Corner asymptotics of the magnetic potential in the eddy-current model
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | DAUGE, Monique | |
| hal.structure.identifier | Applied and Computational Electromagnetics [Liège] [ACE] | |
| dc.contributor.author | DULAR, Patrick | |
| hal.structure.identifier | Ampère, Département Méthodes pour l'Ingénierie des Systèmes [MIS] | |
| dc.contributor.author | KRÄHENBÜHL, Laurent | |
| hal.structure.identifier | Advanced 3D Numerical Modeling in Geophysics [Magique 3D] | |
| hal.structure.identifier | Laboratoire de Mathématiques et de leurs Applications [Pau] [LMAP] | |
| dc.contributor.author | PÉRON, Victor | |
| hal.structure.identifier | Groupe de Recherche en Electromagnétisme [LAPLACE-GRE] | |
| dc.contributor.author | PERRUSSEL, Ronan | |
| hal.structure.identifier | Modélisation, contrôle et calcul [MC2] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | POIGNARD, Clair | |
| dc.date.issued | 2014 | |
| dc.identifier.issn | 0170-4214 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020 | |
| dc.language.iso | en | |
| dc.publisher | Wiley | |
| dc.subject.en | eddy-current model | |
| dc.subject.en | corner asymptotic | |
| dc.subject.en | singular coefficients | |
| dc.title.en | Corner asymptotics of the magnetic potential in the eddy-current model | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1002/mma.2947 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Mathematical Methods in the Applied Sciences | |
| bordeaux.page | 1924-1955 | |
| bordeaux.volume | 37 | |
| bordeaux.issue | 13 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00779067 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00779067v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Methods%20in%20the%20Applied%20Sciences&rft.date=2014&rft.volume=37&rft.issue=13&rft.spage=1924-1955&rft.epage=1924-1955&rft.eissn=0170-4214&rft.issn=0170-4214&rft.au=DAUGE,%20Monique&DULAR,%20Patrick&KR%C3%84HENB%C3%9CHL,%20Laurent&P%C3%89RON,%20Victor&PERRUSSEL,%20Ronan&rft.genre=article |
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