On Two Numerical Methods for Homogenization of Maxwell's Equations

Abstract

When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. The classical way of determination of the homogenized coefficients consists of solving an elliptic problem in a unit cell. This method and the Floquet-Bloch method, where an eigenvalue problem is solved, are numerically compared with respect to accuracy and contrast sensitivity. Moreover, we provide numerical bounds on the effective permittivity. The Floquet-Bloch method is shown to be a good alternative to the classical homogenization method, when the contrast is modest.