Geometry related convergence results for domain decomposition algorithms

Tony F. Chan*, Thomas Y. Hou, P. L. Lions

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

For general second-order elliptic partial differential equations, the Schwarz alternating procedure is proved to converge at a rate independent of the aspect ratio for L-shaped, T-shaped, and C-shaped domains. The results cover both continuous and discrete versions of the Schwarz algorithm. Moreover, they apply to the nonoverlapping Schur complement algorithms with the preconditioner proposed in Chan. In particular, it is shown that the condition number of the preconditioned interface operator is bounded by 2 for all L-shaped and T-shaped domains. This improves similar geometry-independent convergence results for the Schur complement algorithms obtained previously by Chan and Resasco.

Original languageEnglish (US)
Pages (from-to)378-391
Number of pages14
JournalSIAM Journal on Numerical Analysis
Volume28
Issue number2
DOIs
StatePublished - Jan 1 1991
Externally publishedYes

ASJC Scopus subject areas

  • Numerical Analysis

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