Direct Computation of the PEC Body of Revolution Modal Green Function for the Electric Field Integral Equation

We propose a five-term recurrence relation for the direct computation of the modal Green function (MGF) arising in the electric field integral equations (EFIE), when solving the scattering of PEC bodies of revolution. It is shown that, by considering it as an infinite penta-diagonal matrix, the proposed five-term recurrence relation can be solved in a stable manner in $O(M)$ steps for $M$ modes with high and controllable accuracy. By evaluating the performance of the proposed five-term recurrence relation for several scatterers of different geometries, we show that the proposed approach enables an accurate computation with a simple algorithm.