Keywords: acoustic scattering, Helmholtz equation, boundary integral equations, finite element method, coupling, domain decomposition method, cross-points.

The main subject of this contribution is to present some recent methods, specially designed to be implemented on parallel platforms, to deal with acoustic scattering problems involving a bounded zone filled by a heterogeneous medium. The main approach is to couple a finite element method for handling this zone, with a boundary integral equation specially adapted to treat the unbounded part of the computational domain. After giving a short review of some alternative methods, we focus on the methods based on this approach and give a framework which makes it possible to construct almost all the standard boundary integral equations. As is well-known, each instance of this kind of scattering problem can be solved by a manifold of such equations. This framework allows one to have a good insight into the advantages and the drawbacks of each of them. It is seen next that the above coupling gives rise to non standard linear systems, with a matrix being partly sparse and partly dense. Serious difficulties then arise when the solution of such systems has to be tackled on a parallel platform. It is shown how techniques from domain decomposition methods can be used to efficiently overcome these difficulties.

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