Homogenization of Periodic Structures via Bloch Decomposition
Carlos Conca, M. Vanninathan · SIAM Journal on Applied Mathematics · 1997
In this paper, the classical problem of homogenization of elliptic operators in arbitrary domains with periodically oscillating coefficients is considered. Using Bloch wave decomposition, a new proof of convergence is furnished. It sheds new light and offers 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 [Problèmes d'Homogénéisation dans les Equations aux Dérivées Partielles, Cours Peccot au Collège de France, 1977] in his method of homogenization. Further, this technique offers a nontraditional way of calculating the homogenized coefficients which is easy to implement in the computer.