On the influence of the geometry on skin effect in electromagnetismReport as inadecuate




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1 IRMAR - Institut de Recherche Mathématique de Rennes 2 IPSO - Invariant Preserving SOlvers IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique 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.





Author: Gabriel Caloz - Monique Dauge - Erwan Faou - Victor Péron -

Source: https://hal.archives-ouvertes.fr/



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