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

¹ Seminar for Applied Mathematics, ETH Zurich, 8092 Zurich, Switzerland, Project POEMS, INRIA Paris-Rocquencourt, 78153 Le Chesnay, France, currently at TU Berlin and DFG Research center , 10623 Berlin, Germany. kersten.schmidt@math.tu-berlin.de
² Laboratoire de Mathématiques et de leurs Applications, UMR 5142, Université de Pau et des Pays de l'Adour, 64013 Pau, France, Project MAGIQUE-3D, INRIA Bordeaux-Sud-Ouest, 64013 Pau, France. sebastien.tordeux@univ-pau.fr

Received: 17 April 2010
Revised: 16 February 2011

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 ε 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 ε and obtain optimal bound for the modelling error outside the sheet of order for the condition of order N. We end the paper with numerical experiments involving high order finite elements for sheets with varying curvature.