A simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems

Daniel J. Rixen, Charbel Farhat

Research output: Contribution to journalArticlepeer-review

134 Scopus citations

Abstract

Several domain decomposition methods with Lagrange multipliers have been recently designed for solving iteratively large-scale systems of finite element equations. While these methods differ typically by implementational details, they share in most cases the same substructure based preconditioners that were originally developed for the FETI method. The success of these preconditioners is due to the fact that, for homogeneous structural mechanics problems, they ensure a computational performance that scales with the problem size. In this paper, we address the suboptimal behaviour of these preconditioners in the presence of material and/or discretization heterogeneities. We propose a simple and virtually no-cost extension of these preconditioners that exhibits scalability even for highly heterogeneous systems of equations. We consider several intricate structural analysis problems, and demonstrate numerically the optimal performance delivered by the new preconditioners for problems with discontinuities.

Original languageEnglish
Pages (from-to)489-516
Number of pages28
JournalInternational Journal for Numerical Methods in Engineering
Volume44
Issue number4
DOIs
StatePublished - 10 Feb 1999
Externally publishedYes

Keywords

  • Domain decomposition
  • Heterogeneities
  • Preconditioning
  • Scalability

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