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High frequency scattering by convex curvilinear polygons

Langdon, S., Mokgolele, M. and Chandler-Wilde, S.N. (2010) High frequency scattering by convex curvilinear polygons. Journal of Computational and Applied Mathematics, 234 (6). pp. 2020-2026. ISSN 0377-0427

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To link to this article DOI: 10.1016/j.cam.2009.08.053

Abstract/Summary

We consider the scattering of a time-harmonic acoustic incident plane wave by a sound soft convex curvilinear polygon with Lipschitz boundary. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the number of degrees of freedom required to achieve a prescribed level of accuracy grows at least linearly with respect to the frequency of the incident wave. Here we propose a novel Galerkin boundary element method with a hybrid approximation space, consisting of the products of plane wave basis functions with piecewise polynomials supported on several overlapping meshes; a uniform mesh on illuminated sides, and graded meshes refined towards the corners of the polygon on illuminated and shadow sides. Numerical experiments suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy need only grow logarithmically as the frequency of the incident wave increases.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:17791
Uncontrolled Keywords:High frequency scattering; Helmholtz equation; Galerkin boundary element method; Hybrid approximation space; Plane wave basis functions
Publisher:Elsevier

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