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

Peake, M.J.; Trevelyan, J.; Coates, G.

doi:10.1016/j.cma.2014.10.039

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

Peake, M.J.; Trevelyan, J.; Coates, G.

Authors

M.J. Peake

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

G. Coates

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.

Citation

Peake, M., Trevelyan, J., & 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, 762-780. https://doi.org/10.1016/j.cma.2014.10.039

Journal Article Type	Article
Publication Date	Feb 1, 2015
Deposit Date	Oct 28, 2014
Publicly Available Date	Nov 28, 2014
Journal	Computer Methods in Applied Mechanics and Engineering
Print ISSN	0045-7825
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	284
Pages	762-780
DOI	https://doi.org/10.1016/j.cma.2014.10.039
Keywords	Helmholtz, Acoustics, Wave scattering, Isogeometric analysis, Boundary element method, Partition of unity.

Files

Accepted Journal Article (1.7 Mb)
PDF

Copyright 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.