Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

Li, Ruipeng; Saad, Yousef

doi:10.1137/16M110486X

Title: Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

Journal Article · Tue Aug 01 00:00:00 EDT 2017 · SIAM Journal on Matrix Analysis and Applications

DOI:https://doi.org/10.1137/16M110486X· OSTI ID:1438714

Li, Ruipeng ^[1]; Saad, Yousef ^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. of Minnesota, Twin Cities, MN (United States)

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. Comparisons with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1438714

Report Number(s):: LLNL-JRNL-727122

Journal Information:: SIAM Journal on Matrix Analysis and Applications, Vol. 38, Issue 3; ISSN 0895-4798

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 18 works

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Sherman-Morrison-Woodbury formula
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parallel preconditioner
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Title: Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

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