Wave Based Technique: enrichment of the set of basis functions

The recently developed wave based technique for the analysis of vibro-acoustic problems is a promising prediction tool aiming to bridge the existing mid-frequency gap. Instead of simple polynomial shape functions, this method adopts an indirect Trefftz approach in which it uses the exact solutions of the governing differential equation for the field variable approximations. Since a fine discretization is no longer required, the resulting wave based models are substantially numerically smaller than the element based counterparts. However, the prediction accuracy tends to deteriorate in case of a discontinuous boundary condition. This paper reports on the basic concepts of an enrichment strategy, which has been introduced in order to preserve the favourable computational efficiency of the wave based approach. The basic idea of the proposed approach is to enrich the original wave function set with some novel functions, which inherently satisfy the governing differential equation and a priori incorporate the discontinuous boundary condition. The resulting efficiency improvements are demonstrated by a two-dimensional validation example.