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Three-dimensional magnetostatic problem. (English) Zbl 1015.78017

Summary: The paper is devoted to an approximation of the solution of Maxwell’s equations in three-dimensional space. We present two methods which couple a finite element method inside the magnetic materials with a boundary integral method which uses Poincaré-Steklov’s operator to describe the exterior domain. A computer code has been implemented for each method and a number of numerical experiments have been performed to validate each proposed methodology. Namely, we present numerical results concerning a nonlinear magnetostatic problem in \(\mathbb{R}^3\).

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78M15 Boundary element methods applied to problems in optics and electromagnetic theory
78A30 Electro- and magnetostatics
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[1] Silvester, Proceedings of the Institute of Electronics Engineers 118 pp 1743– (1971)
[2] Zienkiewicz, International Journal for Numerical Methods in Engineering 11 pp 355– (1977)
[3] Kikuchi, Japan Journal of Applied Mathematics 6 pp 209– (1989)
[4] A mixed finite element method for the magnetic field. In Proceedings of the Fifth International Symposium on Numerical Methods in Engineering, vol. 2, (eds). Computational Mechanics, Springer: Berlin, 1989; 137-141.
[5] Les Inégalités en Mécanique et en Physique. Dunod: Paris, 1972.
[6] Nédélec, Numerical Mathematics 35 pp 57– (1986)
[7] Exemples en électromagnétisme et en physique quantique. In Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, vol. 5, (eds). Masson: Paris, 1988; Chapter IX, 235-273.
[8] Etablissement d’une formulation variationnelle en champ pour la magnétostatique. Mise en oeuvre numérique dans le cas tridimentionnel par association d’éléments finis et d’intégrale de frontière. Ph.D. Thesis, l’Université de Tours, 1994.
[9] Bandelier, Journal of Physics III France 3 pp 995– (1993)
[10] Bossavit, IEE Proceedings 135 pp 493– (1988)
[11] Bossavit, IEEE Transactions Magnetics 24 pp 74– (1988)
[12] Bossavit, IEEE Transactions on Magnetics MAG-18 pp 431– (1982)
[13] Magnétostatique, Masson: Paris, Dunod, 1968.
[14] Analysis of magnetic fields of 3-D non-linear magnetostatic model (Problem 13). Proceedings of the European TEAM Workshop and International Seminar on Electromagnetic Field Analysis, vol. 107. 1990.
[15] Mixed and Hybrid Finite Element Methods. Springer: New York, 1991.
[16] Augmented Lagrangian Methods. North-Holland: Amsterdam, 1983.
[17] Nédélec, Numerical Mathematics 35 pp 315– (1980)
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