Asymptotic Models and Impedance Conditions for Highly Conductive Sheets in the Time-Harmonic Eddy Current Model - Archive ouverte HAL Access content directly
Journal Articles SIAM Journal on Applied Mathematics Year : 2019

Asymptotic Models and Impedance Conditions for Highly Conductive Sheets in the Time-Harmonic Eddy Current Model

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Abstract

This work is concerned with the time-harmonic eddy current problem for a medium with a highly conductive thin sheet. We present asymptotic models and impedance conditions up to the second order of approximation for the electromagnetic field. The conditions are derived asymptotically for vanishing sheet thickness $\varepsilon$ where the skin depth is scaled like $\varepsilon$. The first order condition is the perfect electric conductor boundary condition. The second order condition turns out to be a Poincaré-Steklov map between tangential components of the magnetic field and the electric field.
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Dates and versions

hal-01505612 , version 1 (11-04-2017)
hal-01505612 , version 2 (04-03-2018)

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Victor Péron. Asymptotic Models and Impedance Conditions for Highly Conductive Sheets in the Time-Harmonic Eddy Current Model. SIAM Journal on Applied Mathematics, 2019, 79 (6), pp. 2242--2264. ⟨10.1137/17M1152498⟩. ⟨hal-01505612v2⟩
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