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

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.