Polar Integration for Exact Space-Time Quadrature in Time-Domain Integral Equations

A space-time polar quadrature technique for numerical integration of Green´s function interactions in time-domain integral equations is presented. The method transforms 2-D surface space-time integrals associated with vector and scalar potentials to a 1-D integral that is performed using Gauss-Legendre integration. The advantage of the presented technique compared to standard 2-D Gaussian quadrature is that time delays between each section of the source basis function and the observation point are accounted for exactly in an analytic manner. This ensures highly accurate temporal behavior of the Green´s function interactions thereby contributing to the stability of the overall time-domain integral equations