A high frequency $hp$ boundary element method for scattering by convex polygons

Hewett, D. P., Langdon, S. and Melenk, J. M. (2013) A high frequency $hp$ boundary element method for scattering by convex polygons. SIAM Journal on Numerical Analysis (SINUM), 51 (1). pp. 629-653. ISSN 0036-1429 doi: 10.1137/110856812

Abstract/Summary

In this paper we propose and analyze a hybrid $hp$ boundary element method for the solution of problems of high frequency acoustic scattering by sound-soft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution. We demonstrate, both theoretically and via numerical examples, exponential convergence with respect to the order of the polynomials, moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern, in which the dependence on the frequency of all constants is explicit. Importantly, these estimates prove that, to achieve any desired accuracy in the computation of these quantities, it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/33321
Identification Number/DOI	10.1137/110856812
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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