Accessibility navigation


A high-wavenumber boundary-element method for an acoustic scattering problem

Chandler-Wilde, S. N., Langdon, S. and Ritter, L. (2004) A high-wavenumber boundary-element method for an acoustic scattering problem. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 362 (1816). pp. 647-671. ISSN 1364-503X

[img] Text - Accepted Version
· Please see our End User Agreement before downloading.

605kB

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: 10.1098/rsta.2003.1339

Abstract/Summary

In this paper we show stability and convergence for a novel Galerkin boundary element method approach to the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree $\nu$) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval $[a,b]$, which only requires the discretization of $[a,b]$, we show theoretically and experimentally that the $L_2$ error in computing the acoustic field on $[a,b]$ is ${\cal O}(\log^{\nu+3/2}|k(b-a)| M^{-(\nu+1)})$, where $M$ is the number of degrees of freedom and $k$ is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:4948
Uncontrolled Keywords:high–frequency scattering; Galerkin boundary–element method; outdoor sound propagation
Publisher:Royal Society Publishing

Downloads

Downloads per month over past year

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

Page navigation