Implementation of a boundary element method for high frequency scattering by convex polygons with impedance boundary conditions

Abstract

Many acoustic and electromagnetic wave scattering problems can be formulated as the Helmholtz equation. Standard finite and boundary element method solution of these problems becomes expensive, as the frequency of incident wave increases. On going research has been devoted to finding methods that do not loose robustness when the wave number increases. Recently, Chandler-Wilde et al. have proposed a novel Galerkin boundary element method to solve the problem of acoustic scattering by a convex polygon with impedance boundary conditions. They applied approximation spaces consisting of piecewise polynomials supported on a graded mesh with smaller elements adjacent to the corners of the polygon and multiplied by plane wave basis functions. They demonstrated via rigorous error analysis that was supported by numerical experiments that the number of degrees of freedom required to achieve a prescribed level of accuracy need only grow logarithmically as frequency increases. In this paper, we discuss issues related to detail implementation of their numerical method.