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

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

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
• Electronic ISSN: 1879-2138
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1442991