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

Monique Dauge; Patrick Dular; Laurent Krähenbühl; Victor Péron; Ronan Perrussel; Clair Poignard

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}

1 IRMAR - Institut de Recherche Mathématique de Rennes

2 ACE - Applied and Computational Electromagnetics [Liège]

3 Ampère

4 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

5 Magique 3D - Advanced 3D Numerical Modeling in Geophysics

LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest

6 LAPLACE - LAboratoire PLasma et Conversion d'Energie

7 IMB - Institut de Mathématiques de Bordeaux

8 MC2 - Modélisation, contrôle et calcul

Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251

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.

Document type :

Conference papers

Domain :

Mathematics [math] / Classical Analysis and ODEs [math.CA]

Mathematics [math] / Numerical Analysis [math.NA]

Complete list of metadatas

https://hal.inria.fr/hal-00931735
Contributor : Victor Péron <>
Submitted on : Wednesday, January 15, 2014 - 4:28:48 PM
Last modification on : Friday, January 10, 2020 - 9:10:05 PM

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

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

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