Corner asymptotics of the magnetic potential in the eddy-current model

Monique Dauge 1 Patrick Dular 2 Laurent Krähenbühl 3 Victor Péron 4, 5 Ronan Perrussel 6 Clair Poignard 7, 8, *
* Auteur correspondant
1 IRMAR - Institut de Recherche Mathématique de Rennes
2 ACE - Applied and Computational Electromagnetics [Liège]
3 Ampère
4 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
5 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
6 LAPLACE - Laboratoire Plasma et Conversion d'Energie [Toulouse]
7 MC2 - Modélisation, contrôle et calcul
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
8 IMB - Institut de Mathématiques de Bordeaux
Abstract : In this paper, we describe the scalar magnetic potential in the vicinity of a corner of a conducting body embedded in a dielectric medium in a bidimensional setting. We make explicit the corner asymptotic expansion for this potential as the distance to the corner goes to zero. This expansion involves singular functions and singular coefficients. We introduce a method for the calculation of the singular functions near the corner and we provide two methods to compute the singular coefficients: the method of moments and the method of quasi-dual singular functions. Estimates for the convergence of both approximate methods are proven. We eventually illustrate the theoretical results with finite element computations. The specific non-standard feature of this problem lies in the structure of its singular functions: They have the form of series whose first terms are harmonic polynomials and further terms are genuine non-smooth functions generated by the piecewise constant zeroth order term of the operator.
Keywords : corner asymptotic eddy-current model singular coefficients
Type de document :
Article dans une revue
Mathematical Methods in the Applied Sciences, Wiley, 2014, 37 (13), pp.1924-1955. 〈10.1002/mma.2947〉
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Monique Dauge, Patrick Dular, Laurent Krähenbühl, Victor Péron, Ronan Perrussel, et al.. Corner asymptotics of the magnetic potential in the eddy-current model. Mathematical Methods in the Applied Sciences, Wiley, 2014, 37 (13), pp.1924-1955. 〈10.1002/mma.2947〉. 〈hal-00779067〉

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