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.