ANZIAM J. 49 (2007), no. 1, pp. 131–150.

A comparative study of the direct boundary element method and the dual reciprocity boundary element method in solving the Helmholtz equation

Song-Ping Zhu Yinglong Zhang
School of Mathematics and Applied Statistics
University of Wollongong
Wollongong
NSW 2522
Australia
spz@uow.edu.au.
Department of Environmental & Biomolecular Systems
OGI School of Science & Engineering
Oregon Health & Science University
Beaverton
OR 97006, USA.
Received 11 June 2006

Abstract

In this paper, we compare the direct boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) for solving the direct interior Helmholtz problem, in terms of their numerical accuracy and efficiency, as well as their applicability and reliability in the frequency domain. For BEM formulation, there are two possible choices for fundamental solutions, which can lead to quite different conclusions in terms of their reliability in the frequency domain. For DRBEM formulation, it is shown that although the DBREM can correctly predict eigenfrequencies even for higher modes, it fails to yield a reasonably accurate numerical solution for the problem when the frequency is higher than the first eigenfrequency.

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2000 Mathematics Subject Classification: primary 65N38; secondary 35Q35
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2378154 Z'blatt-MATH: pre05243896
indicates author for correspondence

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