On the fully analytical integration of singular double integrals arising from the integral equation methods

Singular double integrals of the Green's function and its gradients are calculated fully analytically without numerical integrations from the series expansion of the Green's function. The expansion term integrals are calculated for general 3-D simplexes recursively by lowering the order of the expansion term or the dimension of the integration. The accuracy is verified with some numerical experiments of electromagnetic surface integral equation.