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Corner Asymptotics of the Magnetic Potential in the Eddy-Current Model

Monique Dauge 1 Patrick Dular 2 Laurent Krähenbühl 3 Victor Péron 4 Ronan Perrussel 5 Clair Poignard 6, 7
4 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
5 LAPLACE-GRE - Groupe de Recherche en Electromagnétisme
LAPLACE - LAboratoire PLasma et Conversion d'Energie
7 MC2 - Modélisation, contrôle et calcul
CNRS - Centre National de la Recherche Scientifique : UMR5251, UB - Université de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We describe the 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. We extend the quasi-dual function method to the case of resonances to compute the singular coefficients. Estimates for the convergence of this method are proven. We 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.
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https://hal.inria.fr/hal-00931735
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Submitted on : Friday, March 19, 2021 - 7:50:21 PM
Last modification on : Wednesday, January 26, 2022 - 5:42:06 PM

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  • HAL Id : hal-00931735, version 1

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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. JSA 2013 - Journées Singulières Augmentées, Aug 2013, Rennes, France. ⟨hal-00931735⟩

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