Variational boundary element acoustic modelling over mixed quadrilateral-triangular element meshes

摘要

The variational indirect boundary element method is widely used in many acoustical problems such as simulation of scattering and radiation phenomena. Although it has many advantageous features in dealing with those problems, it suffers from the singularity problem when the double surface integral is done over the same element. In this paper, a straightforward technique for computing the singularity 1 / R over triangular element is presented. It is based on a generalized polar co-ordinates transformation to transform the triangular master element into a square one. The singularity factor is taken as weight function. Consequently, a single straightforward implementation without any special treatment of singularity is possible for meshes involving both quadrilateral and triangular elements of higher order. The efficiency of the proposed method is demonstrated for some numerical examples.