Singularity Evaluation of the Straight-wire Mixed Potential Integral Equation in the Method of Moments Procedure

A rigorous treatment on the computation of the various integrals that arise in the method of moments formulation of the straight-wire electric field integral equation is provided. For triangle basis functions along with delta function, pulse or triangle weights, particular attention is given to integrals whose integrands are weakly singular. A singularity extraction technique is employed that splits the integral under question into two parts: one that is numerically integrable and one that is analytically integrable. Closed-form approximations based on Taylor series techniques are also provided for the former. These approximations are very robust resulting in errors less than 0.1% when 4(N +1)a / (2l ) 1; here N is the number of basis functions, a is the wire radius and 2l is the wire length.