Computation of scattering poles using boundary integrals

Abstract

Scattering resonances have important applications in mathematics, physics and engineering. They can be viewed as the poles of the meromorphic extension of the scattering operator. In this paper, we consider the computation of the scattering poles for sound soft obstacles. The scattering problem is formulated using boundary integrals, which is then discretized by the Nyström method. The discrete scattering poles are computed using the contour integral method. The proposed method is highly accurate, free of spurious modes, and can be extended to treat other obstacles, e.g., sound hard obstacles. Numerical examples are presented to validate the effectiveness and accuracy. The current paper is among the very few computational studies of scattering poles for obstacles.