Novel basis functions for the partition of unity boundary element method for 2D Helmholtz problems.

The boundary element method (BEM) is a popular tool for wave scattering problems. To reduce the number of degrees of freedom required, the partition of unity BEM (PUBEM) was developed in which the approximation space is enriched with a linear combination of plane-waves. Recent work has shown that the element ends are more susceptible to errors in the approximation than the mid-element regions. In this paper we propose that this is due to the reduced order of continuity in the Lagrangian shape function component of the basis functions. It will demonstrated that choosing trigonometric shapes functions, rather than classical quadratic shape functions, provides accuracy benefits