Méthode de décomposition de domaine et éléments finis nodaux pour la résolution de l'équation d'Helmholtz

Translated title of the contribution: Domain decomposition method and nodal finite element for solving Helmholtz equation

Abderrahmane Bendali, Yassine Boubendir

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The utilization of a non-overlapping domain decomposition method, in the framework of a resolution by finite elements, requires a particular treatment of the degrees of freedom shared by more than two subdomains. This is the case, for example, when solving a Laplace or Helmholtz equation by means of a conformal nodal finite element method. For convenience, such degrees of freedom will be called 'cross-points'. We describe here an approach permitting such a treatment. In contrast to a domain decomposition method in the strict sense, our approach requires a post-processing completing each iteration, which consists of solving a system whose size is the number of cross-points. We prove that the algorithm cannot break down and that it converges.

Translated title of the contributionDomain decomposition method and nodal finite element for solving Helmholtz equation
Original languageFrench
Pages (from-to)229-234
Number of pages6
JournalComptes Rendus Mathematique
Volume339
Issue number3
DOIs
StatePublished - Aug 1 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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