Efficient Evaluation of Double Surface Integrals in Time-Domain Integral Equation Formulations

A new integration approach is presented for accurately calculating time-domain EFIE, MFIE, and CFIE matrix elements over triangular domains. It mainly consists of a radial integration scheme for handling weakly singular and near-hypersingular inner integrals and some new smoothing techniques for treating outer two-dimensional (2-D) integrals. The proposed approach has sufficient generality and efficiency for solving time-domain integral equations (TDIE) with arbitrary types of temporal basis functions and temporal discretization schemes, such as marching-on-in-time (MOT), marching-on-in-degree (MOD), and finite difference delay modeling/convolution quadrature (FDDM/CQ), etc. The numerical results for calculating some typical integrals are given to demonstrate its capability, with high accuracy and rapid convergence rate achieved.