modify the amounts that Direct Edge ECN... immediate effectiveness a proposed rule change to amend Direct Edge ECN's (``DECN'') fee schedule for ISE...

75 FR 32528 - Self-Regulatory Organizations; International Securities Exchange, LLC; Notice of Filing and Order...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-06-08

... to a Proposed Rule Change Relating to the Amounts That Direct Edge ECN, in Its Capacity as an... Rule Change The Exchange proposes to modify the amounts that Direct Edge ECN (``DECN''), in its... immediate effectiveness a proposed rule change to amend Direct Edge ECN's (``DECN'') fee schedule for ISE...

75 FR 6782 - Self-Regulatory Organizations; International Securities Exchange, LLC; Notice of Filing and Order...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-02-10

... to a Proposed Rule Change Relating to the Amounts That Direct Edge ECN, in Its Capacity as an... Rule Change The Exchange proposes to modify the amounts that Direct Edge ECN (``DECN''), in its... effectiveness a proposed rule change to amend Direct Edge ECN's (``DECN'') fee schedule for ISE Members \\3\\ to...

75 FR 27034 - Self-Regulatory Organizations; International Securities Exchange, LLC; Notice of Filing and Order...

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2010-05-13

... to a Proposed Rule Change Relating to the Amounts That Direct Edge ECN, in Its Capacity as an... Rule Change The Exchange proposes to modify the amounts that Direct Edge ECN (``DECN''), in its... change to amend Direct Edge ECN's (``DECN'') fee schedule for ISE Members \\4\\ to: (i) Change the rates...

75 FR 6743 - Self-Regulatory Organizations; International Securities Exchange, LLC; Notice of Filing and Order...

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2010-02-10

... to a Proposed Rule Change Relating to the Amounts That Direct Edge ECN, in Its Capacity as an... Rule Change The Exchange proposes to modify the amounts that Direct Edge ECN (``DECN''), in its... effectiveness a proposed rule change to amend Direct Edge ECN's (``DECN'') fee schedule for ISE Members \\3\\ to...

75 FR 19437 - Self-Regulatory Organizations; International Securities Exchange, LLC; Notice of Filing and Order...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-04-14

... to a Proposed Rule Change Relating to the Amounts That Direct Edge ECN, in Its Capacity as an... Rule Change The Exchange proposes to modify the amounts that Direct Edge ECN (``DECN''), in its... rule change to amend Direct Edge ECN's (``DECN'') fee schedule for ISE Members \\4\\ to: (i) Eliminate a...

75 FR 39311 - Self-Regulatory Organizations; International Securities Exchange, LLC; Notice of Filing and Order...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-07-08

... to a Proposed Rule Change Relating to the Amounts That Direct Edge ECN, in Its Capacity as an... Rule Change The Exchange proposes to modify the amounts that Direct Edge ECN (``DECN''), in its... Exchange, Inc. (``EDGA and EDGX Exchanges'') [sic] Direct Edge ECN will cease to operate in its capacity as...

75 FR 17983 - Self-Regulatory Organizations; International Securities Exchange, LLC; Notice of Filing and Order...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-04-08

... to a Proposed Rule Change Relating to the Amounts That Direct Edge ECN, in Its Capacity as an... Rule Change The Exchange proposes to modify the amounts that Direct Edge ECN (``DECN''), in its... effectiveness a proposed rule change to amend Direct Edge ECN's (``DECN'') fee schedule for ISE Members \\4\\ to...

A Child is Not a Little Adult: Modified Approaches to Sport for Australian Children.

ERIC Educational Resources Information Center

Winter, Gillian; And Others

This publication reports on competitive sports played by 6 to 12 year old children in Australia. The information in this two-part report is directed toward teachers, coaches, and parents. Part I, "Modified Approaches to Junior Sport," provides discussion of aspects of physical, social, and emotional development associated with children…

78 FR 69429 - Prospective Grant of Exclusive License: The Development of Modified T-cells for the Treatment of...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-11-19

... Exclusive License: The Development of Modified T-cells for the Treatment of Multiple Myeloma AGENCY... Targeting B-cell Maturation Antigen'' [HHS Ref. E-040-2012/0-US-01]. The patent rights in these inventions..., development, and manufacture of chimeric antigen receptor (CAR)-expressing human T-cells directed against B...

Modified technique for processing multiangle lidar data measured in clear and moderately polluted atmospheres

Treesearch

Vladimir Kovalev; Cyle Wold; Alexander Petkov; Wei Min Hao

2011-01-01

We present a modified technique for processing multiangle lidar data that is applicable for relatively clear atmospheres, where the utilization of the conventional Kano-Hamilton method meets significant issues. Our retrieval algorithm allows computing the two-way transmission and the corresponding extinction-coefficient profile in any slope direction searched during...

Surface-coupling of Cerenkov radiation from a modified metallic metamaterial slab via Brillouin-band folding.

PubMed

Bera, Anirban; Barik, Ranjan Kumar; Sattorov, Matlabjon; Kwon, Ohjoon; Min, Sun-Hong; Baek, In-Keun; Kim, Seontae; So, Jin-Kyu; Park, Gun-Sik

2014-02-10

Metallic metamaterials with positive dielectric responses are promising as an alternative to dielectrics for the generation of Cerenkov radiation [J.-K. So et al., Appl. Phys. Lett. 97(15), 151107 (2010)]. We propose here by theoretical analysis a mechanism to couple out Cerenkov radiation from the slab surfaces in the transverse direction. The proposed method based on Brillouin-zone folding is to periodically modify the thickness of the metamaterial slab in the axial direction. Moreover, the intensity of the surface-coupled radiation by this mechanism shows an order-of-magnitude enhancement compared to that of ordinary Smith-Purcell radiation.

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

Yeung, Yu-Hong; Pothen, Alex; Halappanavar, Mahantesh

We present an augmented matrix approach to update the solution to a linear system of equations when the coefficient matrix is modified by a few elements within a principal submatrix. This problem arises in the dynamic security analysis of a power grid, where operators need to performmore » $N-x$ contingency analysis, i.e., determine the state of the system when up to $x$ links from $N$ fail. Our algorithms augment the coefficient matrix to account for the changes in it, and then compute the solution to the augmented system without refactoring the modified matrix. We provide two algorithms, a direct method, and a hybrid direct-iterative method for solving the augmented system. We also exploit the sparsity of the matrices and vectors to accelerate the overall computation. Our algorithms are compared on three power grids with PARDISO, a parallel direct solver, and CHOLMOD, a direct solver with the ability to modify the Cholesky factors of the coefficient matrix. We show that our augmented algorithms outperform PARDISO (by two orders of magnitude), and CHOLMOD (by a factor of up to 5). Further, our algorithms scale better than CHOLMOD as the number of elements updated increases. The solutions are computed with high accuracy. Our algorithms are capable of computing $N-x$ contingency analysis on a $778K$ bus grid, updating a solution with $x=20$ elements in $$1.6 \\times 10^{-2}$$ seconds on an Intel Xeon processor.« less

Direct characterization of cotton fabrics treated with di-epoxide by nuclear magnetic resonance.

