Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners
Abstract
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.
- Authors:
-
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Univ. of Minnesota, Twin Cities, MN (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1438714
- Report Number(s):
- LLNL-JRNL-727122
Journal ID: ISSN 0895-4798
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- SIAM Journal on Matrix Analysis and Applications
- Additional Journal Information:
- Journal Volume: 38; Journal Issue: 3; Journal ID: ISSN 0895-4798
- Publisher:
- SIAM
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Sherman-Morrison-Woodbury formula; low-rank approximation; distributed sparse linear systems; parallel preconditioner; incomplete LU factorization; Krylov subspace method; domain decomposition
Citation Formats
Li, Ruipeng, and Saad, Yousef. Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners. United States: N. p., 2017.
Web. doi:10.1137/16M110486X.
Li, Ruipeng, & Saad, Yousef. Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners. United States. https://doi.org/10.1137/16M110486X
Li, Ruipeng, and Saad, Yousef. Tue .
"Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners". United States. https://doi.org/10.1137/16M110486X. https://www.osti.gov/servlets/purl/1438714.
@article{osti_1438714,
title = {Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners},
author = {Li, Ruipeng and Saad, Yousef},
abstractNote = {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.},
doi = {10.1137/16M110486X},
journal = {SIAM Journal on Matrix Analysis and Applications},
number = 3,
volume = 38,
place = {United States},
year = {Tue Aug 01 00:00:00 EDT 2017},
month = {Tue Aug 01 00:00:00 EDT 2017}
}
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