Comparison of some domain decomposition algorithms for nonsymmetric elliptic problems

Xiao Chuan Cai*, William D. Gropp, David E. Keyes

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations

Abstract

In recent years, competitive domain-decomposed preconditioned iterative techniques have been developed for nonsymmetric elliptic problems. In these techniques, a large problem is divided into many smaller problems whose requirements for coordination can be controlled to allow effective solution on parallel machines. Central questions are how to choose these small problems and how to arrange the order of their solution. Different specifications of decomposition and solution order lead to a plethora of algorithms possessing complementary advantages and disadvantages. In this report we compare several methods, including the additive Schwarz algorithm, the multiplicative Schwarz algorithm, the tile algorithm, the CGK and CSPD algorithms, and the popular global ILU-family of preconditioners, on some nonsymmetric and/or indefinite elliptic model problems discretized by finite difference methods. The preconditioned problems are solved by the unrestarted GMRES method.

Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods for Partial Differential Equations
PublisherPubl by Soc for Industrial & Applied Mathematics Publ
Pages224-235
Number of pages12
ISBN (Print)0898712882
StatePublished - 1992
Externally publishedYes
EventFifth International Symposium on Domain Decomposition Methods for Partial Differential Equations - Norfolk, VA, USA
Duration: May 6 1991May 8 1991

Other

OtherFifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
CityNorfolk, VA, USA
Period05/6/9105/8/91

ASJC Scopus subject areas

  • Engineering(all)

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