PubMed

Xiao, Min; Chéry, Joronia; Keresztes, Ivan; Zax, David B; Frey, Margaret W

2017-10-15

A non-acid-based, di-functional epoxide, neopentyl glycol diglycidyl ether (NPGDGE), was used to modify cotton fabrics. Direct characterization of the modified cotton was conducted by Nuclear Magnetic Resonance (NMR) without grinding the fabric into a fine powder. NaOH and MgBr 2 were compared in catalyzing the reaction between the epoxide groups of NPGDGE and the hydroxyl groups of cellulose. Possible reaction routes were discussed. Scanning electron microscopy (SEM) images showed that while the MgBr 2 -catalyzed reaction resulted in self-polymerization of NPGDGE, the NaOH-catalyzed reaction did not. Fourier transform infrared spectroscopy (FTIR) showed that at high NaOH concentration cellulose restructures from allomorph I to II. NMR studies verified the incorporation of NPGDGE into cotton fabrics with a clear NMR signal, and confirmed that at higher NaOH concentration the efficiency of grafting of NPGDGE was increased. This demonstrates that use of solid state NMR directly on woven fabric samples can simultaneously characterize chemical modification and crystalline polymorph of cotton. No loss of tensile strength was observed for cotton fabrics modified with NPGDGE. Copyright © 2017 Elsevier Ltd. All rights reserved.

Comparison of modified driver circuit and capacitor-transfer circuit in longitudinally excited N2 laser.

PubMed

Uno, Kazuyuki; Akitsu, Tetsuya; Nakamura, Kenshi; Jitsuno, Takahisa

2013-04-01

We developed a modified driver circuit composed of a capacitance and a spark gap, called a direct-drive circuit, for a longitudinally excited gas laser. The direct-drive circuit uses a large discharge impedance caused by a long discharge length of the longitudinal excitation scheme and eliminates the buffer capacitance used in the traditional capacitor-transfer circuit. We compared the direct-drive circuit and the capacitor-transfer circuit in a longitudinally excited N2 laser (wavelength: 337 nm). Producing high output energy with the capacitor-transfer circuit requires a large storage capacitance and a discharge tube with optimum dimensions (an inner diameter of 4 mm and a length of 10 cm in this work); in contrast, the direct-drive circuit requires a high breakdown voltage, achieved with a small storage capacitance and a large discharge tube. Additionally, for the same input energy of 792 mJ, the maximum output energy of the capacitor-transfer circuit was 174.2 μJ, and that of the direct-drive circuit was 344.7 μJ.

Generation and purification of highly-specific antibodies for detecting post-translationally modified proteins in vivo

PubMed Central

Arur, Swathi; Schedl, Tim

2014-01-01

Post-translational modifications alter protein structure, affecting activity, stability, localization and/or binding partners. Antibodies that specifically recognize post-translationally modified proteins have a number of uses including immuno-cytochemistry and immuno-precipitation of the modified protein to purify protein-protein and protein-nucleic acid complexes. However, antibodies directed at modified sites on individual proteins are often non-specific. Here we describe a protocol to purify polyclonal antibodies that specifically detect the modified protein of interest. The approach uses iterative rounds of subtraction and affinity purification, using stringent washes to remove antibodies that recognize the unmodified protein and low sequence complexity epitopes containing the modified amino acid. Dot and western blots assays are employed to assess antibody preparation specificity. The approach is designed to overcome the common occurrence that a single round of subtraction and affinity purification is not sufficient to obtain a modified protein specific antibody preparation. One full round of antibody purification and specificity testing takes 6 days of discontinuous time. PMID:24457330

Direct plating technique for enumeration of Listeria monocytogenes in foods.

PubMed

Golden, D A; Beuchat, L R; Brackett, R E

1988-01-01

The advantages and disadvantages of various techniques for detecting and enumerating Listeria monocytogenes in foods are reviewed, and results from a study designed to compare 14 direct plating media for their suitability to recover uninjured cells of L. monocytogenes from 4 foods are summarized. McBride Listeria agar (MLA), gum base nalidixic acid tryptone soy agar (GBNTSA), modified Despierres agar (MDA), and modified MLA (MMLA) performed best for recovering all inoculum populations from milk and ice cream mix. For Brie cheese, MLA, MDA, MMLA, and Dominguez Rodriguez isolation agar were superior for recovering L. monocytogenes; GBNTSA, MDA, MMLA, and Donnelly's Listeria enrichment agar were best for recovering the organism from cabbage. Direct plating procedures without prior enrichment can be utilized successfully for recovering L. monocytogenes from foods such as pasteurized milk and ice cream mix, which contain low populations of background microflora. However, recovery of L. monocytogenes from foods such as raw cabbage and Brie cheese, which contain high populations of other microorganisms, was not satisfactory using direct plating procedures.

A double-fibre Fabry-Perot sensor based on modified fringe counting and direct phase demodulation

NASA Astrophysics Data System (ADS)

Li, M.; Tong, B.; Arsad, N.; Guo, J. J.

2013-09-01

A modified double-fibre Fabry-Perot cavity is developed for determination of the fringe moving direction and higher sensitivity in applications of liquid level and displacement sensors. Two fibres are integrated into a silica ferrule where the ends of the two fibres in the ferrule serve as the front surfaces of the Fabry-Perot cavities, and a diaphragm, which is replaced by a moving mirror for measurement of displacement, serves as the rear surface for both cavities in liquid level sensing. Our design has no strict requirements for a specific phase difference between the two optical paths, just a constant difference resulting from the processing error between the two fibre end positions rather than a precise optical path difference of λ/8 to judge the pattern shift direction. Experimental results demonstrate the feasibility of this approach to determining the fringe moving direction, a displacement sensitivity of 3 µm and good linearity for both applications.

76 FR 62653 - Airworthiness Directives; Airbus Model A310 Series Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2011-10-11

... the fuel electrical circuit in the Right Hand (RH) wing must be modified in order to ensure better... 2S of the fuel electrical circuit in the Right Hand (RH) wing must be modified in order to ensure... the wire bundle 2S in the RH wing pylon area to the generator wire bundle of engine 2. The...

26 CFR 301.7481-1 - Date when Tax Court decision becomes final; decision modified or reversed.

Code of Federal Regulations, 2010 CFR

2010-04-01

... the Supreme Court directs that the decision of the Tax Court be modified or reversed, the decision of... 26 Internal Revenue 18 2010-04-01 2010-04-01 false Date when Tax Court decision becomes final... Proceedings Civil Actions by the United States § 301.7481-1 Date when Tax Court decision becomes final...

77 FR 32892 - Airworthiness Directives; Bombardier Inc. Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2012-06-04

... inspection area of the rear spar lower cap from WS 51.00 to WS 49.50 and modifying the ultrasonic inspection... inspection area of the rear spar lower cap from WS 51.00 to WS 49.50 and to modify the ultrasonic inspection... spars at wing station (WS) 51.00, and the wing lower skin. Additional actions, if cracking is found...

The Concepts of PPBS and Approaches to Their Application.

ERIC Educational Resources Information Center

Fielden, John

The basic concepts of the classic PPBS are summarized, and then attention is directed toward the process by which this has been modified by its collision with the values of the university. The form taken by the new modified PPBS is examined and its component concepts and techniques are identified. It is concluded that the new PPBS has limitations…

DNA-directed trypsin immobilization on a polyamidoamine dendrimer-modified capillary to form a renewable immobilized enzyme microreactor.

