A domain decomposition algorithm for elliptic problems in three dimensions
type: Item
instance of: scholarly article
title: A domain decomposition algorithm for elliptic problems in three dimensions
zbMATH Open document ID: 0724.65110
DOI: 10.1007/BF01385722
author: Barry Smith
published in: Numerische Mathematik
publication date: 1992-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133592
review text: Most domain decomposition algorithms have been developed for problems in two dimensions. One reason for this is the difficulty in devising a satisfactory, easy-to-implement, robust method of providing global communication of information for problems in three dimensions. Several methods that work well in two dimensions do not perform satisfactorily in three dimensions. A new iterative substructuring algorithm for three dimensions is proposed. It is shown that the condition number of the resulting preconditioned problem is bounded independently of the number of subdomains and that the growth is quadratic in the logarithm of the number of degrees of freedom associated with a subdomain. The condition number is also bounded independently of the jumps in the coefficients of the differential equation between subdomains. The new algorithm also has more potential parallelism than the iterative substructuring methods previously proposed for problems in three dimensions.
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4195111
zbMATH Keywords: finite elements
zbMATH Keywords: preconditioned conjugate gradient
zbMATH Keywords: domain decomposition algorithms
zbMATH Keywords: iterative substructuring algorithm
zbMATH Keywords: three dimensions
zbMATH Keywords: condition number
MaRDI profile type: Publication
cites work: A second order finite difference analog of the first biharmonic boundary value problem
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cites work: The Construction of Preconditioners for Elliptic Problems by Substructuring, IV
cites work: Q4162607
cites work: Q3811643
cites work: Iterative solvers by substructuring for the \(p\)-version finite element method
cites work: Two-level domain decomposition preconditioning for thep-version finite element method in three dimensions
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description: scientific article; zbMATH DE number 4195111