APPLICATION OF OPERATIONAL QUADRATURE METHODS IN TIME-DOMAIN BOUNDARY-ELEMENT METHODS

The usual time domain Boundary Element Method (BEM) contains fundament al solutions which are convoluted with time-dependent boundary data an d integrated over the boundary surface. Here, a new approach for the e valuation of the convolution integrals, the so-called 'Operational Qua drature Methods' developed by Lubich, is presented. In this formulatio n, the convolution integral is numerically approximated by a quadratur e formula whose weights are determined using the Laplace transform of the fundamental solution and a linear multistep method. To study the b ehaviour of the method, the numerical convolution of a fundamental sol ution with a unit step function is compared with the analytical result . Then, a time domain Boundary Element formulation applying the 'Opera tional Quadrature Methods' is derived. For this formulation only the f undamental solutions in Laplace domain are necessary. The properties o f the new formulation are studied with a numerical example.