Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions

Maksymilian Dryja, Barry F. Smith, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

Domain decomposition methods provide powerful preconditioners for the iterative solution of large systems of algebraic equations that arise in finite element or finite difference approximations of partial differential equations. The preconditioners are constructed from exact or approximate solvers for the same partial differential equations restricted to a set of subregions into which the given region has been divided. The iterative substructuring methods based on decompositions of the region into nonoverlapping subregions form one of the main families of such algorithms. The paper presents a number of possibilities on how a variety of fast algorithms can be designed and analyzed.

Original languageEnglish (US)
Pages (from-to)1662-1694
Number of pages33
JournalSIAM Journal on Numerical Analysis
Volume31
Issue number6
StatePublished - Dec 1994

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Iterative Substructuring
Preconditioner
Elliptic Problems
Partial differential equations
Three-dimension
Partial differential equation
Domain decomposition methods
Finite Difference Approximation
Domain Decomposition Method
Iterative Solution
Iterative methods
Algebraic Equation
Fast Algorithm
Finite Element
Decomposition
Decompose

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions. / Dryja, Maksymilian; Smith, Barry F.; Widlund, Olof B.

In: SIAM Journal on Numerical Analysis, Vol. 31, No. 6, 12.1994, p. 1662-1694.

Research output: Contribution to journalArticle

Dryja, Maksymilian ; Smith, Barry F. ; Widlund, Olof B. / Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions. In: SIAM Journal on Numerical Analysis. 1994 ; Vol. 31, No. 6. pp. 1662-1694.
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