The Experts below are selected from a list of 19149 Experts worldwide ranked by ideXlab platform
Frederic Magoules - One of the best experts on this subject based on the ideXlab platform.
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GPU Accelerated Substructuring Methods for Sparse Linear Systems
2016Co-Authors: Abal-kassim Cheik Ahamed, Frederic MagoulesAbstract:In this paper, we present and analyze parallel substructuring methods based on conjugate gradient method, a iterative Krylov method, for solving Sparse Linear Systems on GPUs. Numerical experiments performed on a set of matrices coming from the finite element analysis of large scale engineering problems, show the efficiency and robustness of substructuring methods based on iterative Krylov method for solving Sparse Linear Systems in a context of a hybrid multi-core-GPU. © 2016 IEEE.
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CSE/EUC/DCABES - GPU Accelerated Substructuring Methods for Sparse Linear Systems
2016 IEEE Intl Conference on Computational Science and Engineering (CSE) and IEEE Intl Conference on Embedded and Ubiquitous Computing (EUC) and 15th , 2016Co-Authors: Abal-kassim Cheik Ahamed, Frederic MagoulesAbstract:In this paper, we present and analyze parallel substructuring methods based on conjugate gradient method, a iterative Krylov method, for solving Sparse Linear Systems on GPUs. Numerical experiments performed on a set of matrices coming from the finite element analysis of large scale engineering problems, show the efficiency and robustness of substructuring methods based on iterative Krylov method for solving Sparse Linear Systems in a context of a hybrid multi-core-GPU.
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Parallel sub-structuring methods for solving Sparse Linear Systems on a cluster of gpus
2014Co-Authors: Abal-kassim Cheik Ahamed, Frederic MagoulesAbstract:The main objective of this work consists in analyzing sub-structuring method for the parallel solution of Sparse Linear Systems with matrices arising from the discretization of partial differential equations such as finite element, finite volume and finite difference. With the success encountered by the general-purpose processing on graphics processing units (GPGPU), we develop an hybrid multi GPUs and CPUs sub-structuring algorithm. GPU computing, with CUDA, is used to accelerate the operations performed on each processor. Numerical experiments have been performed on a set of matrices arising from engineering problems. We compare C+MPI implementation on classical CPU cluster with C+MPI+CUDA on a cluster of GPU. The performance comparison shows a speed-up for the sub-structuring method up to 19 times in double precision by using CUDA.
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Iterative Methods for Sparse Linear Systems on Graphics Processing Unit
2012 IEEE 14th International Conference on High Performance Computing and Communication & 2012 IEEE 9th International Conference on Embedded Software , 2012Co-Authors: Abal-kassim Cheik Ahamed, Frederic MagoulesAbstract:Many engineering and science problems require a computational effort to solve large Sparse Linear Systems. Krylov subspace based iterative solvers have been widely used in that direction. Iterative Krylov methods involve Linear algebra operations such as summation of vectors, dot product, norm, and matrix-vector multiplication. Since these operations could be very costly in computation time on Central Processing Unit (CPU), we propose in this paper to focus on the design of iterative solvers to take advantage of massive parallelism of Graphics Processing Unit (GPU). We consider Stabilized BiConjugate Gradient (BiCGStab), Stabilized BiConjugate Gradient (L) (BiCGStabl), Generalized Conjugate Residual (P-GCR), Bi-Conjugate Gradient Conjugate Residual (P-BiCGCR), transpose-free Quasi Minimal Residual (P-tfQMR) for the solution of Sparse Linear Systems with non symmetric matrices and Conjugate Gradient (CG) for symmetric positive definite matrices. We discuss data format and data structure for Sparse matrices, and how to efficiently implement these solvers on the Nvidia's CUDA platform. The scalability and performance of the methods are tested on several engineering problems, together with numerous numerical experiments which clearly illustrate the robustness, competitiveness and efficiency of our own proper implementation compared to the existing libraries.
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HPCC-ICESS - Iterative Methods for Sparse Linear Systems on Graphics Processing Unit
2012 IEEE 14th International Conference on High Performance Computing and Communication & 2012 IEEE 9th International Conference on Embedded Software , 2012Co-Authors: Abal-kassim Cheik Ahamed, Frederic MagoulesAbstract:Many engineering and science problems require a computational effort to solve large Sparse Linear Systems. Krylov subspace based iterative solvers have been widely used in that direction. Iterative Krylov methods involve Linear algebra operations such as summation of vectors, dot product, norm, and matrix-vector multiplication. Since these operations could be very costly in computation time on Central Processing Unit (CPU), we propose in this paper to focus on the design of iterative solvers to take advantage of massive parallelism of Graphics Processing Unit (GPU). We consider Stabilized BiConjugate Gradient (BiCGStab), Stabilized BiConjugate Gradient (L) (BiCGStabl), Generalized Conjugate Residual (P-GCR), Bi-Conjugate Gradient Conjugate Residual (P-BiCGCR), transpose-free Quasi Minimal Residual (P-tfQMR) for the solution of Sparse Linear Systems with non symmetric matrices and Conjugate Gradient (CG) for symmetric positive definite matrices. We discuss data format and data structure for Sparse matrices, and how to efficiently implement these solvers on the Nvidia's CUDA platform. The scalability and performance of the methods are tested on several engineering problems, together with numerous numerical experiments which clearly illustrate the robustness, competitiveness and efficiency of our own proper implementation compared to the existing libraries.
