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We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calder on projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-dierential calculus allows us to con- struct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all frequencies. An implementation technique is elaborated, where again reasonings from pseudo-dierential calculus play an important r^ ole. Some numerical examples are presented which appear to conrm that the new integral equation leads to linear systems which are much better conditioned than the classical (\direct") integral equations and hence have much better behaviour when solved with iterative techniques and matrix sparsication.

Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes