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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. and 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). pp. 645-664.

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.

Item Type:Article
Keywords:Partition of unity method, Non-uniqueness, CHIEF, Burton–Miller formulation.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1002/nme.4583
Publisher 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.
Date accepted:15 September 2013
Date deposited:18 June 2015
Date of first online publication:December 2013
Date first made open access:No date available

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