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

Abstract

Publisher's 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 re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Computer methods in applied mechanics and engineering, 259, 2013, 10.1016/j.cma.2013.03.016 Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

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

“…Care was taken so that at least 1.4 times as many collocation points were used as degrees of freedom. By doing this, the errors continue to decrease as τ is increased; this is more like the behaviour expected of both the PU-BEM and XIBEM and observed in earlier works [24,32,33].…”

“…It has been shown in two-dimensional XIBEM simulations that this requirement is significantly reduced [24]; this paper will show that this is true for threedimensional problems also.…”

“…The error of each simulation was evaluated using (23) and (24). The results can be seen in Figure 5.…”

“…In previous two-dimensional work [24,33,36], it was observed that the approximation basis enrichment had a strong detrimental effect on the conditioning of the system matrices: condition numbers > 10 16 were recorded. Despite these high condition numbers, solving these systems with SVD still provided very accurate solutions.…”

“…A combined 4 approach benefits from simple meshing, exact geometry and enriched approximation spaces. To this end, the eXtended Isogeometric Boundary Element Method (XIBEM) was developed by the current authors for two-dimensional acoustic scattering problems [24]. XIBEM simulations outperformed IGA-BEM simulations by using fewer degrees of freedom and providing solutions of a greater accuracy.…”