A Galerkin boundary element method for high frequency scattering by convex polygons

Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283 and Langdon, S. (2007) A Galerkin boundary element method for high frequency scattering by convex polygons. SIAM Journal on Numerical Analysis (SINUM), 45 (2). pp. 610-640. ISSN 0036-1429 doi: 10.1137/06065595X

Abstract/Summary

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/924
Identification Number/DOI	10.1137/06065595X
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Society for Industrial and Applied Mathematics
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