Among classical continuum approaches, the finite element method (FEM) and the finite difference method have been previously considered for describing the polarization response of mixed materials. Previous works have provided significant insight into the dielectric behavior of mixtures including elongated and irregularly-shaped microscale inclusions, three-phase mixtures, and random distributions of inclusions. These models often include an explicit interfacial layer, to account for the effects mentioned above. The results of these numerical calculations have prompted modifications to effective medium models, and helped elucidate the conditions under which those models lose their validity.