The Mathematical Institute, University of Oxford, Eprints Archive

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

Hewett, D. P. (2014) Shadow boundary effects in hybrid numerical-asymptotic
methods for high frequency scattering.
Technical Report. Unspecified. (Submitted)

[img]
Preview
PDF - Submitted Version
1MB

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 nonconvex 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.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1859
Deposited By: Helen Taylor
Deposited On:18 Sep 2014 07:42
Last Modified:29 May 2015 19:33

Repository Staff Only: item control page