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Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems

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

Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems Thumbnail


Authors

M.J. Peake

G. Coates



Abstract

Isogeometric analysis is a topic of considerable interest in the field of numerical analysis. The boundary element method (BEM) requires only the bounding surface of geometries to be described; this makes non-uniform rational B-splines (NURBS), which commonly describe the bounding curve or surface of geometries in CAD software, appear to be a natural tool for the approach. This isogeometric analysis BEM (IGABEM) provides accuracy benefits over conventional BEM schemes due to the analytical geometry provided by NURBS. When applied to wave problems, it has been shown that enriching BEM approximations with a partition-of-unity basis, in what has become known as the PU-BEM, allows highly accurate solutions to be obtained with a much reduced number of degrees of freedom. This paper combines these approaches and presents an extended isogeometric BEM (XIBEM) which uses partition-of-unity enriched NURBS functions; this new approach provides benefits which surpass those of both the IGABEM and the PU-BEM. Two numerical examples are given: a single scattering cylinder and a multiple-scatterer made up of two capsules and a cylinder.

Citation

Peake, M., Trevelyan, J., & Coates, G. (2013). Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems. Computer Methods in Applied Mechanics and Engineering, 259, 93-102. https://doi.org/10.1016/j.cma.2013.03.016

Journal Article Type Article
Acceptance Date Mar 24, 2013
Online Publication Date Apr 3, 2013
Publication Date Jun 1, 2013
Deposit Date Apr 16, 2013
Publicly Available Date Mar 25, 2015
Journal Computer Methods in Applied Mechanics and Engineering
Print ISSN 0045-7825
Electronic ISSN 1879-2138
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 259
Pages 93-102
DOI https://doi.org/10.1016/j.cma.2013.03.016
Keywords Helmholtz, Acoustics, Isogeometric analysis, Boundary element method, Partition of unity.
Public URL https://durham-repository.worktribe.com/output/1456252

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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, 259, 2013, 10.1016/j.cma.2013.03.016





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