Volume 11, Issue 2
A High Frequency Boundary Element Method for Scattering by Convex Polygons with Impedance Boundary Conditions

S. N. Chandler-Wilde, S. Langdon & M. Mokgolele

Commun. Comput. Phys., 11 (2012), pp. 573-593.

Published online: 2012-12

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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.

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@Article{CiCP-11-573, author = {}, title = {A High Frequency Boundary Element Method for Scattering by Convex Polygons with Impedance Boundary Conditions}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {2}, pages = {573--593}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.231209.040111s}, url = {http://global-sci.org/intro/article_detail/cicp/7379.html} }
TY - JOUR T1 - A High Frequency Boundary Element Method for Scattering by Convex Polygons with Impedance Boundary Conditions JO - Communications in Computational Physics VL - 2 SP - 573 EP - 593 PY - 2012 DA - 2012/12 SN - 11 DO - http://doi.org/10.4208/cicp.231209.040111s UR - https://global-sci.org/intro/article_detail/cicp/7379.html KW - AB -

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.

S. N. Chandler-Wilde, S. Langdon & M. Mokgolele. (2020). A High Frequency Boundary Element Method for Scattering by Convex Polygons with Impedance Boundary Conditions. Communications in Computational Physics. 11 (2). 573-593. doi:10.4208/cicp.231209.040111s
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