Wenjie Kang - One of the best experts on this subject based on the ideXlab platform.
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a residual based Sparse approximate inverse preconditioning procedure for large Sparse Linear Systems
Numerical Linear Algebra With Applications, 2017Co-Authors: Zhongxiao Jia, Wenjie KangAbstract:The SPAI algorithm, a Sparse approximate inverse preconditioning technique for large Sparse Linear Systems, proposed by Grote and Huckle [SIAM J. Sci. Comput., 18 (1997), pp. 838–853.], is based on the F-norm minimization and computes a Sparse approximate inverse M of a large Sparse matrix A adaptively. However, SPAI may be costly to seek the most profitable indices at each loop and M may be ineffective for preconditioning. In this paper, we propose a residual based Sparse approximate inverse preconditioning procedure (RSAI), which, unlike SPAI, is based on only the dominant rather than all information on the current residual and augments sparsity patterns adaptively during the loops. RSAI is less costly to seek indices and is more effective to capture a good approximate sparsity pattern of A 1 than SPAI. To control the sparsity of M and reduce computational cost, we develop a practical RSAI(tol) algorithm that drops small nonzero entries in magnitude during the loops. Numerical experiments are reported to demonstrate that RSAI(tol) is at least competitive with SPAI and can be considerably more efficient and effective than SPAI. They also indicate that RSAI(tol) is comparable to the PSAI(tol) algorithm proposed by one of the authors in 2009.
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a residual based Sparse approximate inverse preconditioning procedure for large Sparse Linear Systems
arXiv: Numerical Analysis, 2015Co-Authors: Zhongxiao Jia, Wenjie KangAbstract:The SPAI algorithm, a Sparse approximate inverse preconditioning technique for large Sparse Linear Systems, proposed by Grote and Huckle [SIAM J. Sci. Comput., 18 (1997), pp.~838--853.], is based on the F-norm minimization and computes a Sparse approximate inverse $M$ of a large Sparse matrix $A$ adaptively. However, SPAI may be costly to seek the most profitable indices at each loop and $M$ may be ineffective for preconditioning. In this paper, we propose a residual based Sparse approximate inverse preconditioning procedure (RSAI), which, unlike SPAI, is based on only the {\em dominant} rather than all information on the current residual and augments sparsity patterns adaptively during the loops. RSAI is less costly to seek indices and is more effective to capture a good approximate sparsity pattern of $A^{-1}$ than SPAI. To control the sparsity of $M$ and reduce computational cost, we develop a practical RSAI($tol$) algorithm that drops small nonzero entries adaptively during the process. Numerical experiments are reported to demonstrate that RSAI($tol$) is at least competitive with SPAI and can be considerably more efficient and effective than SPAI. They also indicate that RSAI($tol$) is comparable to the PSAI($tol$) algorithm proposed by one of the authors in 2009.
Yousef Saad - One of the best experts on this subject based on the ideXlab platform.
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PPAM - pARMS: A Package for Solving General Sparse Linear Systems on Parallel Computers
Parallel Processing and Applied Mathematics, 2002Co-Authors: Yousef Saad, Masha SosonkinaAbstract:This paper presents an overview of pARMS, a package for solving Sparse Linear Systems on parallel platforms. Preconditioners constitute the most important ingredient in the solution of Linear Systems arising from realistic scientific and engineering applications. The most common parallel preconditioners used for Sparse Linear Systems adapt domain decomposition concepts to the more general framework of "distributed Sparse Linear Systems". The parallel Algebraic Recursive Multilevel Solver (pARMS ) is a recently developed package which integrates together variants from both Schwarz procedures and Schur complement-type techniques. This paper discusses a few of the main ideas and design issues of the package. A few details on the implementation of pARMS are provided.
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Parallel Iterative Methods for Sparse Linear Systems
Studies in Computational Mathematics, 2001Co-Authors: Yousef SaadAbstract:This paper presents an overview of parallel algorithms and their implementations for solving large Sparse Linear Systems which arise in scientific and engineering applications. Preconditioners constitute the most important ingredient in solving such Systems. As will be seen, the most common preconditioners used for Sparse Linear Systems adapt domain decomposition concepts to the more general framework of “distributed Sparse Linear Systems”. Variants of Schwarz procedures and Schur complement techniques will be discussed. We will also report on our own experience in the parallel implementation of a fairly complex simulation of solid-liquid flows.
