LowRank 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 lowrank corrections. The DD approach decouples the matrix and, once inverted, a lowrank approximation is applied by exploiting the ShermanMorrisonWoodbury formula, which yields two variants of the preconditioning methods. The lowrank 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 DDbased 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 Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1438714
 Report Number(s):
 LLNLJRNL727122
Journal ID: ISSN 08954798
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 SIAM Journal on Matrix Analysis and Applications
 Additional Journal Information:
 Journal Volume: 38; Journal Issue: 3; Journal ID: ISSN 08954798
 Publisher:
 SIAM
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ShermanMorrisonWoodbury formula; lowrank approximation; distributed sparse linear systems; parallel preconditioner; incomplete LU factorization; Krylov subspace method; domain decomposition
Citation Formats
Li, Ruipeng, and Saad, Yousef. LowRank Correction Methods for Algebraic Domain Decomposition Preconditioners. United States: N. p., 2017.
Web. doi:10.1137/16M110486X.
Li, Ruipeng, & Saad, Yousef. LowRank Correction Methods for Algebraic Domain Decomposition Preconditioners. United States. doi:10.1137/16M110486X.
Li, Ruipeng, and Saad, Yousef. Tue .
"LowRank Correction Methods for Algebraic Domain Decomposition Preconditioners". United States. doi:10.1137/16M110486X. https://www.osti.gov/servlets/purl/1438714.
@article{osti_1438714,
title = {LowRank 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 lowrank corrections. The DD approach decouples the matrix and, once inverted, a lowrank approximation is applied by exploiting the ShermanMorrisonWoodbury formula, which yields two variants of the preconditioning methods. The lowrank 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 DDbased 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},
issn = {08954798},
number = 3,
volume = 38,
place = {United States},
year = {2017},
month = {8}
}
Web of Science