Accessibility navigation

Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

Chandler-Wilde, S., Graham, I. G., Langdon, S. and Spence, E. A. (2012) Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering. Acta Numerica, 21. pp. 89-305. ISSN 0962-4929

Text - Published Version
· Please see our End User Agreement before downloading.


It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1017/S0962492912000037


In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:28187
Publisher:Cambridge University Press


Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation