Numerical solution of scattering problems using pseudo-differential impedance operators

Direct numerical solutions of scattering problems based on boundary-integral equations are computationally costly at high frequencies. A numerical method is presented that efficiently computes accurate approximations to unknown surface quantities given known surface data (an approximate Dirichlet-to-Neumann map). The method is based on a pseudo-differential impedance operator (PIO) numerically implemented using rational approximations. An example of a PIO is the so-called on-surface radiation condition (OSRC) method. For a convex obstacle, the method can be viewed as applying a parabolic equation directly on the surface of a scatterer. In contrast to past OSRCs, the use of rational approximations provides accuracy for wide scattering angles which is needed for grazing angles of incidence. Generalization to impedance operators for two-dimensional acoustic scatterers with concave parts is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)