Ashley Twigger

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In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of soundsoft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic(More)
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(More)
We propose a numerical-asymptotic boundary element method for problems of time-harmonic acoustic scattering of an incident plane wave by a soundsoft two-dimensional (2D) screen. Standard numerical schemes have a computational cost that grows at least linearly with respect to the frequency of the incident wave. Here, we enrich our approximation space with(More)
There has been considerable interest in recent years in the development of numerical methods for time-harmonic acoustic and electromagnetic wave scattering problems that can efficiently resolve the scattered field at high frequencies. Standard finite or boundary element methods (FEMs and BEMs), with piecewise polynomial approximation spaces, suffer from the(More)
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