Generalized Kirchhoff approximation for Helmholtz equation

We give integral formulas to approximate solutions of Dirichlet and Neumann problems for Helmholtz equation at high frequencies. These approximations are valid in the complementary of a union of convex compact obstacles. The first step of the iterative procedure is the classical Kirchhoff approximation. Convergence is proved by comparison with the geometrical optics asymptotics. The method is shown to be numerically stable.