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On the influence of the geometry on skin effect in electromagnetism

Gabriel Caloz 1 Monique Dauge 1 Erwan Faou 1, 2 Victor Péron 3
2 IPSO - Invariant Preserving SOlvers
Inria Rennes – Bretagne Atlantique , IRMAR - Institut de Recherche Mathématique de Rennes
3 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : We consider the equations of electromagnetism set on a domain made of a dielectric and a conductor subdomain in a regime where the conductivity is large. Assuming smoothness for the dielectric--conductor interface, relying on recent works we prove that the solution of the Maxwell equations admits a multiscale asymptotic expansion with profile terms rapidly decaying inside the conductor. This skin effect is measured by introducing a skin depth function that turns out to depend on the mean curvature of the boundary of the conductor. We then confirm these asymptotic results by numerical experiments in various axisymmetric configurations. We also investigate numerically the case of a nonsmooth interface, namely a cylindrical conductor.
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Gabriel Caloz, Monique Dauge, Erwan Faou, Victor Péron. On the influence of the geometry on skin effect in electromagnetism. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2011, 200 (9-12), pp.1053-1068. ⟨10.1016/j.cma.2010.11.011⟩. ⟨hal-00503170v2⟩

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