# The eddy current model as a low-frequency, high-conductivity asymptotic form of the Maxwell transmission problem

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We study the relationship between the Maxwell and eddy current (EC) models for three-dimensional configurations involving bounded regions with high conductivity $\sigma$ in air and with sources placed remotely from the conducting objects, which typically occur in the numerical simulation of eddy current nondestructive testing (ECT) experiments. The underlying Maxwell transmission problem is formulated using boundary integral formulations of PMCHWT type. In this context, we derive and rigorously justify an asymptotic expansion of the Maxwell integral problem with respect to the non-dimensional parameter $\gamma:=\sqrt{\omega\varepsilon_{0}/\sigma}$. The EC integral problem is shown to constitute the limiting form of the Maxwell integral problem as $\gamma\to0$, i.e. as its low-frequency and high-conductivity limit. Estimates in $\gamma$ are obtained for the solution remainders (in terms of the surface currents, which are the primary unknowns of the PMCHWT problem, and the electromagnetic fields) and the impedance variation measured at the extremities of the excitating coil. In particular, the leading and remainder orders in $\gamma$ of the surface currents are found to depend on the current component (electric or magnetic, charge-free or not). These theoretical results are demonstrated on three-dimensional illustrative numerical examples, where the mathematically established estimates in $\gamma$ are reproduced by the numerical results.
Type de document :
Article dans une revue
Computers & Mathematics with Applications, 2018

https://hal.archives-ouvertes.fr/hal-01956433
Contributeur : Marc Bonnet <>
Soumis le : samedi 15 décembre 2018 - 18:40:04
Dernière modification le : jeudi 17 janvier 2019 - 10:30:33

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• HAL Id : hal-01956433, version 1

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Marc Bonnet, Edouard Demaldent. The eddy current model as a low-frequency, high-conductivity asymptotic form of the Maxwell transmission problem. Computers & Mathematics with Applications, 2018. 〈hal-01956433〉

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