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ACPC - Non-standard Parallel Solution Strategies for Distributed Sparse Linear Systems
Parallel Computation, 1999Co-Authors: Yousef Saad, Maria SosonkinaAbstract:A number of techniques are described for solving Sparse Linear Systems on parallel platforms. The general approach used is a domain-decomposition type method in which a processor is assigned a certain number of rows of the Linear system to be solved. Strategies that are discussed include non-standard graph partitioners, and a forced load-balance technique for the local iterations. A common practice when partitioning a graph is to seek to minimize the number of cut-edges and to have an equal number of equations per processor. It is shown that partitioners that take into account the values of the matrix entries may be more effective.
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Distributed Schur Complement Techniques for General Sparse Linear Systems
SIAM Journal on Scientific Computing, 1999Co-Authors: Yousef Saad, Maria SosonkinaAbstract:This paper presents a few preconditioning techniques for solving general Sparse Linear Systems on distributed memory environments. These techniques utilize the Schur complement system for deriving the preconditioning matrix in a number of ways. Two of these preconditioners consist of an approximate solution process for the global system, which exploits approximate LU factorizations for diagonal blocks of the Schur complement. Another preconditioner uses a Sparse approximate-inverse technique to obtain certain local approximations of the Schur complement. Comparisons are reported for Systems of varying difficulty.
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PARA - Solution of Distributed Sparse Linear Systems Using PSPARSLIB
Lecture Notes in Computer Science, 1998Co-Authors: Yousef Saad, Maria SosonkinaAbstract:In a parallel Linear system solution, an efficient usage of a multiprocessor system is usually achieved by implementing algorithms with high degree of parallelism and good convergence properties as well as by tuning parallel codes to a particular system. Among the software tools that facilitate this development is PSPARSLIB, a suite of codes for solving Sparse Linear Systems of equations. PSPARSLIB takes a modular approach to constructing a solution method and has logic-transparent computational kernels that can be adapted to the problem at hand. Here, we outline a few parallel solution methods incorporated recently in PSPARSLIB. We give a rationale for implementing these techniques and present several numerical experiments.
Zhongxiao Jia - One of the best experts on this subject based on the ideXlab platform.
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a residual based Sparse approximate inverse preconditioning procedure for large Sparse Linear Systems
Numerical Linear Algebra With Applications, 2017Co-Authors: Zhongxiao Jia, Wenjie KangAbstract:The SPAI algorithm, a Sparse approximate inverse preconditioning technique for large Sparse Linear Systems, proposed by Grote and Huckle [SIAM J. Sci. Comput., 18 (1997), pp. 838–853.], is based on the F-norm minimization and computes a Sparse approximate inverse M of a large Sparse matrix A adaptively. However, SPAI may be costly to seek the most profitable indices at each loop and M may be ineffective for preconditioning. In this paper, we propose a residual based Sparse approximate inverse preconditioning procedure (RSAI), which, unlike SPAI, is based on only the dominant rather than all information on the current residual and augments sparsity patterns adaptively during the loops. RSAI is less costly to seek indices and is more effective to capture a good approximate sparsity pattern of A 1 than SPAI. To control the sparsity of M and reduce computational cost, we develop a practical RSAI(tol) algorithm that drops small nonzero entries in magnitude during the loops. Numerical experiments are reported to demonstrate that RSAI(tol) is at least competitive with SPAI and can be considerably more efficient and effective than SPAI. They also indicate that RSAI(tol) is comparable to the PSAI(tol) algorithm proposed by one of the authors in 2009.
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a residual based Sparse approximate inverse preconditioning procedure for large Sparse Linear Systems
arXiv: Numerical Analysis, 2015Co-Authors: Zhongxiao Jia, Wenjie KangAbstract:The SPAI algorithm, a Sparse approximate inverse preconditioning technique for large Sparse Linear Systems, proposed by Grote and Huckle [SIAM J. Sci. Comput., 18 (1997), pp.~838--853.], is based on the F-norm minimization and computes a Sparse approximate inverse $M$ of a large Sparse matrix $A$ adaptively. However, SPAI may be costly to seek the most profitable indices at each loop and $M$ may be ineffective for preconditioning. In this paper, we propose a residual based Sparse approximate inverse preconditioning procedure (RSAI), which, unlike SPAI, is based on only the {\em dominant} rather than all information on the current residual and augments sparsity patterns adaptively during the loops. RSAI is less costly to seek indices and is more effective to capture a good approximate sparsity pattern of $A^{-1}$ than SPAI. To control the sparsity of $M$ and reduce computational cost, we develop a practical RSAI($tol$) algorithm that drops small nonzero entries adaptively during the process. Numerical experiments are reported to demonstrate that RSAI($tol$) is at least competitive with SPAI and can be considerably more efficient and effective than SPAI. They also indicate that RSAI($tol$) is comparable to the PSAI($tol$) algorithm proposed by one of the authors in 2009.
