Initial conditions contribution in a BEM formulation based on the convolution quadrature method

This work presents a two-dimensional boundary element method (BEM) formulation for the analysis of scalar wave propagation problems. The formulation is based on the so-called convolution quadrature method (CQM) by means of which the convolution integral, presented in time-domain BEM formulations, is numerically substituted by a quadrature formula, whose weights are computed using the Laplace transform of the fundamental solution and a linear multistep method. This BEM formulation was initially developed for scalar wave propagation problems with null initial conditions. In order to overcome this limitation, this work presents a general procedure that enables one to take into account non-homogeneous initial conditions, after replacing the initial conditions by equivalent pseudo-forces. The numerical results included in this work show the accuracy of the proposed BEM formulation and its applicability to such kind of analysis.