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

M.J. Peake, J. Trevelyan, G. Coates
2013 Computer Methods in Applied Mechanics and Engineering  
2013) 'Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems.', Computer methods in applied mechanics and engineering., 259 . pp. 93-102. Further information on publisher's website: The 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-prot purposes provided that: • a full bibliographic reference is made to the original
more » ... ce • 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. 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 multiplescatterer made up of two capsules and a cylinder.
doi:10.1016/j.cma.2013.03.016 fatcat:s4chjl7b6ve4rjg6qfsenrsx2e