A new study of the Burton and Miller method for the solution of a 3D Helmholtz problem

Chen, K., Cheng, J. and Harris, P.J. (2009) A new study of the Burton and Miller method for the solution of a 3D Helmholtz problem IMA Journal of Applied Mathematics, 74 (2). pp. 163-177. ISSN 0272-4960

Full text not available from this repository.

Abstract

The exterior Helmholtz problem can be efficiently solved by reformulating the differential equation as an integral equation over the surface of the radiating and/or scattering object. One popular approach for overcoming either non-unique or non-existent problems which occur at certain values of the wave number is the so-called Burton and Miller method which modifies the usual integral equation into one which can be shown to have a unique solution for all real and positive wave numbers. This formulation contains an integral operator with a hypersingular kernel function and for many years, a commonly used method for overcoming this hypersingularity problem has been the collocation method with piecewise-constant polynomials. Viable high-order methods only exist for the more expensive Galerkin method. This paper proposes a new reformulation of the Burton–Miller approach and enables the more practical collocation method to be applied with any high-order piecewise polynomials. This work is expected to lead to much progress in subsequent development of fast solvers. Numerical experiments on 3D domains are included to support the proposed high-order collocation method.

Item Type: Journal article
Uncontrolled Keywords: exterior Helmholtz; boundary integral equation; Burton–Miller; Green theorem; hypersingular operators; collocation method
Subjects: G000 Computing and Mathematical Sciences > G100 Mathematics
G000 Computing and Mathematical Sciences
DOI (a stable link to the resource): 10.1093/imamat/hxp002
Faculties: Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Computational Mathematics
Faculty of Science and Engineering > School of Computing, Engineering and Mathematics
Depositing User: editor cmis
Date Deposited: 14 Jan 2011 10:35
Last Modified: 03 May 2012 08:40
URI: http://eprints.brighton.ac.uk/id/eprint/8074

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year