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

hal.structure.identifierInstitut de Recherche Mathématique de Rennes [IRMAR]
dc.contributor.authorDAUGE, Monique
hal.structure.identifierApplied and Computational Electromagnetics [Liège] [ACE]
dc.contributor.authorDULAR, Patrick
hal.structure.identifierAmpère [AMPERE]
dc.contributor.authorKRÄHENBÜHL, Laurent
hal.structure.identifierAdvanced 3D Numerical Modeling in Geophysics [Magique 3D]
dc.contributor.authorPÉRON, Victor
hal.structure.identifierGroupe de Recherche en Electromagnétisme [LAPLACE-GRE]
dc.contributor.authorPERRUSSEL, Ronan
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierModélisation, contrôle et calcul [MC2]
dc.contributor.authorPOIGNARD, Clair
dc.date.issued2013
dc.date.conference2013-08-26
dc.description.abstractEnWe 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.
dc.language.isoen
dc.title.enCorner Asymptotics of the Magnetic Potential in the Eddy-Current Model
dc.typeCommunication dans un congrès
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
bordeaux.conference.titleJSA 2013 - Journées Singulières Augmentées
bordeaux.countryFR
bordeaux.conference.cityRennes
bordeaux.peerReviewedoui
hal.identifierhal-00931735
hal.version1
hal.invitedoui
hal.proceedingsnon
hal.conference.end2013-08-30
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00931735v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2013&rft.au=DAUGE,%20Monique&DULAR,%20Patrick&KR%C3%84HENB%C3%9CHL,%20Laurent&P%C3%89RON,%20Victor&PERRUSSEL,%20Ronan&rft.genre=unknown


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