Previous |  Up |  Next


magnetic field; variational formulation; two-sided existence and uniqueness condition; finite element method; convergence; finite element method; numerical example; magnetic potential
A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity models used in electrotechnical practice.
[1] K. Chrobáček, F. Melkes, L. Rak: Stationary magnetic field computation of electrical machines. TES 1977, theoretical number, 22–29. (Czech)
[2] P.G. Ciarlet: The Finite Element Method for Elliptic Problems. North-Holland, Amsterodam, 1978. MR 0520174 | Zbl 0383.65058
[3] E.A. Erdelyi, E.F. Fuchs, (D.H. Binkley): Nonlinear magnetic field analysis of DC machines I, II, III. IEEE Trans., PAS-89 (1970), 7, 1546–1583.
[4] A. Foggia, J.C. Sabonnadière, P. Silvester: Finite element solution of saturated travelling magnetic field problems. IEEE Trans., PAS-94 (1975), 866–871.
[5] Glowinski, A. Marrocco: Analyse numerique du champ magnetique d’un alternateur par elements finis et sur-relaxation ponctuelle non lineaire. Comput. Methods Appl. Mech. Engrg. 3 (1974), 55–85. DOI 10.1016/0045-7825(74)90042-5 | MR 0413547
[6] B. Lencová, M. Lenc: A finite element method for the computation of magnetic electron lenses. Scanning Electron Microscopy 1986/III, SEM Inc., AMF O’Hare, Chicago, 1986, pp. 897–915.
[7] F. Melkes: Solving the magnetic field by the finite element method. PhD. Thesis, Czechoslovak Academy of Sciences, Prague, 1970. (Czech—see also report of VÚES Brno, TZ 1481)
[8] F. Melkes: The finite element method for non-linear problems. Apl. Mat. 15 (1970), 177–189. MR 0259695 | Zbl 0209.17201
[9] F. Melkes: Magnetic energy computation using piecewise linear approximations. Acta Tech. ČSAV (1990), 365–373.
[10] J. Polák: Variational Principles and Methods of Electromagnetic Theory. Academia, Prague, 1988. (Czech)
[11] H. Reiche: Die Ermittlung stationärer magnetischer Felder in elektrischen Maschinen. IX. Internat. Kolloquium TH, Ilmenau, 1966.
[12] P. Silvester, H.S. Cabayan, B.T. Browne: Efficient techniques for finite element analysis of electric machines. IEEE Trans., PAS-92 (1973), 1274–1281.
[13] H. Tsuboi, F. Kobayashi, T. Misaki: Two-dimensional magnetic field analysis using edge elements. Proc. of the Third Japanese-Czech-Slovak Joint Seminar on Applied Electromagnetics, Prague, 1995, pp. 53–56.
[14] A.M. Winslow: Numerical solution of the quasilinear Poisson equation in a non-uniform triangle mesh. LRL Livermore California, 1967, pp. 149–172. MR 0241008
[15] A. Ženíšek: The maximum angle condition in the finite element method for monotone problems with applications in magnetostatics. Numer. Math. 71 (1995), 399–417. DOI 10.1007/s002110050151 | MR 1347576
Partner of
EuDML logo