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Floating potential boundary condition in smoothdomains

Annabelle Collin 1 Sergio Corridore 1 Clair Poignard 1
1 MONC - Modélisation Mathématique pour l'Oncologie
IMB - Institut de Mathématiques de Bordeaux, Institut Bergonié [Bordeaux], Inria Bordeaux - Sud-Ouest
Abstract : In electromagnetism, a conductor that is not connected to the ground is an equipo-tential whose value is implicitly determined by the constraint of the problem. It leads to a non-local constraints on the flux along the conductor interface, so-called floating potential problems. Unlike previous numerical study that tackle the floating potential problems with the help of advanced and complex numerical methods, we show how an appropriate use of Steklov-Poincaré operators enables to obtain the solution to this partial differential equations with a non local constraint as a linear (and well-designed) combination of N + 1 Dirichlet problems, N being the number of conductors not connected to a ground potential. In the case of thin highly conductive inclusion, we perform an asymptotic analysis to approach the electroquasistatic potential at any order of accuracy. In particular, we show that the so-called floating potential approaches the electroquasistatic potential with a first order accuracy. This enables us to characterize the configurations for which floating potential approximation has to be used to accurately solve the electroquasistatic problem.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03004806
Contributor : Clair Poignard <>
Submitted on : Friday, November 13, 2020 - 5:52:05 PM
Last modification on : Wednesday, November 18, 2020 - 4:07:58 PM

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Annabelle Collin, Sergio Corridore, Clair Poignard. Floating potential boundary condition in smoothdomains. 2020. ⟨hal-03004806⟩

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