Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions

Maksymilian Dryja, Barry F. Smith, Olof B. Widlund

Research output: Contribution to journalArticle


Domain decomposition methods provide powerful preconditioners for the iterative solution of large systems of algebraic equations that arise in finite element or finite difference approximations of partial differential equations. The preconditioners are constructed from exact or approximate solvers for the same partial differential equations restricted to a set of subregions into which the given region has been divided. The iterative substructuring methods based on decompositions of the region into nonoverlapping subregions form one of the main families of such algorithms. The paper presents a number of possibilities on how a variety of fast algorithms can be designed and analyzed.

Original languageEnglish (US)
Pages (from-to)1662-1694
Number of pages33
JournalSIAM Journal on Numerical Analysis
Issue number6
StatePublished - Jan 1 1994


ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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