PubMed

Wu, Nan; Wang, Siming; Yang, Ye; Song, Jiayi; Su, Ping; Yang, Yi

2018-07-01

A novel type of trypsin capillary microreactor was developed based on a DNA-directed immobilization (DDI) technique applied to a fused-silica capillary modified with polyamidoamine (PAMAM) dendrimers. Trypsin binding to the inner wall of the capillary was confirmed by confocal laser scanning microscopy. The properties of the trypsin-DNA conjugated, PAMAM-modified capillary microreactor were investigated by monitoring hydrolysis of Nα-benzoyl- L -arginine ethyl ester. Through the hybridization and dehybridization of the DNA, the inner wall of the capillary functionalized with trypsin can be regenerated, thus indicating the renewability of this enzyme microreactor. In addition, these results demonstrated that introduction of PAMAM enabled higher amounts of trypsin to be immobilized, markedly improving the enzymolysis efficiency, compared with traditional modified capillaries. The digestion performance of the trypsin capillary microreactor was further evaluated by digesting cytochrome C, and a peptide numbers of 8, and a sequence coverage of 59% were obtained. This renewable and efficient immobilized trypsin capillary microreactor combines advantages of both DDI technology and PAMAM, and is potentially adaptable to high-throughput enzyme assays in biochemical and clinical research. Copyright © 2018. Published by Elsevier B.V.

A modified approach to controller partitioning

NASA Technical Reports Server (NTRS)

Garg, Sanjay; Veillette, Robert J.

1993-01-01

The idea of computing a decentralized control law for the integrated flight/propulsion control of an aircraft by partitioning a given centralized controller is investigated. An existing controller partitioning methodology is described, and a modified approach is proposed with the objective of simplifying the associated controller approximation problem. Under the existing approach, the decentralized control structure is a variable in the partitioning process; by contrast, the modified approach assumes that the structure is fixed a priori. Hence, the centralized controller design may take the decentralized control structure into account. Specifically, the centralized controller may be designed to include all the same inputs and outputs as the decentralized controller; then, the two controllers may be compared directly, simplifying the partitioning process considerably. Following the modified approach, a centralized controller is designed for an example aircraft mode. The design includes all the inputs and outputs to be used in a specified decentralized control structure. However, it is shown that the resulting centralized controller is not well suited for approximation by a decentralized controller of the given structure. The results indicate that it is not practical in general to cast the controller partitioning problem as a direct controller approximation problem.

Surface-modified nanoparticles as anti-biofilm filler for dental polymers

PubMed Central

Zaltsman, Nathan; Ionescu, Andrei C.; Weiss, Ervin I.; Brambilla, Eugenio; Beyth, Shaul

2017-01-01

The objective of the study was to synthesis silica nanoparticles modified with (i) a tertiary amine bearing two t-cinnamaldehyde substituents or (ii) dimethyl-octyl ammonium, alongside the well-studied quaternary ammonium polyethyleneimine nanoparticles. These were to be evaluated for their chemical and mechanical properties, as well for antibacterial and antibiofilm activity. Samples were incorporated in commercial dental resin material and the degree of monomer conversion, mechanical strength, and water contact angle were tested to characterize the effect of the nanoparticles on resin material. Antibacterial activity was evaluated with the direct contact test and the biofilm inhibition test against Streptococcus mutans. Addition of cinnamaldehyde-modified particles preserved the degree of conversion and compressive strength of the base material and increased surface hydrophobicity. Quaternary ammonium functional groups led to a decrease in the degree of conversion and to low compressive strength, without altering the hydrophilic nature of the base material. In the direct contact test and the anti-biofilm test, the polyethyleneimine particles exhibited the strongest antibacterial effect. The cinnamaldehyde-modified particles displayed antibiofilm activity, silica particles with quaternary ammonium were ineffective. Immobilization of t-cinnamaldehyde onto a solid surface via amine linkers provided a better alternative to the well-known quaternary ammonium bactericides. PMID:29244848

77 FR 48469 - Airworthiness Directives; Airbus Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2012-08-14

...-0808; Directorate Identifier 2010-NM-170-AD] RIN 2120-AA64 Airworthiness Directives; Airbus Airplanes... airplanes, and Model A340-200 and A340-300 series airplanes. This proposed AD was prompted by reports of an... require, depending on airplane configuration, modifying three flight control primary computers (FCPCs...

78 FR 27015 - Airworthiness Directives; Airbus Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2013-05-09

... Airworthiness Directives; Airbus Airplanes AGENCY: Federal Aviation Administration (FAA), Department of... Airbus Model A330-200 and A330-300 series airplanes, and Model A340-200 and A340-300 series airplanes... seal on a solenoid. This AD requires, depending on airplane configuration, modifying three flight...

Direct Allocation Costing: Informed Management Decisions in a Changing Environment.

ERIC Educational Resources Information Center

Mancini, Cesidio G.; Goeres, Ernest R.

1995-01-01

It is argued that colleges and universities can use direct allocation costing to provide quantitative information needed for decision making. This method of analysis requires institutions to modify traditional ideas of costing, looking to the private sector for examples of accurate costing techniques. (MSE)

78 FR 17073 - Airworthiness Directives; Bombardier, Inc. Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2013-03-20

... of Transportation (DOT). ACTION: Final rule. SUMMARY: We are adopting a new airworthiness directive..., and CL-604 Variants) airplanes. This AD was prompted by reports of jamming/malfunctioning of the left-hand engine thrust control mechanism. This AD requires modifying the left-hand engine upper core-cowl...

Clustered-dot halftoning with direct binary search.

PubMed

Goyal, Puneet; Gupta, Madhur; Staelin, Carl; Fischer, Mani; Shacham, Omri; Allebach, Jan P

2013-02-01

In this paper, we present a new algorithm for aperiodic clustered-dot halftoning based on direct binary search (DBS). The DBS optimization framework has been modified for designing clustered-dot texture, by using filters with different sizes in the initialization and update steps of the algorithm. Following an intuitive explanation of how the clustered-dot texture results from this modified framework, we derive a closed-form cost metric which, when minimized, equivalently generates stochastic clustered-dot texture. An analysis of the cost metric and its influence on the texture quality is presented, which is followed by a modification to the cost metric to reduce computational cost and to make it more suitable for screen design.

Solution of the exact equations for three-dimensional atmospheric entry using directly matched asymptotic expansions

NASA Technical Reports Server (NTRS)

Busemann, A.; Vinh, N. X.; Culp, R. D.

1976-01-01

The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations.

Complex deformation routes for direct recycling aluminium alloy scrap via industrial hot extrusion

NASA Astrophysics Data System (ADS)

Paraskevas, Dimos; Kellens, Karel; Kampen, Carlos; Mohammadi, Amirahmad; Duflou, Joost R.

2018-05-01

This paper presents the final results of an industrial project, aiming for direct hot extrusion of wrought aluminium alloy scrap at an industrial scale. Two types of complex deformation/extrusion routes were tested for the production of the same profile, starting from AA6060 scrap in form of machining chips. More specifically scrap-based billets were extruded through: a 2-porthole and a 4-porthole die-set, modified for enhanced scrap consolidation and grain refinement. For comparison reasons, cast billets of the same alloy were extruded through the modified 2-porthole die set. The tensile testing results as well as microstructural investigations show that the 4-porthole extrusion route further improves scrap consolidation compared to the 2-porthole die output. The successful implementation of solid state recycling, directly at industrial level, indicates the technological readiness level of this research.

