Plane wave basis finite‐elements for wave scattering in three dimensions

Abstract

Abstract A three‐dimensional finite‐element model for the solution of Helmholtz problems is presented. The element is based on the Melenk and Babuška technique which uses a plane wave basis in combination with conventional polynomial shape functions. This element offers the possibility to compute many wavelengths per nodal spacing. It is constructed by multiplying the shape functions by plane waves propagating in different directions in space. A standard Galerkin–Bubnov weighting is used. The problem of a plane wave scattered by a sphere is presented and the numerical results are compared to the analytical results obtained from the closed‐form series solution. This paper represents the first application of this approach to three dimensions. Copyright © 2003 John Wiley & Sons, Ltd.