Pole condition: A numerical method for Helmholtz-type scattering problems with inhomogeneous exterior domain

This paper presents a new numerical method for the solution of exterior Helmholtz scattering problems, which is applicable to inhomogeneous exterior domains and a wide class of geometries. The algorithm is based on the pole condition, which is a general radiation condition and allows a treatment of exterior Helmholtz problems without an explicit knowledge of Greenʹs functions or a series representation. Our algorithm is based on a numerical approximation of the singularities of a Laplace transform of the exterior solution. Numerical examples illustrate the performance of the method.