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

Published online by Cambridge University Press:  17 February 2009

Song-Ping Zhu  and
Yinglong Zhang
Song-Ping Zhu
Affiliation:
School of Mathematics and Applied Statistics University of WollongongWollongong NSW 2522 Australia; e-mail: spz@uow.edu.au.
Yinglong Zhang
Affiliation:
department of Environmental & Biomolecular Systems OGI School of Science & Engineering Oregon Health & Science UniversityBeaverton OR 97006 USA
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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. 2000 Mathematics subject classification: primary 65N38; secondary 35Q35. Keywords and phrases: the dual reciprocity boundary element method (DRBEM), Helmholtz equation, irregular frequencies.

Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 1 , July 2007 , pp. 131 - 150
Copyright
Copyright © Australian Mathematical Society 2007

References

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