On the structure and packing of the moment matrix in problems supporting simultaneous electric and magnetic surface currents

Abstract

be significant not only for rectangular microstrip patches over ground planes without apertures, but also for rectangular microstrip patches over ground planes with rectangular apertures. Other results also have indicated that dielectric-anisotropy effect is especially significant when the size of the aperture is similar to that of the patch. This last result agrees with that discovered theoretically for circular microstrip patches over ground planes with circular apertures [2]. Fortaki, Uniaxially anisotropic substrate effects on resonance of rectangular microstrip patch antenna, Electron Lett 35 (1999), 255-256. 6. V. Losada, R.R. Boix, and M. Horno, Full-wave analysis of circular microstrip resonators in multilayered media containing uniaxial anisotropic dielectrics, magnetized ferrites, and chiral materials, IEEE The mixed-potential integral equation (MPIE) together with the method of moments (MoM) has been widely applied for the simulation of electromagnetic problems in layered media [1][2][3][4]. In the general approach to solving the MPIE for metallic structures, only electric sources need to be considered. In the case of a slot in an infinite electrical ground plane, magnetic sources and the curl operator can however be considered in addition to One of the main problems with the computational procedure is to overcome the complicated and time-consuming task of calculating the Green's functions; for this reason, it is necessary to fill the moment matrix as efficiently as possible. Even though efficient packing of the moment matrix is essential to reduce execution times and memory, literature on the structure and filling of this matrix is uncommon. Rao, Wilton, and Glisson [9] developed a formulation for triangular basis functions and discussed an efficient implementation of the free-space solution by evaluating matrix elements by face-pair combinations rather than by edgepair combinations. Van Tonder [10] extended this formulation and introduced a filling algorithm that effectively fills symmetric matrices. However, with the exception of the free-space solution, the moment matrix becomes unsymmetrical in the presence of simultaneous electric and magnetic sources. This paper outlines a packing algorithm suitable to analyse hybrid microstrip-slotline multilayered circuits using a triangular mesh. Attention is focussed on filling a global partially symmetric matrix, incorporating the idea of isolation between elements when employing the equivalence principle at dielectric-slotline interfaces. In the standard MoM formulation, the presence of a slot in an infinite electrical conductor would require discretisation of a finite-size ground plane that surrounds the gap. The algorithm developed in this paper has the advantage of supporting both electric and magnetic sources, thus allowing discretisation of the slot interface only. The resultant matrix has fewer unknowns and faster filling times are a result. PROBLEMS INVOLVING BOTH ELECTRIC AND MAGNETIC SOURCESConsider Figure 1. Let S 1 and S 2 denote the surface of...