Abal-kassim Cheik Ahamed - One of the best experts on this subject based on the ideXlab platform.
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GPU Accelerated Substructuring Methods for Sparse Linear Systems
2016Co-Authors: Abal-kassim Cheik Ahamed, Frederic MagoulesAbstract:In this paper, we present and analyze parallel substructuring methods based on conjugate gradient method, a iterative Krylov method, for solving Sparse Linear Systems on GPUs. Numerical experiments performed on a set of matrices coming from the finite element analysis of large scale engineering problems, show the efficiency and robustness of substructuring methods based on iterative Krylov method for solving Sparse Linear Systems in a context of a hybrid multi-core-GPU. © 2016 IEEE.
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CSE/EUC/DCABES - GPU Accelerated Substructuring Methods for Sparse Linear Systems
2016 IEEE Intl Conference on Computational Science and Engineering (CSE) and IEEE Intl Conference on Embedded and Ubiquitous Computing (EUC) and 15th , 2016Co-Authors: Abal-kassim Cheik Ahamed, Frederic MagoulesAbstract:In this paper, we present and analyze parallel substructuring methods based on conjugate gradient method, a iterative Krylov method, for solving Sparse Linear Systems on GPUs. Numerical experiments performed on a set of matrices coming from the finite element analysis of large scale engineering problems, show the efficiency and robustness of substructuring methods based on iterative Krylov method for solving Sparse Linear Systems in a context of a hybrid multi-core-GPU.
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Iterative Methods for Sparse Linear Systems on Graphics Processing Unit
2012 IEEE 14th International Conference on High Performance Computing and Communication & 2012 IEEE 9th International Conference on Embedded Software , 2012Co-Authors: Abal-kassim Cheik Ahamed, Frederic MagoulesAbstract:Many engineering and science problems require a computational effort to solve large Sparse Linear Systems. Krylov subspace based iterative solvers have been widely used in that direction. Iterative Krylov methods involve Linear algebra operations such as summation of vectors, dot product, norm, and matrix-vector multiplication. Since these operations could be very costly in computation time on Central Processing Unit (CPU), we propose in this paper to focus on the design of iterative solvers to take advantage of massive parallelism of Graphics Processing Unit (GPU). We consider Stabilized BiConjugate Gradient (BiCGStab), Stabilized BiConjugate Gradient (L) (BiCGStabl), Generalized Conjugate Residual (P-GCR), Bi-Conjugate Gradient Conjugate Residual (P-BiCGCR), transpose-free Quasi Minimal Residual (P-tfQMR) for the solution of Sparse Linear Systems with non symmetric matrices and Conjugate Gradient (CG) for symmetric positive definite matrices. We discuss data format and data structure for Sparse matrices, and how to efficiently implement these solvers on the Nvidia's CUDA platform. The scalability and performance of the methods are tested on several engineering problems, together with numerous numerical experiments which clearly illustrate the robustness, competitiveness and efficiency of our own proper implementation compared to the existing libraries.
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HPCC-ICESS - Iterative Methods for Sparse Linear Systems on Graphics Processing Unit
2012 IEEE 14th International Conference on High Performance Computing and Communication & 2012 IEEE 9th International Conference on Embedded Software , 2012Co-Authors: Abal-kassim Cheik Ahamed, Frederic MagoulesAbstract:Many engineering and science problems require a computational effort to solve large Sparse Linear Systems. Krylov subspace based iterative solvers have been widely used in that direction. Iterative Krylov methods involve Linear algebra operations such as summation of vectors, dot product, norm, and matrix-vector multiplication. Since these operations could be very costly in computation time on Central Processing Unit (CPU), we propose in this paper to focus on the design of iterative solvers to take advantage of massive parallelism of Graphics Processing Unit (GPU). We consider Stabilized BiConjugate Gradient (BiCGStab), Stabilized BiConjugate Gradient (L) (BiCGStabl), Generalized Conjugate Residual (P-GCR), Bi-Conjugate Gradient Conjugate Residual (P-BiCGCR), transpose-free Quasi Minimal Residual (P-tfQMR) for the solution of Sparse Linear Systems with non symmetric matrices and Conjugate Gradient (CG) for symmetric positive definite matrices. We discuss data format and data structure for Sparse matrices, and how to efficiently implement these solvers on the Nvidia's CUDA platform. The scalability and performance of the methods are tested on several engineering problems, together with numerous numerical experiments which clearly illustrate the robustness, competitiveness and efficiency of our own proper implementation compared to the existing libraries.