Direct Measurement of Cyclic Current-Voltage Responses of Integral Membrane Proteins at a Self-Assembled Lipid-Bilayer-Modified Electrode: Cytochrome f and Cytochrome c Oxidase

NASA Astrophysics Data System (ADS)

Salamon, Z.; Hazzard, J. T.; Tollin, G.

1993-07-01

Direct cyclic voltage-current responses, produced in the absence of redox mediators, for two detergent-solubilized integral membrane proteins, spinach cytochrome f and beef heart cytochrome c oxidase, have been obtained at an optically transparent indium oxide electrode modified with a self-assembled lipid-bilayer membrane. The results indicate that both proteins interact with the lipid membrane so as to support quasi-reversible electron transfer redox reactions at the semiconductor electrode. The redox potentials that were obtained from analysis of the cyclic "voltammograms," 365 mV for cytochrome f and 250 and 380 mV for cytochrome c oxidase (vs. normal hydrogen electrode), compare quite well with the values reported by using conventional titration methods. The ability to obtain direct electrochemical measurements opens up another approach to the investigation of the properties of integral membrane redox proteins.

Influence of Shear Stiffness Degradation on Crack Paths in Uni-Directional Composite Laminates

NASA Technical Reports Server (NTRS)

Satyanarayana, Arunkumar; Bogert, Phil B.

2017-01-01

Influence of shear stiffness degradation in an element, due to damage, on crack paths in uni-directional laminates has been demonstrated. A new shear stiffness degradation approach to improve crack path prediction has been developed and implemented in an ABAQUS/Explicit frame work using VUMAT. Three progressive failure analysis models, built-in ABAQUS (TradeMark), original COmplete STress Reduction (COSTR) and the modified COSTR damage models have been utilized in this study to simulate crack paths in five unidirectional notched laminates, 15deg, 30deg, 45deg, 60deg and 75deg under uniaxial tension load. Results such as crack paths and load vs. edge displacement curves are documented in this report. Modified COSTR damage model shows better accuracy in predicting crack paths in all the uni-directional laminates compared to the ABAQUS (TradeMark) and the original COSTR damage models.

Application of modified Rosenbrock's method for optimization of nutrient media used in microorganism culturing.

PubMed

Votruba, J; Pilát, P; Prokop, A

1975-12-01

The Rosenbrock's procedure has been modified for optimization of nutrient medium composition and has been found to be less tedious than the Box-Wilson method, especially for larger numbers of optimized parameters. Its merits are particularly obvious with multiparameter optimization where the gradient method, so far the only one employed in microbiology from a variety of optimization methods (e.g., refs, 9 and 10), becomes impractical because of the excessive number of experiments required. The method suggested is also more stable during optimization than the gradient methods which are very sensitive to the selection of steps in the direction of the gradient and may thus easily shoot out of the optimized region. It is also anticipated that other direct search methods, particularly simplex design, may be easily adapted for optimization of medium composition. It is obvious that direct search methods may find an application in process improvement in antibiotic and related industries.

Strategies used for genetically modifying bacterial genome: ite-directed mutagenesis, gene inactivation, and gene over-expression*

PubMed Central

Xu, Jian-zhong; Zhang, Wei-guo

2016-01-01

With the availability of the whole genome sequence of Escherichia coli or Corynebacterium glutamicum, strategies for directed DNA manipulation have developed rapidly. DNA manipulation plays an important role in understanding the function of genes and in constructing novel engineering bacteria according to requirement. DNA manipulation involves modifying the autologous genes and expressing the heterogenous genes. Two alternative approaches, using electroporation linear DNA or recombinant suicide plasmid, allow a wide variety of DNA manipulation. However, the over-expression of the desired gene is generally executed via plasmid-mediation. The current review summarizes the common strategies used for genetically modifying E. coli and C. glutamicum genomes, and discusses the technical problem of multi-layered DNA manipulation. Strategies for gene over-expression via integrating into genome are proposed. This review is intended to be an accessible introduction to DNA manipulation within the bacterial genome for novices and a source of the latest experimental information for experienced investigators. PMID:26834010

40 CFR 230.23 - Current patterns and water circulation.

Code of Federal Regulations, 2012 CFR

2012-07-01

... or fill material can modify current patterns and water circulation by obstructing flow, changing the direction or velocity of water flow, changing the direction or velocity of water flow and circulation, or otherwise changing the dimensions of a water body. As a result, adverse changes can occur in: Location...

40 CFR 230.23 - Current patterns and water circulation.

Code of Federal Regulations, 2011 CFR

2011-07-01

... or fill material can modify current patterns and water circulation by obstructing flow, changing the direction or velocity of water flow, changing the direction or velocity of water flow and circulation, or otherwise changing the dimensions of a water body. As a result, adverse changes can occur in: Location...

40 CFR 230.23 - Current patterns and water circulation.

Code of Federal Regulations, 2014 CFR

2014-07-01

... or fill material can modify current patterns and water circulation by obstructing flow, changing the direction or velocity of water flow, changing the direction or velocity of water flow and circulation, or otherwise changing the dimensions of a water body. As a result, adverse changes can occur in: Location...

Direct cellobiose production from cellulose using sextuple beta-glucosidase gene deletion Neurospora crassa mutants

USDA-ARS?s Scientific Manuscript database

Direct cellobiose production from cellulose by a genetically modified fungus—Neurospora crassa, was explored in this study. A library of N. crassa sextuple beta-glucosidase (bgl) gene deletion strains was constructed. Various concentrations of cellobiose were detected in the culture broth of the N. ...

BIOSENSOR FOR DIRECT DETERMINATION OF ORGANOPHOSPHATE NERVE AGENTS. 1. POTENTIOMETRIC ENZYME ELECTRODE. (R823663)

EPA Science Inventory

A potentiometric enzyme electrode for the direct measurement of organophosphate (OP)
nerve agents was developed. The basic element of this enzyme electrode was a pH electrode
modified with an immobilized organophosphorus hydrolase (OPH) layer formed by cross-linking
OPH ...

76 FR 55614 - Airworthiness Directives; Pacific Aerospace Limited Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2011-09-08

...-0971; Directorate Identifier 2011-CE-030-AD] RIN 2120-AA64 Airworthiness Directives; Pacific Aerospace... (AD) for Pacific Aerospace Limited Models FU24-954 and FU24A-954 airplanes modified with an unapproved... INFORMATION CONTACT: Karl Schletzbaum, Aerospace Engineer, FAA, Small Airplane Directorate, 901 Locust, Room...

Lip Movement Exaggerations during Infant-Directed Speech

ERIC Educational Resources Information Center

Green, Jordan R.; Nip, Ignatius S. B.; Wilson, Erin M.; Mefferd, Antje S.; Yunusova, Yana

2010-01-01

Purpose: Although a growing body of literature has identified the positive effects of visual speech on speech and language learning, oral movements of infant-directed speech (IDS) have rarely been studied. This investigation used 3-dimensional motion capture technology to describe how mothers modify their lip movements when talking to their…

Center for Adaptive Optics | Home

Science.gov Websites

Center for Adaptive Optics A University of California Science and Technology Center home Directions to The Center for Adaptive Optics Building Directions to the Center for Adaptive Optics Building * Seaway Inn * West Cliff Inn Last Modified: Apr 3, 2012 Center for Adaptive Optics | Search | The Center

77 FR 20746 - Airworthiness Directives; Bombardier, Inc. Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2012-04-06

...). SUMMARY: We propose to adopt a new airworthiness directive (AD) for certain Bombardier, Inc. Model CL-600.../ malfunctioning of the left-hand engine thrust control mechanism. This proposed AD would require modifying the left-hand engine upper core- cowl. We are proposing this AD to prevent jamming/malfunctioning of the...

