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Homogenization of time harmonic Maxwell equations: the effect of interfacial currents
Author(s) -
Amirat Youcef,
Shelukhin Vladimir V.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4229
Subject(s) - homogenization (climate) , permittivity , maxwell's equations , conductivity , boundary value problem , dielectric , mathematics , mathematical analysis , permeability (electromagnetism) , electrical resistivity and conductivity , materials science , condensed matter physics , physics , chemistry , quantum mechanics , biodiversity , ecology , biology , biochemistry , membrane
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.