TY - JOUR

T1 - Homogenization of time harmonic Maxwell equations

T2 - the effect of interfacial currents

AU - Amirat, Youcef

AU - Shelukhin, Vladimir V.

PY - 2017/5/30

Y1 - 2017/5/30

N2 - 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.

AB - 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.

KW - homogenization

KW - interfacial currents

KW - Maxwell equations

KW - two-scale convergence

KW - 2-SCALE CONVERGENCE

KW - TRACES

KW - DECOMPOSITION

UR - http://www.scopus.com/inward/record.url?scp=85018722828&partnerID=8YFLogxK

U2 - 10.1002/mma.4229

DO - 10.1002/mma.4229

M3 - Article

AN - SCOPUS:85018722828

VL - 40

SP - 3140

EP - 3162

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 8

ER -