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Homogenization of time harmonic Maxwell equations: the effect of interfacial currents
Authors:Youcef Amirat  Vladimir V Shelukhin
Institution:1. Laboratoire de Mathématiques, CNRS UMR 6620, Université Blaise Pascal, Aubière Cedex, France;2. Lavrentyev Institute of Hydrodynamics, Novosibirsk State University, Novosibirsk, Russia
Abstract:We consider the Maxwell equations for a composite material consisting of two phases and enjoying a periodical structure in the presence of a time‐harmonic current source. We perform the two‐scale homogenization taking into account both the interfacial layer thickness and the complex conductivity of the interfacial layer. We introduce a variational formulation of the differential system equipped with boundary and interfacial conditions. We show the unique solvability of the variational problem. Then, we analyze the low frequency case, high and very high frequency cases, with different strength of the interfacial currents. We find the macroscopic equations and determine the effective constant matrices such as the magnetic permeability, dielectric permittivity, and electric conductivity. The effective matrices depend strongly on the frequency of the current source; the dielectric permittivity and electric conductivity also depend on the strength of the interfacial currents. Copyright © 2016 John Wiley & Sons, Ltd.
Keywords:Maxwell equations  interfacial currents  homogenization  two‐scale convergence
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