Reduction of singular surface integrals to non-singular line integrals for matrix elements of tensor and vector green functions for arbitrarily oriented pairs of flat surface elements

We consider an approach allowing conversion of surface integrals (over planar surface elements) to line integrals with nonsingular integrand, in evaluating matrix elements of Helmholtz-equation Green function and its derivatives, in particular the vector Green function in electromagnetics. A general procedure is outlined consisting of finding suitable auxiliary functions applicable to particular kernel operators. Explicit analytical for expressions for the resulting line integrals can be obtained for arbitrary frequency and are provided in the static limit. The accuracy and the computational cost of proposed technique for its analytical and numerical line integral versions is compared on representative examples involving different surface elements geometrical configurations.