Non-overlapping domain decomposition method for a nodal finite element method

Abderrahmane Bendali, Yassine Boubendir

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

A new approach is proposed for constructing nonoverlapping domain decomposition procedures for solving a linear system related to a nodal finite element method. It applies to problems involving either positive semi-definite or complex indefinite local matrices. The main feature of the method is to preserve the continuity requirements on the unknowns and the finite element equations at the nodes shared by more than two subdomains and to suitably augment the local matrices. We prove that the corresponding algorithm can be seen as a converging iterative method for solving the finite element system and that it cannot break down. Each iteration is obtained by solving uncoupled local finite element systems posed in each subdomain and, in contrast to a strict domain decomposition method, is completed by solving a linear system whose unknowns are the degrees of freedom attached to the above special nodes.

Original languageEnglish (US)
Pages (from-to)515-537
Number of pages23
JournalNumerische Mathematik
Volume103
Issue number4
DOIs
StatePublished - Jun 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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