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On a certain two-sided symmetric condition in magnetic field analysis and computations. (English) Zbl 0902.65078

A finite element method for solving a nonlinear boundary value problem of elliptic type with mixed boundary conditions is investigated. The problem describes the nonlinear stationary magnetic field distributed in a planar domain composed of different isotropic media. The authors introduce a special two-sided condition for the incremental magnetic reductivity which guarantees the existence and uniqueness of the weak and approximate solutions. The main theorem establishes the convergence of the finite element method in the Sobolev \(H^1(\Omega)\)-norm. A numerical example for the calculation of a magnetic potential in a synchronous rotary machine is given.

MSC:

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A30 Electro- and magnetostatics
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References:

[1] K. Chrobáček, F. Melkes, L. Rak: Stationary magnetic field computation of electrical machines. TES 1977, theoretical number, 22-29.
[2] P.G. Ciarlet: The Finite Element Method for Elliptic Problems. North-Holland, Amsterodam, 1978. · 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. · Zbl 0288.65068
[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. · Zbl 0209.17201
[8] F. Melkes: The finite element method for non-linear problems. Apl. Mat. 15 (1970), 177-189. · 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.
[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. · Zbl 0254.65069
[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. · Zbl 0832.65124
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