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Equivalent Transmission Conditions for the time-harmonic Maxwell equations in 3D for a Medium with a Highly Conductive Thin Sheet

Péron, Victor and Schmidt, Kersten and Duruflé, Marc :
Equivalent Transmission Conditions for the time-harmonic Maxwell equations in 3D for a Medium with a Highly Conductive Thin Sheet.
In: SIAM J. Appl. Math., 76 (3) pp. 1031-1052.
[Article] , (2016)

Abstract

We propose equivalent transmission conditions of order 1 and 2 for thin and highly conducting sheets for the time-harmonic Maxwell's equation in three dimensions. The transmission conditions are derived asymptotically for vanishing sheet thickness \varepsilon where the skin depth is kept proportional to \varepsilon. The condition of order 1 turns out to be the perfect electric conductor boundary condition. The conditions of order 2 appear as generalized Poincaré--Steklov maps between tangential components of the magnetic field and the electric field, and they are of Wentzell type involving second order surface differential operators. Numerical results with finite elements of higher order validate the asymptotic convergence for \varepsilon\to0 and the robustness of the equivalent transmission condition of order 2.

Item Type: Article
Erschienen: 2016
Creators: Péron, Victor and Schmidt, Kersten and Duruflé, Marc
Title: Equivalent Transmission Conditions for the time-harmonic Maxwell equations in 3D for a Medium with a Highly Conductive Thin Sheet
Language: English
Abstract:

We propose equivalent transmission conditions of order 1 and 2 for thin and highly conducting sheets for the time-harmonic Maxwell's equation in three dimensions. The transmission conditions are derived asymptotically for vanishing sheet thickness \varepsilon where the skin depth is kept proportional to \varepsilon. The condition of order 1 turns out to be the perfect electric conductor boundary condition. The conditions of order 2 appear as generalized Poincaré--Steklov maps between tangential components of the magnetic field and the electric field, and they are of Wentzell type involving second order surface differential operators. Numerical results with finite elements of higher order validate the asymptotic convergence for \varepsilon\to0 and the robustness of the equivalent transmission condition of order 2.

Journal or Publication Title: SIAM J. Appl. Math.
Volume: 76
Number: 3
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 19 Nov 2018 21:07
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