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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 ; Schmidt, Kersten ; 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) S. 1031-1052.
[Artikel] , (2016)

Kurzbeschreibung (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.

Typ des Eintrags: Artikel
Erschienen: 2016
Autor(en): Péron, Victor ; Schmidt, Kersten ; Duruflé, Marc
Titel: Equivalent Transmission Conditions for the time-harmonic Maxwell equations in 3D for a Medium with a Highly Conductive Thin Sheet
Sprache: Englisch
Kurzbeschreibung (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.

Titel der Zeitschrift, Zeitung oder Schriftenreihe: SIAM J. Appl. Math.
Band: 76
(Heft-)Nummer: 3
Fachbereich(e)/-gebiet(e): 04 Fachbereich Mathematik
04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen
Hinterlegungsdatum: 19 Nov 2018 21:07
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