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

Abderrahmane Bendali (1, 2) , Yacine Boubendir (3) , Nicolas Zerbib (4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
3 NJIT - Department of Mathematical Sciences [Newark, NJ]
4 ESIGroup

The wave propagation problems addressed in this paper involve a relatively large and impenetrable surface on which is posed a comparatively small penetrable heterogeneous material. Typically the numerical solution of such kinds of problems is solved by coupling boundary and finite element methods. However, a straightforward application of this technique gives rise to some difficulties which mainly are 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.

Mots clés: Helmholtz equation; domain decomposition methods; finite element methods; boundary element method

Domaines: Analyse numérique [math.NA]

Abderrahmane Bendali, Yacine Boubendir, Nicolas Zerbib. Localized adaptive radiation condition for coupling boundary with finite element methods applied to wave propagation problems. IMA Journal of Numerical Analysis, 2014, 34 (3), pp.1240-1265. ⟨10.1093/imanum/drt038⟩. ⟨hal-00716863⟩