Uniform estimates for transmission problems in electromagnetism with high contrast in magnetic permeabilities

2024/06/21 by Péron, Victor
#Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2406.15276

Abstract

We consider the time-harmonic Maxwell equations set on a domain made up of two subdomains that represent a magnetic conductor and a non-magnetic material, and we assume that the relative magnetic permeability μ_r between the two materials is high. We prove uniform a priori estimates for Maxwell solutions when the interface between the two subdomains is supposed to be Lipschitz. Assuming smoothness for the interface between the subdomains, we prove also that the magnetic field possesses a multiscale expansion in powers of 1/ √μ_r with profiles rapidly decaying inside the magnetic conductor.

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