Homogenization of periodic structures via Bloch decomposition

Conca, Carlos ; Vanninathan, Muthusamy (1997) Homogenization of periodic structures via Bloch decomposition SIAM Journal on Applied Mathematics, 57 (6). pp. 1639-1659. ISSN 0036-1399

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Official URL: http://epubs.siam.org/siap/resource/1/smjmap/v57/i...

Related URL: http://dx.doi.org/10.1137/S0036139995294743


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 [Problémes d'Homogénéisation dans les Equations aux Dérivées Partielles, Cours Peccot au Collége 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.

Item Type:Article
Source:Copyright of this article belongs to Society for Industrial and Applied Mathematics.
Keywords:Homogenization; Periodic Structures; Bloch Waves
ID Code:55267
Deposited On:18 Aug 2011 07:03
Last Modified:18 Aug 2011 07:03

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