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Extended isogeometric boundary element method (XIBEM) for three-dimensional medium-wave acoustic scattering problems.

Peake, M.J. and Trevelyan, J. and Coates, G. (2015) 'Extended isogeometric boundary element method (XIBEM) for three-dimensional medium-wave acoustic scattering problems.', Computer methods in applied mechanics and engineering., 284 . pp. 762-780.

Abstract

A boundary element method (BEM), based on non-uniform rational B-splines (NURBS), is used to find solutions to three-dimensional wave scattering problems governed by the Helmholtz equation. The method is extended in a partition-of-unity sense, multiplying the NURBS functions by families of plane waves; this method is called the eXtended Isogeometric Boundary Element Method (XIBEM). In this paper, the collocation XIBEM formulation is described and numerical results are given. The numerical results are compared against closed-form or converged solutions. Comparisons are made against the conventional boundary element method and the non-enriched isogeometric BEM (IGABEM). When compared to non-enriched boundary element simulations, using XIBEM significantly reduces the number of degrees of freedom required to obtain a solution of a given error; thus, with a fixed computational resource, problems of a shorter wavelength can be solved.

Item Type:Article
Keywords:Helmholtz, Acoustics, Wave scattering, Isogeometric analysis, Boundary element method, Partition of unity.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1016/j.cma.2014.10.039
Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, 284, 1 February 2015, 10.1016/j.cma.2014.10.039.
Date accepted:No date available
Date deposited:28 November 2014
Date of first online publication:February 2015
Date first made open access:No date available

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