We study the electromagnetic wave propagation in three-dimensional (3-D) dense random discrete media containing dielectric spheroidal scatterers. We employ a Monte Carlo method in conjunction with the Method of Moments to solve the volume integral equation for the electric field. We calculate the effective permittivity of the random medium through a coherent-field approach and compare our results with a classical mixing formula. A parametric study on the dependence of the effective permittivity on particle elongation and fractional volume is included.

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 thansform (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.