77 FR 37342 - Airworthiness Directives; Bombardier, Inc. Airplanes

Federal Register 2010, 2011, 2012, 2013, 2014

2012-06-21

...). SUMMARY: We propose to adopt a new airworthiness directive (AD) for certain Bombardier, Inc. Model CL-600... was prompted by reports of jamming/malfunctioning of the left-hand engine thrust control mechanism. This proposed AD would require modifying the left-hand engine upper core-cowl. We are proposing this AD...

Direct parametric reconstruction in dynamic PET myocardial perfusion imaging: in vivo studies.

PubMed

Petibon, Yoann; Rakvongthai, Yothin; El Fakhri, Georges; Ouyang, Jinsong

2017-05-07

Dynamic PET myocardial perfusion imaging (MPI) used in conjunction with tracer kinetic modeling enables the quantification of absolute myocardial blood flow (MBF). However, MBF maps computed using the traditional indirect method (i.e. post-reconstruction voxel-wise fitting of kinetic model to PET time-activity-curves-TACs) suffer from poor signal-to-noise ratio (SNR). Direct reconstruction of kinetic parameters from raw PET projection data has been shown to offer parametric images with higher SNR compared to the indirect method. The aim of this study was to extend and evaluate the performance of a direct parametric reconstruction method using in vivo dynamic PET MPI data for the purpose of quantifying MBF. Dynamic PET MPI studies were performed on two healthy pigs using a Siemens Biograph mMR scanner. List-mode PET data for each animal were acquired following a bolus injection of ~7-8 mCi of 18 F-flurpiridaz, a myocardial perfusion agent. Fully-3D dynamic PET sinograms were obtained by sorting the coincidence events into 16 temporal frames covering ~5 min after radiotracer administration. Additionally, eight independent noise realizations of both scans-each containing 1/8th of the total number of events-were generated from the original list-mode data. Dynamic sinograms were then used to compute parametric maps using the conventional indirect method and the proposed direct method. For both methods, a one-tissue compartment model accounting for spillover from the left and right ventricle blood-pools was used to describe the kinetics of 18 F-flurpiridaz. An image-derived arterial input function obtained from a TAC taken in the left ventricle cavity was used for tracer kinetic analysis. For the indirect method, frame-by-frame images were estimated using two fully-3D reconstruction techniques: the standard ordered subset expectation maximization (OSEM) reconstruction algorithm on one side, and the one-step late maximum a posteriori (OSL-MAP) algorithm on the other side, which incorporates a quadratic penalty function. The parametric images were then calculated using voxel-wise weighted least-square fitting of the reconstructed myocardial PET TACs. For the direct method, parametric images were estimated directly from the dynamic PET sinograms using a maximum a posteriori (MAP) parametric reconstruction algorithm which optimizes an objective function comprised of the Poisson log-likelihood term, the kinetic model and a quadratic penalty function. Maximization of the objective function with respect to each set of parameters was achieved using a preconditioned conjugate gradient algorithm with a specifically developed pre-conditioner. The performance of the direct method was evaluated by comparing voxel- and segment-wise estimates of [Formula: see text], the tracer transport rate (ml · min -1 · ml -1 ), to those obtained using the indirect method applied to both OSEM and OSL-MAP dynamic reconstructions. The proposed direct reconstruction method produced [Formula: see text] maps with visibly lower noise than the indirect method based on OSEM and OSL-MAP reconstructions. At normal count levels, the direct method was shown to outperform the indirect method based on OSL-MAP in the sense that at matched level of bias, reduced regional noise levels were obtained. At lower count levels, the direct method produced [Formula: see text] estimates with significantly lower standard deviation across noise realizations than the indirect method based on OSL-MAP at matched bias level. In all cases, the direct method yielded lower noise and standard deviation than the indirect method based on OSEM. Overall, the proposed direct reconstruction offered a better bias-variance tradeoff than the indirect method applied to either OSEM and OSL-MAP. Direct parametric reconstruction as applied to in vivo dynamic PET MPI data is therefore a promising method for producing MBF maps with lower variance.

Direct parametric reconstruction in dynamic PET myocardial perfusion imaging: in-vivo studies

PubMed Central

Petibon, Yoann; Rakvongthai, Yothin; Fakhri, Georges El; Ouyang, Jinsong

2017-01-01

Dynamic PET myocardial perfusion imaging (MPI) used in conjunction with tracer kinetic modeling enables the quantification of absolute myocardial blood flow (MBF). However, MBF maps computed using the traditional indirect method (i.e. post-reconstruction voxel-wise fitting of kinetic model to PET time-activity-curves -TACs) suffer from poor signal-to-noise ratio (SNR). Direct reconstruction of kinetic parameters from raw PET projection data has been shown to offer parametric images with higher SNR compared to the indirect method. The aim of this study was to extend and evaluate the performance of a direct parametric reconstruction method using in-vivo dynamic PET MPI data for the purpose of quantifying MBF. Dynamic PET MPI studies were performed on two healthy pigs using a Siemens Biograph mMR scanner. List-mode PET data for each animal were acquired following a bolus injection of ~7-8 mCi of 18F-flurpiridaz, a myocardial perfusion agent. Fully-3D dynamic PET sinograms were obtained by sorting the coincidence events into 16 temporal frames covering ~5 min after radiotracer administration. Additionally, eight independent noise realizations of both scans - each containing 1/8th of the total number of events - were generated from the original list-mode data. Dynamic sinograms were then used to compute parametric maps using the conventional indirect method and the proposed direct method. For both methods, a one-tissue compartment model accounting for spillover from the left and right ventricle blood-pools was used to describe the kinetics of 18F-flurpiridaz. An image-derived arterial input function obtained from a TAC taken in the left ventricle cavity was used for tracer kinetic analysis. For the indirect method, frame-by-frame images were estimated using two fully-3D reconstruction techniques: the standard Ordered Subset Expectation Maximization (OSEM) reconstruction algorithm on one side, and the One-Step Late Maximum a Posteriori (OSL-MAP) algorithm on the other side, which incorporates a quadratic penalty function. The parametric images were then calculated using voxel-wise weighted least-square fitting of the reconstructed myocardial PET TACs. For the direct method, parametric images were estimated directly from the dynamic PET sinograms using a maximum a posteriori (MAP) parametric reconstruction algorithm which optimizes an objective function comprised of the Poisson log-likelihood term, the kinetic model and a quadratic penalty function. Maximization of the objective function with respect to each set of parameters was achieved using a preconditioned conjugate gradient algorithm with a specifically developed pre-conditioner. The performance of the direct method was evaluated by comparing voxel- and segment-wise estimates of K1, the tracer transport rate (mL.min−1.mL−1), to those obtained using the indirect method applied to both OSEM and OSL-MAP dynamic reconstructions. The proposed direct reconstruction method produced K1 maps with visibly lower noise than the indirect method based on OSEM and OSL-MAP reconstructions. At normal count levels, the direct method was shown to outperform the indirect method based on OSL-MAP in the sense that at matched level of bias, reduced regional noise levels were obtained. At lower count levels, the direct method produced K1 estimates with significantly lower standard deviation across noise realizations than the indirect method based on OSL-MAP at matched bias level. In all cases, the direct method yielded lower noise and standard deviation than the indirect method based on OSEM. Overall, the proposed direct reconstruction offered a better bias-variance tradeoff than the indirect method applied to either OSEM and OSL-MAP. Direct parametric reconstruction as applied to in-vivo dynamic PET MPI data is therefore a promising method for producing MBF maps with lower variance. PMID:28379843

