Homogenization of periodic structures via bloch decomposition

Conca, C; Vanninathan M.

Keywords: simulation, structures, decomposition, convergence, operators, boundary, numerical, wave, computer, homogenization, methods, value, mathematical, problems, periodic, Calculations, of, Bloch, Elliptic

Abstract

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.

Más información

Título de la Revista: SIAM JOURNAL ON APPLIED MATHEMATICS
Volumen: 57
Número: 6
Editorial: SIAM PUBLICATIONS
Fecha de publicación: 1997
Página de inicio: 1639
Página final: 1659
URL: http://www.scopus.com/inward/record.url?eid=2-s2.0-0031352502&partnerID=q2rCbXpz