THE APPROXIMATE DIRICHLET DOMAIN DECOMPOSITION METHOD .1. AN ALGEBRAIC APPROACH

被引：53

作者：

HAASE, G ^{[1
]}

LANGER, U ^{[1
]}

MEYER, A ^{[1
]}

机构：

[1] INST MECH CHEMNITZ,O-9010 KARL MARX STADT,GERMANY

来源：

COMPUTING | 1991年 / 47卷 / 02期

关键词：

ELLIPTIC PROBLEMS; FINITE ELEMENTS; SUBSTRUCTURING; DOMAIN DECOMPOSITION; PRECONDITIONERS; PARALLEL ALGORITHMS;

D O I：

10.1007/BF02253431

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We present a new approach to the construction of Domain Decomposition (DD) preconditioners for the conjugate gradient method applied to the solution of symmetric and positive definite finite element equations. The DD technique is based on a non-overlapping decomposition of the domain-OMEGA into p subdomains connected later with the p processors of a MIMD computer. The DD preconditioner derived contains three block matrices which must be specified for the specific problem considered. One of the matrices is used for the transformation of the nodal finite element basis into the approximate discrete harmonic basis. The other two matrices are block preconditioners for the Dirichlet problems arising on the subdomains and for a modified Schur complement defined over all nodes on the coupling boundaries between the subdomains. The relative spectral condition number is estimated. Relations to the additive Schwarz method are discussed. In the second part of this paper, we will apply the results of this paper to two-dimensional, symmetric, second-order, elliptic boundary value problems and present numerical results performed on a transputer-network.

引用

页码：137 / 151

页数：15

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