Homogenization of periodic structures via bloch decomposition

Abstract

In this paper, the classical problem of homogenization of elliptic operators in arbitrary domains with periodically oscillating coe cients is considered. Using Bloch wave decomposition, a new proof of convergence is furnished. It sheds new light and o ers an alternate way to view the classical results. In a natural way, this method leads us to work in the Fourier space and thus in a framework dual to the one used by L. Tartar [Probl emes d'Homog en eisation dans les Equations aux D eriv ees Partielles, Cours Peccot au Coll ege de France, 1977] in his method of homogenization. Further, this technique o ers a nontraditional way of calculating the homogenized coe cients which is easy to implement in the computer.