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

A stable and high-order method for solving the Helmholtz equation on a twodimensional 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 wellconditioned high-order spectral-Galerkin solver. The method is further enhanced with numerical analytic continuation, implemented via Padé approximation. Ample numerical results are presented to show the accuracy, stability, and versatility of the proposed method.