Closed-form Evaluation of the Singular Terms in Electric Field Integral Equations

Using Surface Integral Equations, such as the Method of Moments (MoM), the integral of singular or nearly-singular functions over pairs of Basis function (BF) and Testing function (TF) must be evaluated. In particular, the Electric Field Integral Equation (EFIE) requires the integration of the Green's function, which asymptotically behaves as 1/R for source and observation points that are getting closer. In this paper, we provide a closed-form expression of the integral of the 1/R function for BF and TF on a polygonal domain. The method presented has been made as general as possible, in order to be easily adapted to different geometries.