Transient boundary element method and numerical evaluation of retarded potentials

Abstract

We discuss the modeling of transient wave propagation with the boundary element method (BEM) in three dimensions. The special structure of the fundamental solution of the wave equation leads to a close interaction of space and time variables in a so-called retarded time-argument. We give a detailed derivation of the discretization scheme and analyse a new kind of "geometrical light cone" singularity of the retarded potential function. Moreover, we present numerical experiments that show these singularities. © 2008 Springer-Verlag Berlin Heidelberg.