Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T14:23:32.526Z Has data issue: false hasContentIssue false
  • English
  • Français

A Slideing Mesh-Mortar Method for a two Dimensional Currents Model of Electric Engines

Published online by Cambridge University Press:  15 April 2002

Annalisa Buffa ,
Yvon Maday  and
Francesca Rapetti
Annalisa Buffa
Affiliation:
Dipartimento di Matematica, Universitá di Pavia, Via Abbiategrasso 209, 27100 Pavia, Italy. (annalisa@dimat.unipv.it)
Yvon Maday
Affiliation:
Applications Scientifiques du Calcul Intensif, UPR 9029 CNRS, bâtiment 506, Université Paris XI, 91403 Orsay, France. Laboratoire d'Analyse Numérique, Université Paris VI, 4 place Jussieu, 75252 Paris, France.
Francesca Rapetti
Affiliation:
Laboratoire d'Analyse Numérique, Université Paris VI, 4 place Jussieu, 75252 Paris, France.
Get access

Abstract

The paper deals with the application of a non-conforming domaindecomposition methodto the problem of the computation of induced currents in electric engineswith moving conductors.The eddy currents model is considered as a quasi-staticapproximation of Maxwellequations and we study its two-dimensional formulation with either themodified magnetic vector potential or the magnetic field as primary variable.Two discretizations are proposed, the first one based on curved finiteelementsand the second one based on iso-parametric finite elements in both thestatic and movingparts. The coupling is obtained by means of the mortar element method(see [CITE])and the approximation on the whole domain turns out to be non-conforming.In bothcases optimal error estimates are provided. Numerical tests are then proposed in the case of standard first order finiteelements to test the reliability and precision of the method. An applicationof the method to study the influence of the free part movement on thecurrents distribution is also provided.

Keywords

Eddy currents problemnon-conforming finite element approximationdomain decomposition methods.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 2 , March 2001 , pp. 191 - 228
Copyright
© EDP Sciences, SMAI, 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

R. Adams, Sobolev spaces. Academic Press, London (1976).
R. Albanese and G. Rubinacci, Formulation of the eddy-current problem. IEEE proceedings 137 (1990).
G. Anagnostou, A. Patera and Y. Maday, A sliding mesh for partial differential equations in nonstationary geometries: application to the incompressible Navier-Stockes equations. Tech. rep., Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie (1994).
Ben Belgacem, F. and Maday, Y., Non-conforming spectral element methodology tuned to parallel implementation. Comput. Meth. Appl. Mech. Engrg. 116 (1994) 59-67. CrossRef
Ben Belgacem, F., Maday, Y., The mortar element method for three dimensional finite elements. RAIRO-Modél. Math. Anal. Numér. 2 (1997) 289-302. CrossRef
Bernardi, C., Optimal finite element interpolation of curved domains. SIAM J. Numer. Anal. 26 (1989) 1212-1240. CrossRef
C. Bernardi, Y. Maday and A.T. Patera, A new nonconforming approach to domain decomposition: The mortar elements method, in Nonlinear partial differential equations and their applications, H. Brezis and J. Lions, Eds., Collège de France Seminar, Paris, Vol. XI (1994) 13-51.
A. Bossavit, Électromagnétisme en vue de la modélisation, Springer-Verlag, Paris (1986).
Bossavit, A., Calcul des courants induits et des forces électromagnétiques dans un système de conducteurs mobiles. RAIRO-Modél. Math. Anal. Numér. 23 (1989) 235-259. CrossRef
Bossavit, A., Le calcul des courants de Foucault en dimension 3, avec le champ électrique comme inconnue. I: Principes. Rev. Phys. Appl. 25 (1990) 189-197. CrossRef
Bouillault, F., Ren, Z. and Razek, A., Modélisation tridimensionnelle des courants de Foucault à l'aide de méthodes mixtes avec différentes formulations. Rev. Phys. Appl. 25 (1990) 583-592. CrossRef
Carpenter, C.J., Comparison of alternative formulations of 3-dimensional magnetic-field and eddy-current problems at power frequencies. IEEE proceedings 124 (1977) 1026-1034.
P. Ciarlet, The finite element method for elliptic problems. North-Holland, Amsterdam (1978).
R. Dautray and J.L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, 2nd edn. Masson, Paris (1987).
B. Davat, Z. Ren and M. Lajoie-Mazenc, The movement in field modeling. IEEE, Trans. Magn. 21 (1985) 2296-2298.
C.R.I. Emson, C.P. Riley, D.A. Walsh, K. Ueda and T. Kumano, Modeling eddy currents induced by rotating systems. IEEE, Trans. Magn. 34 (1998) 2593-2596.
Goldman, Y., Joly, P. and Kern, M., The electric field in the conductive half-space as a model in mining and petroleum prospection. Math. Meth. Appl. Sci. 11 (1989) 373-401. CrossRef
J. Jackson, Classical electrodynamics. Wiley, New York (1952).
S. Kurz, J. Fetzer, G. Lehenr, and W. Rucker, A novel formulation for 3d eddy current problems with moving bodies using a Lagrangian description and bem-fem coupling. IEEE, Trans. Magn. 34 (1998) 3068-3073.
R. Leis, Initial Boundary value problems in mathematical physics. John Wiley and Sons (1986).
Y. Marechal, G. Meunier, J. Coulomb and H. Magnin, A general purpose for restoring inter-element continuity. IEEE, Trans. Magn. 28 (1992) 1728-1731.
Nicolet, A., Delincé, F., Genon, A. and Legros, W., Finite elements-boundary elements coupling for the movement modeling in two dimensional structures. J. Phys. III 2 (1992) 2035-2044.
A. Quarteroni and A. Valli, Numerical approximation of partial differential equations. Ser. Comput. Math. 23, Springer-Verlag (1993).
Rapetti, F., Santandrea, L., Bouillault, F. and Razek, A., Simulating eddy currents distributions by a finite element method on moving non-matching grids. COMPEL 19 (2000) 10-29. CrossRef
A. Razek, J. Coulomb, M. Felliachi and J. Sobonnadière, Conception of an air-gap element for dynamic analysis of the electromagnetic fields in electric machines. IEEE, Trans. Magn. 18 (1982) 655-659. CrossRef
D. Rodger, H. Lai and P. Leonard, Coupled elements for problems involving movement. IEEE, Trans. Magn. 26 (1990) 548-550.
V. Thomeé, Galerkin finite element methods for parabolic problems. Ser. Comput. Math. 25, Springer (1997).