# A multi-step solution algorithm for Maxwell boundary integral equations applied to low-frequency electromagnetic testing of conductive objects

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We consider the solution, using boundary elements (BE), of the surface integral equation system arising in electromagnetic testing of conducting bodies, with emphasis on situations such that $o(1) \leq \sqrt{\omega\varepsilon_{0}/\sigma} \leq O(1)$, $L \sqrt{\omega\sigma\mu_{0}} =O(1)$ which includes in particular the case of eddy current testing) and assuming $L\omega\sqrt{\varepsilon_0 \mu_{0}}\leq 2\pi$, i.e. low-frequency conditions ($L$: diameter of conducting body). Earlier approaches for dielectric objects at low frequencies are not applicable in the present context. After showing that a simple normalization of the BE system significantly improves its conditioning, we propose a multi-step solution method based on block SOR iterations, which facilitates the use of direct solvers and converges within a few iterations for the considered range of physical parameters. This novel, albeit simple, treatment allows to perform eddy current-type analyses using standard Maxwell SIE formulations, avoiding the adverse consequences of ill-conditioning for low frequencies and high conductivities. Its performance and limitations are studied on three numerical examples involfing low frequencies and high conductivities.
Type de document :
Article dans une revue
IEEE Transactions on Magnetics, Institute of Electrical and Electronics Engineers, 2016, 52, pp.7005208. <10.1109/TMAG.2016.2584018>
Domaine :

https://hal.archives-ouvertes.fr/hal-01336835
Contributeur : Marc Bonnet <>
Soumis le : jeudi 23 juin 2016 - 22:33:11
Dernière modification le : samedi 18 février 2017 - 01:12:43
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### Citation

Audrey Vigneron, Edouard Demaldent, Marc Bonnet. A multi-step solution algorithm for Maxwell boundary integral equations applied to low-frequency electromagnetic testing of conductive objects. IEEE Transactions on Magnetics, Institute of Electrical and Electronics Engineers, 2016, 52, pp.7005208. <10.1109/TMAG.2016.2584018>. <hal-01336835>

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