A separable approximation for convolution with the retarded Green's function and its application to time domain integral equations

A scheme for the evaluation of retarded potential integrals is presented wherein the convolution of the retarded potential Green's function with the basis functions is approximated using an expansion of separable functions in time and space. The proposed scheme renders the spatial integrands required in this computation smooth over both the source and testing domains, which is typically not true in the traditional TDIE formulation. Numerical experiments have been performed to quantify the error in this approximation and results to a selection of canonical geometries are presented.