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A unified analysis of transmission conditions for thin conducting sheets in the time-harmonic eddy current model

Schmidt, Kersten ; Chernov, Alexey :
A unified analysis of transmission conditions for thin conducting sheets in the time-harmonic eddy current model.
[Online-Edition: http://epubs.siam.org/doi/abs/10.1137/120901398]
In: SIAM J. Appl. Math., 73 (6) S. 1980-2003.
[Artikel] , (2013)

Offizielle URL: http://epubs.siam.org/doi/abs/10.1137/120901398

Kurzbeschreibung (Abstract)

We introduce tools for a unified analysis and a comparison of impedance transmission conditions (ITCs) for thin conducting sheets within the time-harmonic eddy current model in two dimensions. The first criterion is the robustness with respect to the frequency or skin depth, that means if they give meaningful results for small and for large frequencies or conductivities. As a second tool we study the accuracy for a range of sheet thicknesses and frequencies for a relevant example, and analyse finally their asymptotic order in different asymptotic regimes. For the latter we write all the ITCs in a common form and show how they can be realised within the finite element method. Two new conditions which we call ITC-2-0 and ITC-2-1 are introduced in this article which appear in a symmetric form. They are derived by asymptotic expansions in the asymptotic regime of constant ratio between skin depth and thickness like those in 26. We analyse these ITCs in comparison with the often used perfect electric boundary condition, the shielding element by Nakata et.al. 23, the thin layer impedance boundary conditions by Mayergoyz and Bedrosian 22 and a family of ITCs derived by asymptotic expansions in the asymptotic regime of constant shielding by Schmidt and Tordeux 28. Our analysis shows the superiority of the transmission conditions derived by asymptotic expansions where especially the worst-case error level of the ITC-2-1 is remarkably lower than for all the other conditions.

Typ des Eintrags: Artikel
Erschienen: 2013
Autor(en): Schmidt, Kersten ; Chernov, Alexey
Titel: A unified analysis of transmission conditions for thin conducting sheets in the time-harmonic eddy current model
Sprache: Englisch
Kurzbeschreibung (Abstract):

We introduce tools for a unified analysis and a comparison of impedance transmission conditions (ITCs) for thin conducting sheets within the time-harmonic eddy current model in two dimensions. The first criterion is the robustness with respect to the frequency or skin depth, that means if they give meaningful results for small and for large frequencies or conductivities. As a second tool we study the accuracy for a range of sheet thicknesses and frequencies for a relevant example, and analyse finally their asymptotic order in different asymptotic regimes. For the latter we write all the ITCs in a common form and show how they can be realised within the finite element method. Two new conditions which we call ITC-2-0 and ITC-2-1 are introduced in this article which appear in a symmetric form. They are derived by asymptotic expansions in the asymptotic regime of constant ratio between skin depth and thickness like those in 26. We analyse these ITCs in comparison with the often used perfect electric boundary condition, the shielding element by Nakata et.al. 23, the thin layer impedance boundary conditions by Mayergoyz and Bedrosian 22 and a family of ITCs derived by asymptotic expansions in the asymptotic regime of constant shielding by Schmidt and Tordeux 28. Our analysis shows the superiority of the transmission conditions derived by asymptotic expansions where especially the worst-case error level of the ITC-2-1 is remarkably lower than for all the other conditions.

Titel der Zeitschrift, Zeitung oder Schriftenreihe: SIAM J. Appl. Math.
Band: 73
(Heft-)Nummer: 6
Fachbereich(e)/-gebiet(e): 04 Fachbereich Mathematik
04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen
Hinterlegungsdatum: 19 Nov 2018 21:38
DOI: 10.1137/120901398
Offizielle URL: http://epubs.siam.org/doi/abs/10.1137/120901398
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