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Shadow boundary effects in hybrid numerical-asymptotic methods for high-frequency scattering

Published online by Cambridge University Press:  30 June 2015

D. P. HEWETT
D. P. HEWETT*
Affiliation:
Department of Mathematics and Statistics, University of Reading, UK
*
Current address: Mathematical Institute, University of Oxford, UK Email: [email protected]
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Abstract

The hybrid numerical-asymptotic (HNA) approach aims to reduce the computational cost of conventional numerical methods for high-frequency wave scattering problems by enriching the numerical approximation space with oscillatory basis functions, chosen based on partial knowledge of the high-frequency solution asymptotics. In this paper, we propose a new methodology for the treatment of shadow boundary effects in HNA boundary element methods, using the classical geometrical theory of diffraction phase functions combined with mesh refinement. We develop our methodology in the context of scattering by a class of sound-soft non-convex polygons, presenting a rigorous numerical analysis (supported by numerical results) which proves the effectiveness of our HNA approximation space at high frequencies. Our analysis is based on a study of certain approximation properties of the Fresnel integral and related functions, which govern the shadow boundary behaviour.

Keywords

high frequency scatteringdiffractionboundary element methodnumerical analysisfresnel integral
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Special Anniversay Issue 5: Celebrating 75 years , October 2015 , pp. 773 - 793
Copyright
Copyright © Cambridge University Press 2015 

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