Some nonoverlapping domain decomposition methods

Jinchao Xu, Jun Zou

Research output: Contribution to journalArticlepeer-review

164 Scopus citations


The purpose of this paper is to give a unified investigation of a class of nonoverlapping domain decomposition methods for solving second-order elliptic problems in two and three dimensions. The methods under scrutiny fall into two major categories: the substructuring-type methods and the Neumann-Neumann-type methods. The basic framework used for analysis is the parallel subspace correction method or additive Schwarz method, and other technical tools include local-global and global-local techniques. The analyses for both two- and three-dimensional cases are carried out simultaneously. Some internal relationships between various algorithms are observed and several new variants of the algorithms are also derived.

Original languageEnglish (US)
Pages (from-to)857-914
Number of pages58
JournalSIAM Review
Issue number4
StatePublished - Dec 1998

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics


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