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

Kersten Schmidt 1 Sébastien Tordeux 2, 3
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
2 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : 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 essentially smaller or at the order of the skin depth. 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. Numerical experiments with high order finite elements for sheets with varying curvature verify the theoretical findings.
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Kersten Schmidt, Sébastien Tordeux. High order transmission conditions for thin conductive sheets in magneto-quasistatics. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2011, 45, pp.1115-1140. ⟨10.1051/m2an/2011009⟩. ⟨inria-00473213v1⟩

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