Abstract

Standard Boundary Element Methods (BEM) for linear wave scattering problems, with piecewise polynomial approximation spaces, can be prohibitively expensive when the wavelength of the scattered wave is small compared to typical lengthscales of the scatterer, due to rapid oscillations in the solution. Hybrid Numerical-Asymptotic (HNA) BEMs, with enriched approximation spaces consisting of the products of piecewise polynomials with carefully chosen oscillatory basis functions, have been shown to be effective in overcoming this limitation for a range of problems, mostly focused on single convex scatterers or very specific non-convex or multiple scattering configurations. In this talk, we review progress on the extension of the HNABEM approach to multiple scattering problems, and propose a novel approach to the problem of two-dimensional scattering by a pair of screens, which we anticipate may serve as a building block towards algorithms for more general high frequency multiple scattering problems.