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Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2011

On the influence of the geometry on skin effect in electromagnetism

Résumé

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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Dates et versions

hal-00503170 , version 1 (16-07-2010)
hal-00503170 , version 2 (01-11-2010)

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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, 2011, 200 (9-12), pp.1053-1068. ⟨10.1016/j.cma.2010.11.011⟩. ⟨hal-00503170v2⟩
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