Reduction of surface to line integrals in matrix elements for arbitrarily oriented surface elements: The vector green function

We present an approach allowing conversion of surface integrals (over planar surface elements) to line integrals, in evaluating matrix elements of the derivatives of the Helmholtz-equation Green function, in particular the vector Green function in electromagnetics. A general procedure is outlined and explicit expressions are provided in the static limit. In the latter case, the accuracy and the computational cost of the proposed technique are compared to those of a more conventional approach based on evaluating surface integrals of a known closed-form potential.