A High Frequency Bem for Scattering by Non-convex Obstacles

Traditional numerical methods for time-harmonic acoustic scattering problems become prohibitively expensive in the high-frequency regime where the scatterer is large compared to the wavelength of the incident wave. In this paper we propose and analyse a hybrid boundary element method (BEM) for a class of non-convex polygonal scatterers. In this method the approximation space is enriched with oscillatory functions which efficiently capture the high-frequency asymptotics of the solution, so that only O(log f) degrees of freedom are required as the frequency f → ∞. This appears to be the first effective hybrid BEM for a class of non-convex obstacles.