On the influence of the geometry on skin effect in electromagnetism

Gabriel Caloz, Monique Dauge, Erwan Faou, Victor Péron

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.

16 Juillet 2010 -- Prépublication IRMAR 10-48

15 Novembre 2010 -- Accepted for publication
Computer Methods in Applied Mechanics and Engineering 200, 9-12 (2011) 1053-1068.

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Slides at the Workshop on "Non-Standard Numerical Methods for PDE's" in Pavia.

Slides at the International Symposium on Maxwell Equations: Theoretical and Numerical Issues with Applications July 25-30, 2010, at Fudan University, Shanghai.