Direct parametric reconstruction in dynamic PET myocardial perfusion imaging: in vivo studies

NASA Astrophysics Data System (ADS)

Petibon, Yoann; Rakvongthai, Yothin; El Fakhri, Georges; Ouyang, Jinsong

2017-05-01

Dynamic PET myocardial perfusion imaging (MPI) used in conjunction with tracer kinetic modeling enables the quantification of absolute myocardial blood flow (MBF). However, MBF maps computed using the traditional indirect method (i.e. post-reconstruction voxel-wise fitting of kinetic model to PET time-activity-curves-TACs) suffer from poor signal-to-noise ratio (SNR). Direct reconstruction of kinetic parameters from raw PET projection data has been shown to offer parametric images with higher SNR compared to the indirect method. The aim of this study was to extend and evaluate the performance of a direct parametric reconstruction method using in vivo dynamic PET MPI data for the purpose of quantifying MBF. Dynamic PET MPI studies were performed on two healthy pigs using a Siemens Biograph mMR scanner. List-mode PET data for each animal were acquired following a bolus injection of ~7-8 mCi of 18F-flurpiridaz, a myocardial perfusion agent. Fully-3D dynamic PET sinograms were obtained by sorting the coincidence events into 16 temporal frames covering ~5 min after radiotracer administration. Additionally, eight independent noise realizations of both scans—each containing 1/8th of the total number of events—were generated from the original list-mode data. Dynamic sinograms were then used to compute parametric maps using the conventional indirect method and the proposed direct method. For both methods, a one-tissue compartment model accounting for spillover from the left and right ventricle blood-pools was used to describe the kinetics of 18F-flurpiridaz. An image-derived arterial input function obtained from a TAC taken in the left ventricle cavity was used for tracer kinetic analysis. For the indirect method, frame-by-frame images were estimated using two fully-3D reconstruction techniques: the standard ordered subset expectation maximization (OSEM) reconstruction algorithm on one side, and the one-step late maximum a posteriori (OSL-MAP) algorithm on the other side, which incorporates a quadratic penalty function. The parametric images were then calculated using voxel-wise weighted least-square fitting of the reconstructed myocardial PET TACs. For the direct method, parametric images were estimated directly from the dynamic PET sinograms using a maximum a posteriori (MAP) parametric reconstruction algorithm which optimizes an objective function comprised of the Poisson log-likelihood term, the kinetic model and a quadratic penalty function. Maximization of the objective function with respect to each set of parameters was achieved using a preconditioned conjugate gradient algorithm with a specifically developed pre-conditioner. The performance of the direct method was evaluated by comparing voxel- and segment-wise estimates of {{K}1} , the tracer transport rate (ml · min-1 · ml-1), to those obtained using the indirect method applied to both OSEM and OSL-MAP dynamic reconstructions. The proposed direct reconstruction method produced {{K}1} maps with visibly lower noise than the indirect method based on OSEM and OSL-MAP reconstructions. At normal count levels, the direct method was shown to outperform the indirect method based on OSL-MAP in the sense that at matched level of bias, reduced regional noise levels were obtained. At lower count levels, the direct method produced {{K}1} estimates with significantly lower standard deviation across noise realizations than the indirect method based on OSL-MAP at matched bias level. In all cases, the direct method yielded lower noise and standard deviation than the indirect method based on OSEM. Overall, the proposed direct reconstruction offered a better bias-variance tradeoff than the indirect method applied to either OSEM and OSL-MAP. Direct parametric reconstruction as applied to in vivo dynamic PET MPI data is therefore a promising method for producing MBF maps with lower variance.

Pesticide Multiresidue Analysis in Cereal Grains Using Modified QuEChERS Method Combined with Automated Direct Sample Introduction GC-TOFMS and UPLC-MS/MS Techniques

USDA-ARS?s Scientific Manuscript database

The QuEChERS (quick, easy, cheap, effective, rugged, and safe) sample preparation method was modified to accommodate various cereal grain matrices (corn, oat, rice and wheat) and provide good analytical results (recoveries in the range of 70-120% and RSDs <20%) for the majority of the target pestici...

Chemically-modified cellulose paper as a microstructured catalytic reactor.

PubMed

Koga, Hirotaka; Kitaoka, Takuya; Isogai, Akira

2015-01-15

We discuss the successful use of chemically-modified cellulose paper as a microstructured catalytic reactor for the production of useful chemicals. The chemical modification of cellulose paper was achieved using a silane-coupling technique. Amine-modified paper was directly used as a base catalyst for the Knoevenagel condensation reaction. Methacrylate-modified paper was used for the immobilization of lipase and then in nonaqueous transesterification processes. These catalytic paper materials offer high reaction efficiencies and have excellent practical properties. We suggest that the paper-specific interconnected microstructure with pulp fiber networks provides fast mixing of the reactants and efficient transport of the reactants to the catalytically-active sites. This concept is expected to be a promising route to green and sustainable chemistry.

Modified Gaussian influence function of deformable mirror actuators.

PubMed

Huang, Linhai; Rao, Changhui; Jiang, Wenhan

2008-01-07

A new deformable mirror influence function based on a Gaussian function is introduced to analyze the fitting capability of a deformable mirror. The modified expressions for both azimuthal and radial directions are presented based on the analysis of the residual error between a measured influence function and a Gaussian influence function. With a simplex search method, we further compare the fitting capability of our proposed influence function to fit the data produced by a Zygo interferometer with that of a Gaussian influence function. The result indicates that the modified Gaussian influence function provides much better performance in data fitting.

Biofouling-resistant ceragenin-modified materials and structures for water treatment

DOEpatents

Hibbs, Michael; Altman, Susan J.; Jones, Howland D. T.; Savage, Paul B.

2013-09-10

This invention relates to methods for chemically grafting and attaching ceragenin molecules to polymer substrates; methods for synthesizing ceragenin-containing copolymers; methods for making ceragenin-modified water treatment membranes and spacers; and methods of treating contaminated water using ceragenin-modified treatment membranes and spacers. Ceragenins are synthetically produced antimicrobial peptide mimics that display broad-spectrum bactericidal activity. Alkene-functionalized ceragenins (e.g., acrylamide-functionalized ceragenins) can be attached to polyamide reverse osmosis membranes using amine-linking, amide-linking, UV-grafting, or silane-coating methods. In addition, silane-functionalized ceragenins can be directly attached to polymer surfaces that have free hydroxyls.

The application of epoxy resin coating in grounding grid

NASA Astrophysics Data System (ADS)

Hu, Q.; Chen, Z. R.; Xi, L. J.; Wang, X. Y.; Wang, H. F.

