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Main Title: A unified analysis of transmission conditions for thin conducting sheets in the time-harmonic eddy current model
Author(s): Schmidt, Kersten
Chernov, Alexey
Type: Research Paper
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 [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.
Subject(s): impedance transmission conditions
thin conducting sheets
asymptotic expansions
Issue Date: 5-Nov-2012
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
35C20 Asymptotic expansions
35J25 Boundary value problems for second-order, elliptic equations
41A60 Asymptotic approximations, asymptotic expansions
35B40 Asymptotic behavior of solutions
78M30 Variational methods
78M35 Asymptotic analysis
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2012, 36
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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