Additive Schwarz methods for elliptic finite element problems in three dimensions

Maksymilian Dryja; Olof B. Widlund

Additive Schwarz methods for elliptic finite element problems in three dimensions

Maksymilian Dryja, Olof B. Widlund

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Domain Decomposition Methods for Partial Differential Equations
Publisher	Publ by Soc for Industrial & Applied Mathematics Publ
Pages	3-18
Number of pages	16
ISBN (Print)	0898712882
State	Published - 1992
Event	Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations - Norfolk, VA, USA Duration: May 6 1991 → May 8 1991

Publication series

Name	Domain Decomposition Methods for Partial Differential Equations

Other

Other	Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
City	Norfolk, VA, USA
Period	5/6/91 → 5/8/91

ASJC Scopus subject areas

General Engineering

Cite this

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 (Domain Decomposition Methods for Partial Differential Equations).

Research output: Chapter in Book/Report/Conference proceeding › Conference 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. 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.

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AB - 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.

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T2 - Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations

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ER -

Additive Schwarz methods for elliptic finite element problems in three dimensions

Abstract

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