Muthusamy Vanninathan

Homogenization of periodic structures via Bloch decomposition

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 dHomogeneisation dans les Equations aux Derivees Partielles, Cours Peccot au College 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.

BLOCH APPROXIMATION IN HOMOGENIZATION AND APPLICATIONS

The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in this paper. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions

Spectral asymptotics of the Helmholtz model in fluid–solid structures

u^varepsilon

OPTIMAL BOUNDS ON DISPERSION COEFFICIENT IN ONE-DIMENSIONAL PERIODIC MEDIA

of boundary value problems associated with such operators when the period

Feedback stabilization of a simplified model of fluid–structure interaction on a tree

varepsilon>0

Fluids and periodic structures

of the coefficients is small. In a previous work by C. Conca and M. Vanninathan [SIAM J. Appl. Math., 57 (1997), pp. 1639--1659], a new proof of weak convergence as

Bloch wave homogenization of scalar elliptic operators

varepsilonto 0

EXACT CONTROLLABILITY IN FLUID - SOLID STRUCTURE: THE HELMHOLTZ MODEL ∗

towards the homogenized solution was furnished using Bloch wave decomposition.Following the same approach here, we go further and introduce what we call Bloch approximation, which will provide energy norm approximation for the solution

Fourier approach to homogenization problems

u^varepsilon

Bloch wave spectral analysis in the class of generalized Hashin-Shtrikman micro-structures

. We develop several of its main features. As a simple application of this new object, we show that it contains both the first and second order correctors. Necessarily, the Bloch approximation will have to captur...