On the double potential integrals arising in the method of moments and their analytic-numeric hybrid treatment

A very simple alternative analytical approach to calculate the free space static potential integral associated to uniform source distributions over arbitrary oriented flat polygons is presented. The technique is based on a novel integral transformation and the resulting formula is equivalent to others existing in literature, being also suitable within a singularity subtraction framework. The numerical integration of the obtained analytical expression is performed by utilizing Generalized Cartesian product rules built on the double exponential formula. Therefore, the problems linked to the endpoint singularities in the derivative of the potential are eased. These techniques are used within a surface integral equation-Method of Moments framework.