A comparison of techniques for overcoming non-uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering

Diwan, G.C.; Trevelyan, J.; Coates, G.

doi:10.1002/nme.4583

A comparison of techniques for overcoming non-uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering

Diwan, G.C.; Trevelyan, J.; Coates, G.

Authors

G.C. Diwan

Professor Jon Trevelyan jon.trevelyan@durham.ac.uk
Emeritus Professor

G. Coates

Abstract

The Partition of Unity Method has become an attractive approach for extending the allowable frequency range for wave simulations beyond that available using piecewise polynomial elements. The non-uniqueness of solution obtained from the conventional boundary integral equation (CBIE) is well known. The CBIE derived through Green's identities suffers from a problem of non-uniqueness at certain characteristic frequencies. Two of the standard methods of overcoming this problem are the so-called Combined Helmholtz Integral Equation Formulation (CHIEF) method and that of Burton and Miller. The latter method introduces a hypersingular integral, which may be treated in various ways. In this paper, we present the collocation partition of unity boundary element method (PUBEM) for the Helmholtz problem and compare the performance of CHIEF against a Burton–Miller formulation regularised using the approach of Li and Huang.

Citation

Diwan, G., Trevelyan, J., & Coates, G. (2013). A comparison of techniques for overcoming non-uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering. International Journal for Numerical Methods in Engineering, 96(10), 645-664. https://doi.org/10.1002/nme.4583

Journal Article Type	Article
Acceptance Date	Sep 15, 2013
Publication Date	Dec 7, 2013
Deposit Date	Jan 17, 2014
Publicly Available Date	Jun 18, 2015
Journal	International Journal for Numerical Methods in Engineering
Print ISSN	0029-5981
Electronic ISSN	1097-0207
Publisher	Wiley
Peer Reviewed	Peer Reviewed
Volume	96
Issue	10
Pages	645-664
DOI	https://doi.org/10.1002/nme.4583
Keywords	Partition of unity method, Non-uniqueness, CHIEF, Burton–Miller formulation.

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Copyright Statement
This is the accepted version of the following article: Diwan, G.C., Trevelyan, J. and Coates, G. (2013), A comparison of techniques for overcoming non-uniqueness of boundary integral equations for the collocation partition of unity method in two-dimensional acoustic scattering. International Journal for Numerical Methods in Engineering, 96(10): 645-664, which has been published in final form at http://dx.doi.org/10.1002/nme.4583. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.