A high frequency boundary element method for scattering by a class of nonconvex obstacles

Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283, Hewett, D. P., Langdon, S. and Twigger, A. (2015) A high frequency boundary element method for scattering by a class of nonconvex obstacles. Numerische Mathematik, 129 (4). pp. 647-689. ISSN 0029-599X doi: 10.1007/s00211-014-0648-7

Abstract/Summary

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic behaviour of the solution. We demonstrate via a rigorous error analysis, supported by numerical examples, that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. This appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle. Our analysis is based on new frequency-explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/37431
Identification Number/DOI	10.1007/s00211-014-0648-7
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	65N38 65R20 78A45 78M15 78M35
Publisher	Springer
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