Bloch-wave homogenization for spectral asymptotic analysis of the periodic Maxwell operatorReportar como inadecuado




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1 Cardiff School of Mathematics 2 FRESNEL - Institut FRESNEL 3 Department of Maths Sciences

Abstract : This paper is devoted to the asymptotic behavior of the spectrum of the three-dimensional Maxwell operator in a bounded periodic heterogeneous dielectric medium T = -T,T3, T > 0, as the structure period , such that -1 T is a positive integer, tends to 0. The domain T is extended periodically to the whole of 3, so that the original operator is understood as acting in a space of T-periodic functions. We use the so-called Bloch-wave homogenization technique which, unlike the classical homogenization method, is capable of characterizing a renormalized limit of the spectrum called the Bloch spectrum 6. The related procedure is concerned with sequences of eigenvalues of the resolvent of the order of the square of the medium period, which correspond to the oscillations of high-frequencies of order -1. The Bloch-wave description is obtained via the notion of two-scale convergence for bounded self-adjoint operators, and a proof of the -completeness- of the limiting spectrum is provided. The results obtained theoretically are illustrated by finite element computations.





Autor: Kirill Cherednichenko - Sébastien Guenneau -

Fuente: https://hal.archives-ouvertes.fr/



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