On the evaluation of spatial domain MoM matrix entries containing closed form Green´s functions

The method of moments (MoM) is widely-used for the solution of mixed potential integral equations (MPIE) arising in the analysis of planar stratified geometries. However, the application of this technique in the spatial domain poses some difficulties since the associated spatial-domain Green´s functions for these geometries are improper oscillatory integrals, known as Sommerfeld integrals, that are very computationally-intensive to evaluate. It is possible to eliminate the time-consuming task of computing these integrals by using closed form versions of the spatial domain Green´s functions and the time required to evaluate the reaction integrals in the MoM matrix can be reduced considerably. Furthermore, the reaction integrals resulting from the application of the MoM can also be evaluated analytically by using piecewise linear basis and testing functions (Alatan et al., 1996). Hence, an efficient EM simulation algorithm can be developed by using the closed form Green´s functions in the MoM formulation that involves no numerical integration. However, despite the time-saving realized from the analytical evaluation of the reaction integrals with the closed-form Green´s functions, the need for further reducing the matrix fill-time is not obviated for many problems. Thus the objective of this paper is to present a hybrid technique for the evaluation of the MoM reaction integrals in a numerically-efficient manner that further reduces the time needed for their computation. A microstrip patch antenna is used as an example.