A Stable High-Order Method for Two-Dimensional Bounded-Obstacle Scattering

A stable and high-order method for solving the Helmholtz equation on a two-dimensional domain exterior to a bounded obstacle is developed in this paper. The method is based on a boundary perturbation technique (“transformed field expansions”) coupled with a well-conditioned high-order spectral-Galerkin solver. The method is further enhanced with numerical analytic continuation, implemented via Pade´ approximation. Ample numerical results are presented to show the accuracy, stability, and versatility of the proposed method.

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