A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering

Abstract

An efficient and high-order algorithm for three-dimensional bounded obstacle scattering is developed. The method is a non-trivial extension of recent work of the authors for two-dimensional bounded obstacle scattering, and is based on a boundary perturbation technique coupled to a well-conditioned high-order spectral-Galerkin solver. This boundary perturbation approach is justified by rigorous theoretical results on analyticity of the scattered field with respect to boundary variations which show that, in fact, the domain of analyticity can be extended to a neighborhood of the entire real axis. The numerical method is augmented by Padé approximation techniques to access this region of extended analyticity so that configurations which are large deformations of the base (spherical) geometry can be simulated. Several numerical results are presented to exemplify the accuracy, stability, and versatility of the proposed method.