Additive Schwarz methods for elliptic finite element problems in three dimensions

Maksymilian Dryja, Olof B. Widlund

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Many domain decomposition algorithms and certain multigrid methods can be described and analyzed as additive Schwarz methods. When designing and analyzing domain decomposition methods, we encounter special difficulties in the case of three dimensions and if the coefficients are discontinuous and vary over a large range. In this paper, we first introduce a general framework for Schwarz methods. Three classes of applications are then considered: certain wire basket based iterative substructuring methods, Neumann-Neumann algorithms with low dimensional, global subspaces and a modified form of a multilevel algorithm introduced by Bramble, Pasciak and Xu.

Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods for Partial Differential Equations
PublisherPubl by Soc for Industrial & Applied Mathematics Publ
Pages3-18
Number of pages16
ISBN (Print)0898712882
StatePublished - Dec 1 1992
EventFifth International Symposium on Domain Decomposition Methods for Partial Differential Equations - Norfolk, VA, USA
Duration: May 6 1991May 8 1991

Publication series

NameDomain Decomposition Methods for Partial Differential Equations

Other

OtherFifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
CityNorfolk, VA, USA
Period5/6/915/8/91

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    Dryja, M., & Widlund, O. B. (1992). Additive Schwarz methods for elliptic finite element problems in three dimensions. In Domain Decomposition Methods for Partial Differential Equations (pp. 3-18). (Domain Decomposition Methods for Partial Differential Equations). Publ by Soc for Industrial & Applied Mathematics Publ.