Computation of longwave electromagnetic response of nonhomogeneous media

A method for the numeric estimation of the effective permittivity of any nonhomogeneous medium that admits the effective medium approximation under the longwave approximation is presented. Media are modeled as inclusions embedded in a continuous matrix. We show how the potentials at the inclusion boundaries are sufficient information for the estimation of the effective permittivity. We also show efficient implementation techniques to estimate them computationally, either by Monte Carlo random walk or by relaxation. We provide numerical results for several regular two- and three-dimensional structures and show the dependence of the effective response on the shape of the inclusions and their spatial arrangement, and the influence of the percolation threshold.