Computing the effective permittivity of composite materials using a finite difference method

A finite difference method is used to determine the effective or average properties of a two-dimensional composite material. The host material and several inclusions dispersed through it have different values for the electric permittivity, and the problem is to compute the permittivity of the total structure. Results are explored as a function of the filling factor of the inclusions and of the mismatch between the permittivity values of the two constituent materials. The results are compared to the predictions of analytic, approximate effective medium methods. The calculations can be extended to treat a variety of electrostatic and magnetostatic problems.