An extended isogeometric boundary element method for two-dimensional wave scattering problems.

Isogeometric analysis, using the same basis functions that describe a geometry in CAD software to approximate unknown fields in numerical simulations, is a topic of considerable interest. Until recently, much of the research in this field has concentrated on using this approach for finite element analysis (FEA); however, now, there is an increased focus on boundary integral methods. In contrast to FEA, the boundary element method (BEM) requires only the bounding surfaces of a domain to be meshed. Non-uniform, rational basis splines (NURBS), used commonly in CAD software, describe only the boundary of geometries; hence, NURBS would appear to be a natural tool for the BEM and isogeometric analysis. The partition of unity method has provided significant benefits over conventional, piecewise boundary element methods; here, a partition-of-unity extended, isogeometric BEM is presented and numerical results of an acoustic wave scattering problem given