Methods for Efficiently Computing the MoM Impedance Matrix for APEx Type Basis Functions

Alternative methods for efficiently computing the elements of the impedance matrix arising in the method-of-moments (MoM) based asymptotic phasefront extraction (APEx) method are presented. In APEx, the number of unknowns can be drastically reduced by making use of the phasefront characteristics of the local currents at smooth parts of the scatterer obtained at a lower frequency. At the high frequency of interest, the scaled basis functions are in the form of linearly phased constant amplitude currents or traveling waves (TWs) defined on supports that are significantly larger than the ones for the conventional MoM. The standard way of computing the mutual coupling impedance between these TW basis/test functions requires a 4-fold numerical surface integration on the supports (or patches) that typically are a few wavelengths long over a single dimension. Specifically, three different methods are investigated to efficiently and accurately compute the mutual coupling impedance. The advantages and disadvantages as well as the range of applicability of each method are discussed. Accuracy and CPU time comparisons are provided