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High order transmission conditions for thin conductive sheets in magneto-quasistatics

Please always quote using this URN:urn:nbn:de:0296-matheon-8371
  • We propose transmission conditions of order $1$, $2$ and $3$ approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses $\eps$ are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t.~to the small parameter $\eps$ and obtain optimal bound for the modelling error outside the sheet of order $\eps^{N+1}$ for the condition of order $N$. We end the paper with numerical experiments involving high order finite elements for sheets with varying curvature.

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Metadaten
Author:Kersten Schmidt, Sébastien Tordeux
URN:urn:nbn:de:0296-matheon-8371
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/06/28
Release Date:2011/06/28
Tag:
Institute:Technische Universität Berlin
Project:D Optics and Electronics (Electronic and photonic devices) / D26 Asymptotic analysis of the wave-propagation in realistic photonic crystal wave-guides
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B40 Asymptotic behavior of solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Cxx Representations of solutions / 35C20 Asymptotic expansions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J25 Boundary value problems for second-order elliptic equations
41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78Mxx Basic methods / 78M30 Variational methods
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78Mxx Basic methods / 78M35 Asymptotic analysis
Preprint Number:801
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