Localized adaptive radiation condition for coupling boundary and finite element methods applied to wave propagation problems

Abderrahmane Bendali, Yassine Boubendir, Nicolas Zerbib

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The wave propagation problems addressed in this paper involve a relatively large and impenetrable surface on which a comparatively small penetrable heterogeneous material is positioned. Typically the numerical solution of such problems is by coupling boundary and finite element methods. However, a straightforward application of this technique gives rise to some difficulties that are mainly related to the solution of a large linear system whose matrix consists of sparse and dense blocks. To face such difficulties, the adaptive radiation condition technique is modified by localizing the truncation interface only around the heterogeneous material. Stability and error estimates are established for the underlying approximation scheme. Some alternative methods are recalled or designed making it possible to compare the numerical efficiency of the proposed approach.

Original languageEnglish (US)
Pages (from-to)1240-1265
Number of pages26
JournalIMA Journal of Numerical Analysis
Volume34
Issue number3
DOIs
StatePublished - Jul 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Helmholtz equation
  • boundary element method
  • domain decomposition methods
  • finite element methods

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