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

In this paper, we analyze the BEM-FEM non-overlapping domain decomposition method introduced in Boubendir [Techniques de Decomposition de Domaine et Methode d'Equations Integrales, Ph.D. Thesis, INSA, Toulouse, France, 2002] and improved in Boubendirer 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 Despres [Methodes de decomposition de domaine pour les problemes de propagation d'ondes en regime harmonique, Le theoreme de Borg pour l'equation 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. (c) 2006 Elsevier B.V. All rights reserved.