A numerical method, based on the use of vector-valued finite elements with tangential continuity (edge elements), is proposed for the computation of eddy-currents induced by a time-varying source current in a ferromagnetic conductor.
Get full access to this article
View all access options for this article.
References
1.
AhnC.-H., LeeS.-Y., RaJ.-W., Analysis of ‘Felix’ brick with hole by 3-dimensional ‘Eddynet’ computer code", IEEE Trans., MAG-24, 1 (1988) 193–96.
BidanJ.Y., CahouetJ., ChaussecourteP., VéritéJ. C., in: Proc. Int. Symp. & TEAM Workshop (3DMAG), Okayama, 1989, to appear, COMPEL (1990).
4.
BiroO., PreisK., Finite element analysis of 3-D eddy currents, in: Proc. Conf. COMPUMAG, Tokyo, 1989, IEEE Trans. on Magn. (1990).
5.
BossavitA., A rationale for ‘edge-elements’ in 3-D fields computations, IEEE Trans. MAG-24, 1 (1988) 74–79.
6.
BossavitA., Solving Maxwell's equations in a closed cavity, and the question of ‘spurious modes', in: Proc. Conf. COMPUMAG, Tokyo, 1989, to appear, IEEE Trans. on Magn. (1990).
7.
BossavitA., VéritéJ. C., A mixed FEM-BIEM method to solve 3D eddy-current problems, IEEE Trans., MAG-18, 2 (1982) 431–35.
8.
CarpenterC.J., Comparison of alternative formulations of 3-dimensional magnetic-field and eddy-current problems at power frequencies, Proc. IEEE, 124, 11 (1977) 1026–34.
9.
DodziukJ., Finite-difference approach to the Hodge theory of harmonic forms, Amer. J. Math.98, 1 (1976) 79–104.
10.
ElliottC.M., On the finite element approximation of an elliptic variational inequality arising from an implicit time discretization of the Stefan problem, IMA J. Numer. Anal.1 (1981) 115–25.
11.
EmsonC.R.I., TrowbridgeC.W., Transient 3D eddy currents using modified magnetic vector potentials and magnetic scalar potentials, IEEE Trans., MAG-24, 1 (1989) 86–89.
12.
FerrariR.L., Complementary variational formulations for eddy-current problems using the field variables E and H directly, IEE Proc, Pt. A, 132, 4 (1985) 157–64.
13.
HammondP., PenmanJ., Calculation of eddy currents by dual energy methods, Proc. IEE, 125, 7 (1978) 701–08.
HodgdonM., Applications of a theory of ferromagnetic hysteresis, IEEE Trans., MAG-24, 1 (1988) 218–21.
16.
KameariA., Three dimensional eddy current calculation using edge elements for magnetic vector potentials, in: Applied Electromagnetics in Materials (MiyaK., ed.) (Pergamon Press, Oxford, 1989) pp. 225-36.
17.
KikuchiF., Mixed and penalty formulations for finite elements analysis of an eigenvalue problem in electromagnetism, Comp. Meth. Appl. Mech. Engng.64 (1987) 509–21.
18.
KomorowskiJ., On finite-dimensional approximations of the exterior differential, codifferential and Laplacian on a Riemannian manifold, Bull. Acad. Polonaise Sc. (Math., Astr., Phys.), 23, 9 (1975) 999–1005.
19.
MayergoyzI., FriedmanG., Generalized Preisach model of hysteresis, IEEE Trans., MAG-24, 1 (1988) 212–17.
20.
MiyataK., MiyaK., Magnetic field and stress analysis of saturated steel, IEEE Trans., MAG-24, 1 (1988) 230–33.
21.
MoreauJ.J., Fonctionnelles convexes, Séminaire Leray, Collège de France, Paris (1966).
22.
MoreauJ.J., Applications of convex analysis to the treatment of elastoplastic systems, in: Applications of methods of Functional Analysis to problems in Mechanics, Symp. IUTAM-IMU, Lecture Notes in Math.503 (GermainP., NayrolesB., eds.) (Springer, Berlin, 1976).
23.
NakataT., TakahashiN., FujiwaraK., ShirakiY., Comparison of different finite elements for 3-D eddy current analysis, in: Proc. Conf. COMPUMAG, Tokyo, 1989, to appear, Trans IEEE, on Magn. (1990).
24.
NayrolesB., Quelques applications variationnelles de la théorie des fonctions duales à la mécanique des solides, J. de Mécanique, 10, 2 (1971) 263–89.
25.
OdenJ.T., ReddyJ.N., On dual complementary variational principles in mathematical physics, Int. J. Engng. Sci.12 (1974) 1–29.
26.
PanagiotopoulosP.D., Inequality problems in mechanics and applications, (Birkhaiiser, Boston, 1985).
27.
PenmanJ., FraserJ.R., Dual and complementary energy methods in electromagnetism, IEEE Trans., MAG-19, 6 (1983) 2311–16.
28.
RenZ., BouillultF., RazekA., BossavitA., VéritéJ. C., A new hybrid model using electric field formulation for 3-D eddy current problems, in: Proc. Conf. COMPUMAG, Tokyo, 1989, to appear, Trans IEEE, on Magn. (1990).
29.
RikabiJ., BryantC.F., FreemanE.M., Error-based derivation of complementary formulations for the eddy-current problem, IEE Proc, 135, Pt. A, 4 (1988) 208-16.
30.
SaitoIkeguchi S., HayanoS., Faster eddy current computation using Voronoi-Delaunay transformation, in: Applied Electromagnetics in Materials (MiyaK., ed.) (Pergamon, Oxford, 1989) pp. 271-82.
31.
WhitneyH., Geometric Integration Theory (Princeton University Press, Princeton, 1957).
