Convergence rate estimate for a domain decomposition method

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ℝ2. We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.

Original languageEnglish (US)
Pages (from-to)153-169
Number of pages17
JournalNumerische Mathematik
Issue number1
StatePublished - Dec 1992
Externally publishedYes


  • Mathematics Subject Classification (1991): 65N30, 65F10

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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