A sparse-matrix/canonical grid method for analyzing microstrip structures

In this paper, we illustrate the analysis of microstrip structures with a large number of unknowns using the sparse-matrix/canonical grid method. This fast Fourier transform (FFT) based iterative method reduces both CPU time and computer storage memory requirements. We employ the Mixed-Potential Integral Equation (MPIE) formulation in conjunction with the RWG triangular discretization. The required spatial-domain Green's functions are obtained efficiently and accurately using the Complex Image Method (CIM). The impedance matrix is decomposed into a sparse matrix which corresponds to near interactions and its complementary matrix which corresponds to far interactions among the subsectional current elements on the microstrip structures. During the iterative process, the near-interaction portion of the matrix-vector multiplication is computed directly as the conventional MPIE formulation. The far-interaction portion of the matrix-vector multiplication is computed indirectly using fast Fourier transforms (FFTs). This is achieved by a Taylor series expansion of the Green's function about the grid points of a uniformly-spaced canonical grid overlaying the triangular discretization.