An analysis of the BEM-FEM non-overlapping domain decomposition method for a scattering problem

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Abstract

In this paper, we analyze the BEM-FEM non-overlapping domain decomposition method introduced in Boubendir [Techniques de Décomposition de Domaine et Méthode d'Equations Intégrales, Ph.D. Thesis, INSA, Toulouse, France, 2002] and improved in Boubendir et al. [A coupling BEM-FEM method using a FETI-LIKE domain decomposition method, in: Proceedings of Waves 2005, Providence, RI, 2005, pp. 188-190] and Bendali et al. [A FETI-like domain decomposition method for coupling FEM and BEM in large-size problems of acoustic scattering, to appear.] The transmission conditions used in this method introduce a quantity that prevents the approach of Després [Méthodes de décomposition de domaine pour les problèmes de propagation d'ondes en régime harmonique, Le théorème de Borg pour l'équation de Hill vectorielle, Ph.D. Thesis, Paris VI University, France, 1991] to establish convergence to be adapted. However, we show that convergence can be established when the geometry allows for a decomposition of the solution into propagating and evanescent portions with a methodology based on modal analysis. Here, we exemplify this in the case of circular cylindrical geometries where the derivations can be based on properties of Bessel functions.

Original languageEnglish (US)
Pages (from-to)282-291
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume204
Issue number2 SPEC. ISS.
DOIs
StatePublished - Jul 15 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Bessel functions
  • Coupling BEM-FEM
  • Domain decomposition method
  • Helmholtz equation

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