A FETI-like Domain Decomposition Method for coupling Finite Elements and Boundary Elements in large-size problems of acoustic scattering A. Bendali MIP Laboratory -UMR CNRS-INSA-UPS 5640 Mathematical Engineering Department INSA - 135 Avenue de Rangueil, 31077 Toulouse CEDEX 4, France and CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse CEDEX 1, France Y. Boubendir School of Mathematics, University of Minnesota 127 Vincent Hall, 206 Church St., S. E.Minneapolis, MN 55455, USA M. Fares CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse CEDEX 1, France June 27, 2005 Abstract Numerical simulations of acoustic scattering in the frequency domain based on hybrid methods coupling finite elements and boundary elements are the most suited for dealing with problems involving wave propagation in inhomogeneous media. Furthermore, it is necessary to resort to high performance computing to effectively solve the large size problems. How- ever, the direct coupling yields a linear system with a matrix which is partly dense and partly sparse and thus not adapted to high performance computing. To avoid this difficulty, we present a new iterative method constructed from a non overlapping domain decomposition technique. 1 Introduction The problem that we address in this paper concerns the numerical computation, using the finite element method, of a radiated or a scattered time-harmonic 1