Homogenization of periodic structures via Bloch decomposition

Conca, Carlos and Vanninathan, Muthusamy (1997) Homogenization of periodic structures via Bloch decomposition. In: SIAM Journal on Applied Mathematics, 57 (6). pp. 1639-1659.

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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 [Problemes d'Homogeneisation dans les Equations aux: Derivees Partielles, Cours Peccot au College de Prance, 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.

Item Type:	Journal Article
Publication:	SIAM Journal on Applied Mathematics
Publisher:	Society for Industrial and Applied Mathematics
Additional Information:	Copyright of this article belongs to Society for Industrial and Applied Mathematics.
Keywords:	homogenization;periodic structures;Bloch waves
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	19 Oct 2011 07:48
Last Modified:	30 Jan 2019 10:30
URI:	http://eprints.iisc.ac.in/id/eprint/38266

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