Homogenization of Periodic Structures Using the FEM

Homogenization is an efficient for simulating multiscale problems using the finite-element method. Three different forms of homogenization are available to model small scale electromagnetic fields: a homogeneous sheet isotropic/anisotropic impedance boundary condition for thin 2-D structures, a dielectric slab made of homogenous effective permittivity and permeability for thick 2-D structures, and a general 3-D isotropic/anisotropic homogeneous material for 3-D structures. This paper gives an overview of homogenization including new improvements to the three procedures using the finite-element solution of a unit cell. Applications are presented to demonstrate the efficiency of the method.