Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems

Xiao Chuan Cai, Olof B. Widlund

Research output: Contribution to journalArticlepeer-review


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
Issue number4
StatePublished - 1993

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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