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Novel basis functions for the partition of unity boundary element method for Helmholtz problems.

Peake, M.J. and Trevelyan, J. and Coates, G. (2012) 'Novel basis functions for the partition of unity boundary element method for Helmholtz problems.', International journal for numerical methods in engineering., 93 (9). pp. 905-918.

Abstract

The BEM is a popular technique for wave scattering problems given its inherent ability to deal with infinite domains. In the last decade, the partition of unity BEM, in which the approximation space is enriched with a linear combination of plane waves, has been developed; this significantly reduces the number of DOFs required per wavelength. It has been shown that the element ends are more susceptible to errors in the approximation than the mid-element regions. In this paper, the authors propose that this is due to the use of a collocation approach in combination with a reduced order of continuity in the Lagrangian shape function component of the basis functions. It is demonstrated, using numerical examples, that choosing trigonometric shape functions, rather than classical polynomial shape functions (quadratic in this case), provides accuracy benefits. Collocation schemes are investigated; it is found that the somewhat arbitrary choice of collocating at equally spaced points about the surface of a scatterer is better than schemes based on the roots of polynomials or consideration of the Fock domain.

Item Type:Article
Keywords:Boundary element methods, Partition-of-unity, Acoustics, Shape functions, Collocation.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1002/nme.4411
Publisher statement:This is the accepted version of the following article: Peake, M.J., Trevelyan, J. and Coates, G. (2013), Novel basis functions for the partition of unity boundary element method for Helmholtz problems. International Journal for Numerical Methods in Engineering, 93(9): 905-918, which has been published in final form at http://dx.doi.org/10.1002/nme.4411. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
Date accepted:08 August 2012
Date deposited:18 June 2015
Date of first online publication:October 2012
Date first made open access:No date available

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