We present a novel hybrid numerical-asymptotic boundary element method for transmission problems describing high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. We demonstrate by means of a range of numerical experiments that our boundary element method can achieve a fixed accuracy of approximation using only a relatively small, frequency-independent number of degrees of freedom. Our numerical approximation space, which can be applied in the context of any direct boundary integral equation formulation, approximates the unknown boundary solution as a sum of the classical geometrical optics approximation, computed by a beam tracing algorithm, plus a contribution due to diffraction, computed by a boundary element method using oscillatory basis functions chosen to efficiently capture the high frequency behaviour. For the scattering scenarios we consider, we show that the inclusion of the diffraction term provides an order of magnitude improveme 查看全文>>