A time domain Boundary Element formulation based on a multistep time discretization

The usual time domain Boundary Element Method (BEM) contains time-dependent fundamental solutions which are convoluted with time-dependent boundary data and integrated over the boundary surface. Here, a new approach for the evaluation of the convolution integrals, the so-called "Operational Quadrature Methods" developed by LUBICH, is presented. In this formulation, the convolution integral is numerically approximated by a quadrature formula whose weights are determined using the Laplace transform of the fundamental solution and a linear multistep method. To study the behaviour of the method, the numerical convolution of a fundamental solution with a unit step function is compared with the analytical result. Then, applying this "Operational Quadrature Methods", a time domain Boundary Element method for elastodynamic problems is derived. The properties of this new formulation are studied by a numerical example. Obviously, requiring only Laplace domain fundamental solutions, accurate and stable time-dependent results are produced.