An analysis of a FETI-DP algorithm on irregular subdomains in the plane

Axel Klawonn, Oliver Rheinbach, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

In the theory for domain decomposition algorithms of the iterative substructuring family, each subdomain is typically assumed to be the union of a few coarse triangles or tetrahedra. This is an unrealistic assumption, in particular if the subdomains result from the use of a mesh partitioner, in which case they might not even have uniformly Lipschitz continuous boundaries. The purpose of this study is to derive bounds for the condition number of these preconditioned conjugate gradient methods which depend only on a parameter in an isoperimetric inequality, two geometric parameters characterizing John and uniform domains, and the maximum number of edges of any subdomain. A related purpose is to explore to what extent well-known technical tools previously developed for quite regular subdomains can be extended to much more irregular subdomains. Some of these results are valid for any John domain, while an extension theorem, which is needed in this study, requires that the subdomains have complements which are uniform. The results, so far, are complete only for problems in two dimensions. Details are worked out for a FETI-DP algorithm and numerical results support the findings. Some of the numerical experiments illustrate that care must be taken when selecting the scaling of the preconditioners in the case of irregular subdomains.

Original languageEnglish (US)
Pages (from-to)2484-2504
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume46
Issue number5
DOIs
StatePublished - 2008

Fingerprint

FETI-DP
Irregular
Conjugate gradient method
Iterative Substructuring
John Domains
Preconditioned Conjugate Gradient Method
Extension Theorem
Isoperimetric Inequality
Decomposition Algorithm
Triangular pyramid
Domain Decomposition
Condition number
Decomposition
Preconditioner
Lipschitz
Triangle
Two Dimensions
Union
Complement
Numerical Experiment

Keywords

  • Domain decomposition
  • Dual-primal FETI
  • Fractal subdomains
  • Iterative substructures
  • John and uniform domains
  • Preconditioned

ASJC Scopus subject areas

  • Numerical Analysis

Cite this

An analysis of a FETI-DP algorithm on irregular subdomains in the plane. / Klawonn, Axel; Rheinbach, Oliver; Widlund, Olof B.

In: SIAM Journal on Numerical Analysis, Vol. 46, No. 5, 2008, p. 2484-2504.

Research output: Contribution to journalArticle

Klawonn, Axel ; Rheinbach, Oliver ; Widlund, Olof B. / An analysis of a FETI-DP algorithm on irregular subdomains in the plane. In: SIAM Journal on Numerical Analysis. 2008 ; Vol. 46, No. 5. pp. 2484-2504.
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