Performance Issues for Iterative Solvers in Device Simulation

Qing, Fan; McMacken, J.; Tang, Wei-Pai

doi:10.1137/0917009

Cited by 8 publications

(4 citation statements)

References 32 publications

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“…Dense blocks have been used successfully in the past [6,7,18,29,31,34,35,36,39,45,48,55] to enhance the performance of incomplete factorization preconditioners. Many of these block algorithms are designed for symmetric positive definite (SPD) systems, which we covered in an earlier publication [29].…”

Section: Related Work LI Saad and Chowmentioning

confidence: 99%

Enhancing Performance and Robustness of ILU Preconditioners by Blocking and Selective Transposition

Gupta¹

2017

SIAM J. Sci. Comput.

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Incomplete factorization is one of the most effective general-purpose preconditioning methods for Krylov subspace solvers for large sparse systems of linear equations. Two techniques for enhancing the robustness and performance of incomplete LU factorization for sparse unsymmetric systems are described. A block incomplete factorization algorithm based on the Crout variation of LU factorization is presented. The algorithm is suitable for incorporating threshold-based dropping as well as unrestricted partial pivoting, and it overcomes several limitations of existing incomplete LU factorization algorithms with and without blocking. It is shown that blocking has a threepronged impact: it speeds up the computation of incomplete factors and the solution of the associated triangular systems, it permits denser and more robust factors to be computed economically, and it permits a trade-off with the restart parameter of GMRES to further improve the overall speed and robustness. A highly effective heuristic for improving the quality of preconditioning and subsequent convergence of the associated iterative method is presented. The choice of the Crout variant as the underlying factorization algorithm enables efficient implementation of this heuristic, which has the potential to improve both incomplete and complete sparse LU factorization of matrices that require pivoting for numerical stability.

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Section: Related Work LI Saad and Chowmentioning

confidence: 99%

Enhancing Performance and Robustness of ILU Preconditioners by Blocking and Selective Transposition

Gupta¹

2017

SIAM J. Sci. Comput.

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“…Therefore, we can expect that the degree of coupling of the off-diagonal blocks has been reduced to some extent This decoupling operator was proposed by Bank et al 27 as the Alternate-Block Factorization (ABF) procedure and is subject to further analysis in other works 28,29 . The ABF operator was successfully applied by Klie 13 for two-phase flow problems where Properties 1-5 from above were shown to be strongly satisfied under mild conditions (e.g., if blocks ps A and sp A satisfy the M-matrix condition).…”

Section: Decoupling Operatorsmentioning

confidence: 99%

“…However, in most cases reported in the literature, D 2 =I and D 1 is defined in terms of the main diagonal of the blocks involved. For instance, for the case ns np = (i.e., a two-phase flow case), we can define D 1 as13,26,29 …”

mentioning

confidence: 99%

Algebraic Multigrid Methods (AMG) for the Efficient Solution of Fully Implicit Formulations in Reservoir Simulation

Stueben

Clees

Klíe

et al. 2007

SPE Reservoir Simulation Symposium

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fax 01-972-952-9435. AbstractA primary challenge for a new generation of reservoir simulators is the accurate description of multiphase flow in highly heterogeneous media and very complex geometries. However, many initiatives in this direction have encountered difficulties in that current solver technology is still insufficient to account for the increasing complexity of coupled linear systems arising in fully implicit formulations. In this respect, a few works have made particular progress in partially exploiting the physics of the problem in the form of two-stage preconditioners.

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“…With the scaling, the performance of these same techniques are very different compared to without scaling. The benefits of scaling were discussed in several papers (for example, [25]). Table 3.6 is a comparison for test problem Pores 2.…”

Section: Wavelet Compressionmentioning

confidence: 99%

Toward an Effective Sparse Approximate Inverse Preconditioner

Tang¹

1999

SIAM J. Matrix Anal. & Appl.

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Sparse approximate inverse preconditioners have attracted much attention recently, because of their potential usefulness in a parallel environment. In this paper, we explore several performance issues related to effective sparse approximate inverse preconditioners (SAIPs) for the matrices derived from PDEs. Our refinements can significantly improve the quality of existing SAIPs and/or reduce the cost of computing them. For the test problems from the Harwell-Boeing collection and some other applications, the performance of our preconditioners can be comparable or superior to incomplete LU (ILU) preconditioners with similar preconditioning cost.

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Performance Issues for Iterative Solvers in Device Simulation

Cited by 8 publications

References 32 publications

Enhancing Performance and Robustness of ILU Preconditioners by Blocking and Selective Transposition

Enhancing Performance and Robustness of ILU Preconditioners by Blocking and Selective Transposition

Algebraic Multigrid Methods (AMG) for the Efficient Solution of Fully Implicit Formulations in Reservoir Simulation

Toward an Effective Sparse Approximate Inverse Preconditioner

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