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A high frequency boundary element method for scattering by convex polygons with impedance boundary conditions

Chandler-Wilde, S. N., Langdon, S. and Mokgolele, M. (2012) A high frequency boundary element method for scattering by convex polygons with impedance boundary conditions. Communications in Computational Physics, 11 (2). pp. 573-593. ISSN 1991-7120

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To link to this article DOI: 10.4208/cicp.231209.040111s

Abstract/Summary

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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:17790
Uncontrolled Keywords:Boundary integral equation method, high frequency scattering, convex polygons, impedance boundary conditions
Publisher:Global Science Press

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