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A High Frequency Boundary Element Method for Scattering by Convex Polygons with Impedance Boundary Conditions

Published online by Cambridge University Press:  20 August 2015

S. N. Chandler-Wilde ,
S. Langdon  and
M. Mokgolele
S. N. Chandler-Wilde*
Affiliation:
Department of Mathematics, University of Reading, Whiteknights PO Box 220, Reading RG6 6AX, U.K
S. Langdon*
Affiliation:
Department of Mathematics, University of Reading, Whiteknights PO Box 220, Reading RG6 6AX, U.K
M. Mokgolele*
Affiliation:
Department of Mathematics, University of Reading, Whiteknights PO Box 220, Reading RG6 6AX, U.K
*
Email address:[email protected]
*Corresponding author.Email:[email protected]
Email address:[email protected]
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Abstract

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the 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. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.

Keywords

35J0565N3865R20Boundary integral equation methodhigh frequency scatteringconvex polygonsimpedance boundary conditions
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 573 - 593
Copyright
Copyright © Global Science Press Limited 2012

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