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 - 1992
EventFifth International Symposium on Domain Decomposition Methods for Partial Differential Equations - Norfolk, VA, USA
Duration: May 6 1991May 8 1991

Other

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

Fingerprint

Domain decomposition methods
Iterative methods
Wire
Decomposition

ASJC Scopus subject areas

  • Engineering(all)

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). Publ by Soc for Industrial & Applied Mathematics Publ.

Additive Schwarz methods for elliptic finite element problems in three dimensions. / Dryja, Maksymilian; Widlund, Olof B.

Domain Decomposition Methods for Partial Differential Equations. Publ by Soc for Industrial & Applied Mathematics Publ, 1992. p. 3-18.

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

Dryja, M & Widlund, OB 1992, Additive Schwarz methods for elliptic finite element problems in three dimensions. in Domain Decomposition Methods for Partial Differential Equations. Publ by Soc for Industrial & Applied Mathematics Publ, pp. 3-18, Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Norfolk, VA, USA, 5/6/91.
Dryja M, Widlund OB. Additive Schwarz methods for elliptic finite element problems in three dimensions. In Domain Decomposition Methods for Partial Differential Equations. Publ by Soc for Industrial & Applied Mathematics Publ. 1992. p. 3-18
Dryja, Maksymilian ; Widlund, Olof B. / Additive Schwarz methods for elliptic finite element problems in three dimensions. Domain Decomposition Methods for Partial Differential Equations. Publ by Soc for Industrial & Applied Mathematics Publ, 1992. pp. 3-18
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