Low-rank correction methods for algebraic domain decomposition preconditioners

Ruipeng Li, Yousef Saad

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

This paper 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.

Original languageEnglish (US)
Pages (from-to)807-828
Number of pages22
JournalSIAM Journal on Matrix Analysis and Applications
Volume38
Issue number3
DOIs
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Society for Industrial and Applied Mathematics.

Keywords

  • Distributed sparse linear systems
  • Domain decomposition
  • Incomplete LU factorization
  • Krylov subspace method
  • Low-rank approximation
  • Parallel preconditioner
  • Sherman–Morrison–Woodbury formula

Fingerprint

Dive into the research topics of 'Low-rank correction methods for algebraic domain decomposition preconditioners'. Together they form a unique fingerprint.

Cite this