2018-01-01

Epoxy resin anticorrosion coating is widely used in grounding grid corrosion protection because of its wide range of materials, good antiseptic effect and convenient processing. Based on the latest research progress, four kinds of epoxy anticorrosive coatings are introduced, which are structural modified epoxy coating, inorganic modified epoxy coating, organic modified epoxy coating and polyaniline / epoxy resin composite coating. In this paper, the current research progress of epoxy base coating is analyzed, and prospected the possible development direction of the anti-corrosion coating in the grounding grid, which provides a reference for coating corrosion prevention of grounding materials.

Biocompatible patterning of proteins on wettability gradient surface by thermo-transfer printing.

PubMed

Kim, Sungho; Ryu, Yong-Sang; Suh, Jeng-Hun; Keum, Chang-Min; Sohn, Youngjoo; Lee, Sin-Doo

2014-08-01

We develop a simple and biocompatible method of patterning proteins on a wettability gradient surface by thermo-transfer printing. The wettability gradient is produced on a poly(dimethylsiloxane) (PDMS)-modified glass substrate through the temperature gradient during thermo-transfer printing. The water contact angle on the PDMS-modified surface is found to gradually increase along the direction of the temperature gradient from a low to a high temperature region. Based on the wettability gradient, the gradual change in the adsorption and immobilization of proteins (cholera toxin B subunit) is achieved in a microfluidic cell with the PDMS-modified surface.

Modified locking thread form for fastener

NASA Technical Reports Server (NTRS)

Roopnarine, (Inventor); Vranish, John D. (Inventor)

1998-01-01

A threaded fastener has a standard part with a standard thread form characterized by thread walls with a standard included angle, and a modified part complementary to the standard part having a modified thread form characterized by thread walls which are symmetrically inclined with a modified included angle that is different from the standard included angle of the standard part's thread walls, such that the threads of one part make pre-loaded edge contact with the thread walls of the other part. The thread form of the modified part can have an included angle that is greater, less, or compound as compared to the included angle of the standard part. The standard part may be a bolt and the modified part a nut, or vice versa. The modified thread form holds securely even under large vibrational forces, it permits bi-directional use of standard mating threads, is impervious to the build up of tolerances and can be manufactured with a wider range of tolerances without loss of functionality, and distributes loading stresses (per thread) in a manner that decreases the possibility of single thread failure.

Effect of Alloy 625 Buffer Layer on Hardfacing of Modified 9Cr-1Mo Steel Using Nickel Base Hardfacing Alloy

NASA Astrophysics Data System (ADS)

Chakraborty, Gopa; Das, C. R.; Albert, S. K.; Bhaduri, A. K.; Murugesan, S.; Dasgupta, Arup

2016-04-01

Dashpot piston, made up of modified 9Cr-1Mo steel, is a part of diverse safety rod used for safe shutdown of a nuclear reactor. This component was hardfaced using nickel base AWS ER NiCr-B alloy and extensive cracking was experienced during direct deposition of this alloy on dashpot piston. Cracking reduced considerably and the component was successfully hardfaced by application of Inconel 625 as buffer layer prior to hardface deposition. Hence, a separate study was undertaken to investigate the role of buffer layer in reducing the cracking and on the microstructure of the hardfaced deposit. Results indicate that in the direct deposition of hardfacing alloy on modified 9Cr-1Mo steel, both heat-affected zone (HAZ) formed and the deposit layer are hard making the thickness of the hard layer formed equal to combined thickness of both HAZ and deposit. This hard layer is unable to absorb thermal stresses resulting in the cracking of the deposit. By providing a buffer layer of Alloy 625 followed by a post-weld heat treatment, HAZ formed in the modified 9Cr-1Mo steel is effectively tempered, and HAZ formed during the subsequent deposition of the hardfacing alloy over the Alloy 625 buffer layer is almost completely confined to Alloy 625, which does not harden. This reduces the cracking susceptibility of the deposit. Further, unlike in the case of direct deposition on modified 9Cr-1Mo steel, dilution of the deposit by Ni-base buffer layer does not alter the hardness of the deposit and desired hardness on the deposit surface could be achieved even with lower thickness of the deposit. This gives an option for reducing the recommended thickness of the deposit, which can also reduce the risk of cracking.

Beta-globin LCR and intron elements cooperate and direct spatial reorganization for gene therapy.

PubMed

Buzina, Alla; Lo, Mandy Y M; Moffett, Angela; Hotta, Akitsu; Fussner, Eden; Bharadwaj, Rikki R; Pasceri, Peter; Garcia-Martinez, J Victor; Bazett-Jones, David P; Ellis, James

2008-04-11

The Locus Control Region (LCR) requires intronic elements within beta-globin transgenes to direct high level expression at all ectopic integration sites. However, these essential intronic elements cannot be transmitted through retrovirus vectors and their deletion may compromise the therapeutic potential for gene therapy. Here, we systematically regenerate functional beta-globin intron 2 elements that rescue LCR activity directed by 5'HS3. Evaluation in transgenic mice demonstrates that an Oct-1 binding site and an enhancer in the intron cooperate to increase expression levels from LCR globin transgenes. Replacement of the intronic AT-rich region with the Igmu 3'MAR rescues LCR activity in single copy transgenic mice. Importantly, a combination of the Oct-1 site, Igmu 3'MAR and intronic enhancer in the BGT158 cassette directs more consistent levels of expression in transgenic mice. By introducing intron-modified transgenes into the same genomic integration site in erythroid cells, we show that BGT158 has the greatest transcriptional induction. 3D DNA FISH establishes that induction stimulates this small 5'HS3 containing transgene and the endogenous locus to spatially reorganize towards more central locations in erythroid nuclei. Electron Spectroscopic Imaging (ESI) of chromatin fibers demonstrates that ultrastructural heterochromatin is primarily perinuclear and does not reorganize. Finally, we transmit intron-modified globin transgenes through insulated self-inactivating (SIN) lentivirus vectors into erythroid cells. We show efficient transfer and robust mRNA and protein expression by the BGT158 vector, and virus titer improvements mediated by the modified intron 2 in the presence of an LCR cassette composed of 5'HS2-4. Our results have important implications for the mechanism of LCR activity at ectopic integration sites. The modified transgenes are the first to transfer intronic elements that potentiate LCR activity and are designed to facilitate correction of hemoglobinopathies using single copy vectors.

Selective Enrichment and Direct Analysis of Protein S-Palmitoylation Sites.

PubMed

Thinon, Emmanuelle; Fernandez, Joseph P; Molina, Henrik; Hang, Howard C

2018-05-04

S-Fatty-acylation is the covalent attachment of long chain fatty acids, predominately palmitate (C16:0, S-palmitoylation), to cysteine (Cys) residues via a thioester linkage on proteins. This post-translational and reversible lipid modification regulates protein function and localization in eukaryotes and is important in mammalian physiology and human diseases. While chemical labeling methods have improved the detection and enrichment of S-fatty-acylated proteins, mapping sites of modification and characterizing the endogenously attached fatty acids are still challenging. Here, we describe the integration and optimization of fatty acid chemical reporter labeling with hydroxylamine-mediated enrichment of S-fatty-acylated proteins and direct tagging of modified Cys residues to selectively map lipid modification sites. This afforded improved enrichment and direct identification of many protein S-fatty-acylation sites compared to previously described methods. Notably, we directly identified the S-fatty-acylation sites of IFITM3, an important interferon-stimulated inhibitor of virus entry, and we further demonstrated that the highly conserved Cys residues are primarily modified by palmitic acid. The methods described here should facilitate the direct analysis of protein S-fatty-acylation sites and their endogenously attached fatty acids in diverse cell types and activation states important for mammalian physiology and diseases.

