Abstract
We present two numerical methods for the simulation of ferromagnetic phenomenons in a metallic plate, with or without holes. First we briefly recall the physical model we use for describing the ferromagnetic phenomenon. This model is based on the use of a scalar potential while other models rather use a vector potential as in [1] or [2]. Next we present the discretization methods we use. We then apply these methods on the simple test-case of a thin ferromagnetic plate placed in front of a rectilineal electric conductor. We show the various obtained results: magnetic field on a line perpendicular to the plate and relative permeability on a given line in the plate. Finally we illustrate our results with an industrial device.
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References
O. Bíró and K. Preis. On the use of magnetic vector potential in the finite element analysis of three-dimensional eddy currents. IEEE Trans. Magn., 25(4):3145–3159, 1989.
O. Bíró, K. Preis, and K. R. Richter. On the use of the magnetic vector potential in the nodal and edge finite element analysis of 3D magnetostatic problems. IEEE Trans. Magn., 32(3):651–654, 1996.
J. Descloux, M. Flueck, and M. V. Romerio. A problem of magnetostatics related to thin plates. RAIRO Modél. Math. Anal. Numér., 32(7):859–876, 1998.
M. Flück, T. Hofer, A. Janka, and J. Rappaz. Numerical methods for ferromagnetic plates. Research report 08.2007, Institute of Analysis and Scientific Computing (IACS), EPFL, 2007.
A. Masserey, J. Rappaz, R. Rozsnyo, and M. Swierkosz. Numerical integration of the three-dimensional Green kernel for an electromagnetic problem. J. Comput. Phys., 205(1):48–71, 2005.
A. Masud and T. J. R. Hughes. A stabilized mixed finite element method for Darcy flow. Comput. Methods Appl. Mech. Engrg., 191(39–40):4341–4370, 2002.
J.-C. Nédélec. Acoustic and electromagnetic equations. Integral representations for harmonic problems, volume 144 of Applied Mathematical Sciences. Springer, New York, 2001.
J. Rappaz. About the ferromagnetic effects. Some mathematical results. Research report, Institute of Analysis and Scientific Computing (IACS), EPFL. To appear.
P. Vaněk, M. Brezina, and J. Mandel. Convergence of algebraic multigrid based on smoothed aggregation. Numer. Math., 88(3):559–579, 2001.
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Flück, M., Hofer, T., Janka, A., Rappaz, J. (2010). Numerical Methods for Ferromagnetic Plates. In: Fitzgibbon, W., Kuznetsov, Y., Neittaanmäki, P., Périaux, J., Pironneau, O. (eds) Applied and Numerical Partial Differential Equations. Computational Methods in Applied Sciences, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3239-3_13
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DOI: https://doi.org/10.1007/978-90-481-3239-3_13
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