Fast and Accurate Evaluation of Double Surface Integrals in Time-Domain Integral Equation Formulations

摘要

A novel integration approach is developed for efficiently evaluating double surface integrals in time-domain integral equation formulations. The approach mainly consists of an angular integration scheme for inner 2-D integrals and a modified outer integration scheme. The approach proposed can handle the singularity and near-hypersingularity of the 4-D integrals, and is sufficiently general for arbitrary types of basis functions over planar domains. As several numerical results will demonstrate, the proposed approach has high accuracy and rapid convergence rate for a variety of integral kernels.