Abstract
Let Ω⊂R3 be an obstacle that is a simply connected bounded domain. The exterior Dirichlet problem for the Helmholtz equation in R3\Ω with the Sommerfeld radiation condition at infinity is considered. Based on an integral representation formula, a new method to compute the solution of the exterior boundary value problem mentioned above is proposed. This method generalizes the formalism introduced for an unbounded obstacle by Milder [J. Acoust. Soc. Am. 89, 529–541 (1991)] and consists in computing a perturbation series whose coefficients are integrals. These integrals are independent one from the other so that the computation of the series is fully parallelizable. Finally, some numerical results obtained on test problems are shown. In particular, numerical experiments for obstacles with nonsmooth boundaries such as polyhedra and obstacles with multiscale corrugations are shown.
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