×

Analysis of an eddy current problem involving a thin inductor. (English) Zbl 0881.65124

Summary: We consider the justification of a two-dimensional eddy current problem using a thin inductor. It is shown in particular that the resistivity of the inductor has to be small enough in order to justify such an approximation. Furthermore, the Kirchhoff circuit equation in the case of a single thin conductor appears as a limit problem.

MSC:

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A25 Electromagnetic theory (general)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Clain, S.; Rappaz, J.; Swierkosz, M.; Touzani, R., Numerical modeling of induction heating for two-dimensional geometries, \(M^3\) AS, 3, 6, 805-822 (1993) · Zbl 0801.65120
[2] Lions, J.-L., (Lecture Notes in Mathematics (1973), Springer-Verlag: Springer-Verlag Berlin), No. 323
[3] Bossavit, A., On finite elements for the electricity equation, (The Mathematics of Finite Elements and Applications (1981), Pitman: Pitman London) · Zbl 0541.73139
[4] Neff, J. R., Introductory Electromagnetics (1991), Wiley: Wiley New York
[5] Rodriguez, J. M.; Viaño, J. M., Analyse asymptotique de l’équation de Poisson dans un domaine mince. Application à la théorie de torsion des poutres élastiques à profil mince. I. Domaines “sans jonctions”, C.R. Acad. Sci. Paris, 317, 423-428 (1993), Série 1 · Zbl 0781.73033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.