Additive Schwarz domain decomposition methods for elliptic problems on unstructured meshes

Tony F. Chan*, Jun Zou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We give several additive Schwarz domain decomposition methods for solving finite element problems which arise from the discretizations of elliptic problems on general unstructured meshes in two and three dimensions. Our theory requires no assumption (for the main results) on the substructures which constitute the whole domain, so each substructure can be of arbitrary shape and of different size. The global coarse mesh is allowed to be non-nested to the fine grid on which the discrete problem is to be solved and both the coarse meshes and the fine meshes need not be quasi-uniform. In this general setting, our algorithms have the same optimal convergence rate of the usual domain decomposition methods on structured meshes. The condition numbers of the preconditioned systems depend only on the (possibly small) overlap of the substructures and the size of the coares grid, but is independent of the sizes of the subdomains.

Original languageEnglish (US)
Pages (from-to)329-346
Number of pages18
JournalNumerical Algorithms
Issue number2
StatePublished - Sep 1994
Externally publishedYes


  • AMS(MOS) subject classification: 65N30, 65F10
  • Unstructured meshes
  • additive Schwarz algorithm
  • non-nested coarse meshes
  • optimal convergence rate

ASJC Scopus subject areas

  • Applied Mathematics


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