TY - GEN
T1 - Additive Schwarz methods for elliptic finite element problems in three dimensions
AU - Dryja, Maksymilian
AU - Widlund, Olof B.
PY - 1992
Y1 - 1992
N2 - 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.
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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M3 - Conference contribution
AN - SCOPUS:0026978939
SN - 0898712882
T3 - Domain Decomposition Methods for Partial Differential Equations
SP - 3
EP - 18
BT - Domain Decomposition Methods for Partial Differential Equations
PB - Publ by Soc for Industrial & Applied Mathematics Publ
T2 - Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations
Y2 - 6 May 1991 through 8 May 1991
ER -