[The effect of modified Nance arch on treating maxillary impacted canine transposed with first premolar].

PubMed

Xu, Qing-chao; Sun, Hao; Lin, Yan; Wang, Xiu-ying; Hu, Rong-dang

2015-10-01

To explore the effect of modified Nance arch on treating maxillary canine-first premolar transposition cases, in which the anchorage and force direction were discussed. Modified Nance arch was applied to 5 cases with maxillary impacted canine-first premolar transposition. First, a lingual knot button was bonded on the surface of the canine crown. Modified Nance arch was decorated with a hook that moved horizontally and buccally. Then the location of the hook was gradually adjusted in order to move the canine cross the root of the first premolar and move the canine to the right position. At last the canine was moved downward by straight wire appliance. Five maxillary transposed canines were fully erupted in their right position, with normal pulp activity and gingival morphology. No obvious root resorption was detected. The mean treatment time was 30 months. Modified Nance arch has advantages in treating canine-first premolar transposition.

Ecological trade-offs between jasmonic acid-dependent direct and indirect plant defences in tritrophic interactions

PubMed Central

Wei, Jianing; Wang, Lizhong; Zhao, Jiuhai; Li, Chuanyou; Ge, Feng; Kang, Le

2011-01-01

Recent studies on plants genetically modified in jasmonic acid (JA) signalling support the hypothesis that the jasmonate family of oxylipins plays an important role in mediating direct and indirect plant defences. However, the interaction of two modes of defence in tritrophic systems is largely unknown. In this study, we examined the preference and performance of a herbivorous leafminer (Liriomyza huidobrensis) and its parasitic wasp (Opius dissitus) on three tomato genotypes: a wild-type (WT) plant, a JA biosynthesis (spr2) mutant, and a JA-overexpression 35S::prosys plant. Their proteinase inhibitor production and volatile emission were used as direct and indirect defence factors to evaluate the responses of leafminers and parasitoids. Here, we show that although spr2 mutant plants are compromised in direct defence against the larval leafminers and in attracting parasitoids, they are less attractive to adult flies compared with WT plants. Moreover, in comparison to other genotypes, the 35S::prosys plant displays greater direct and constitutive indirect defences, but reduced success of parasitism by parasitoids. Taken together, these results suggest that there are distinguished ecological trade-offs between JA-dependent direct and indirect defences in genetically modified plants whose fitness should be assessed in tritrophic systems and under natural conditions. PMID:21039561

P-CSI v1.0, an accelerated barotropic solver for the high-resolution ocean model component in the Community Earth System Model v2.0

NASA Astrophysics Data System (ADS)

Huang, Xiaomeng; Tang, Qiang; Tseng, Yuheng; Hu, Yong; Baker, Allison H.; Bryan, Frank O.; Dennis, John; Fu, Haohuan; Yang, Guangwen

2016-11-01

In the Community Earth System Model (CESM), the ocean model is computationally expensive for high-resolution grids and is often the least scalable component for high-resolution production experiments. The major bottleneck is that the barotropic solver scales poorly at high core counts. We design a new barotropic solver to accelerate the high-resolution ocean simulation. The novel solver adopts a Chebyshev-type iterative method to reduce the global communication cost in conjunction with an effective block preconditioner to further reduce the iterations. The algorithm and its computational complexity are theoretically analyzed and compared with other existing methods. We confirm the significant reduction of the global communication time with a competitive convergence rate using a series of idealized tests. Numerical experiments using the CESM 0.1° global ocean model show that the proposed approach results in a factor of 1.7 speed-up over the original method with no loss of accuracy, achieving 10.5 simulated years per wall-clock day on 16 875 cores.

A fast and robust computational method for the ionization cross sections of the driven Schrödinger equation using an O (N) multigrid-based scheme

NASA Astrophysics Data System (ADS)

Cools, S.; Vanroose, W.

2016-03-01

This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schrödinger equation. Adding a Coupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycle efficiently removes the errors that remain after the V-cycle sweep. The combined iterative solution scheme (MG-CCCS) is shown to feature significantly improved convergence rates over the classical MG method at energies where bound states dominate the solution, resulting in a fast and scalable solution method for the complex-valued Schrödinger break-up problem for any energy regime. The proposed solver displays optimal scaling; a solution is found in a time that is linear in the number of unknowns. The method is validated on a 2D Temkin-Poet model problem, and convergence results both as a solver and preconditioner are provided to support the O (N) scalability of the method. This paper extends the applicability of the complex contour approach for far field map computation (Cools et al. (2014) [10]).

Final Report - Subcontract B623760

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

Bank, R.

2017-11-17

During my visit to LLNL during July 17{27, 2017, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from hp adaptive finite element calculations, and is implemented in the PLTMG software package, version 12. This preconditioner typically requires 3-20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive de nite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite Helmholtz equations, among others). The convergence rate is not independent ofmore » the polynomial degree p as p ! 1, but but remains strong for p 9, which is the highest polynomial degree allowed in PLTMG, due to limitations of the numerical quadrature rules implemented in the software package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.« less

Final Technical Report: Quantification of Uncertainty in Extreme Scale Computations (QUEST)

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

Knio, Omar M.

QUEST is a SciDAC Institute comprising Sandia National Laboratories, Los Alamos National Laboratory, University of Southern California, Massachusetts Institute of Technology, University of Texas at Austin, and Duke University. The mission of QUEST is to: (1) develop a broad class of uncertainty quantification (UQ) methods/tools, and (2) provide UQ expertise and software to other SciDAC projects, thereby enabling/guiding their UQ activities. The Duke effort focused on the development of algorithms and utility software for non-intrusive sparse UQ representations, and on participation in the organization of annual workshops and tutorials to disseminate UQ tools to the community, and to gather inputmore » in order to adapt approaches to the needs of SciDAC customers. In particular, fundamental developments were made in (a) multiscale stochastic preconditioners, (b) gradient-based approaches to inverse problems, (c) adaptive pseudo-spectral approximations, (d) stochastic limit cycles, and (e) sensitivity analysis tools for noisy systems. In addition, large-scale demonstrations were performed, namely in the context of ocean general circulation models.« less

Optimization of Regional Geodynamic Models for Mantle Dynamics

NASA Astrophysics Data System (ADS)

Knepley, M.; Isaac, T.; Jadamec, M. A.

2016-12-01

The SubductionGenerator program is used to construct high resolution, 3D regional thermal structures for mantle convection simulations using a variety of data sources, including sea floor ages and geographically referenced 3D slab locations based on seismic observations. The initial bulk temperature field is constructed using a half-space cooling model or plate cooling model, and related smoothing functions based on a diffusion length-scale analysis. In this work, we seek to improve the 3D thermal model and test different model geometries and dynamically driven flow fields using constraints from observed seismic velocities and plate motions. Through a formal adjoint analysis, we construct the primal-dual version of the multi-objective PDE-constrained optimization problem for the plate motions and seismic misfit. We have efficient, scalable preconditioners for both the forward and adjoint problems based upon a block preconditioning strategy, and a simple gradient update is used to improve the control residual. The full optimal control problem is formulated on a nested hierarchy of grids, allowing a nonlinear multigrid method to accelerate the solution.