Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems

Xiao Chuan Cai, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

The classical Schwarz alternating method has recently been generalized in several directions. This effort has resulted in a number of new powerful domain decomposition methods for elliptic problems, in new insight into multigrid methods, and in the development of a very useful framework for the analysis of a variety of iterative methods. Most of this work has focused on positive definite, symmetric problems. In this paper, a general framework is developed for multiplicative Schwarz algorithms for nonsymmetric and indefinite problems. Several applications are then discussed including two- and multilevel Schwarz methods and iterative substructuring algorithms. Some new results on additive Schwarz methods are also presented.

Original languageEnglish (US)
Pages (from-to)936-952
Number of pages17
JournalSIAM Journal on Numerical Analysis
Volume30
Issue number4
StatePublished - Aug 1993

Fingerprint

Multiplicative
Iterative Substructuring
Schwarz Alternating Method
Additive Schwarz Method
Schwarz Methods
Domain decomposition methods
Multilevel Methods
Multigrid Method
Domain Decomposition Method
Iterative methods
Elliptic Problems
Positive definite
Iteration
Framework

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems. / Cai, Xiao Chuan; Widlund, Olof B.

In: SIAM Journal on Numerical Analysis, Vol. 30, No. 4, 08.1993, p. 936-952.

Research output: Contribution to journalArticle

Cai, Xiao Chuan ; Widlund, Olof B. / Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems. In: SIAM Journal on Numerical Analysis. 1993 ; Vol. 30, No. 4. pp. 936-952.
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