Vol. 153
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2015-10-21
Numerical Study of a Time-Domain Finite Element Method for Nonlinear Magnetic Problems in Three Dimensions (Invited Paper)
By
Progress In Electromagnetics Research, Vol. 153, 69-91, 2015
Abstract
In this work, numerical analysis of nonlinear ferromagnetic problems is presented using the three-dimensional time-domain finite element method (TDFEM). Formulated with the secondorder nonlinear partial differential equation (PDE) combined with the inverse Jiles-Atherton (J-A) vector hysteresis model, the nonlinear problems are solved in the time domain with the Newton-Raphson method. To solve the ordinary differential equation (ODE) representing the magnetic hysteresis accurately and efficiently, several ODE solvers are specifically designed and investigated. To improve the computational efficiency of the Newton-Raphson method, the multi-dimensional secant methods, aka Broyden's methods, are incorporated in the nonlinear TDFEM solver. A nonuniform time-stepping scheme is also developed using the weighted residual approach to remove the requirement of a uniform time-step size during the simulation. The capability and the performance of the proposed methods are demonstrated by various numerical examples.
Citation
Su Yan Jian-Ming Jin Chao-Fu Wang Joseph D. Kotulski , "Numerical Study of a Time-Domain Finite Element Method for Nonlinear Magnetic Problems in Three Dimensions (Invited Paper)," Progress In Electromagnetics Research, Vol. 153, 69-91, 2015.
doi:10.2528/PIER15091006
http://www.jpier.org/PIER/pier.php?paper=15091006
References

1. Yan, S. and J.-M. Jin, "Theoretical formulation of a time-domain finite element method for nonlinear magnetic problems in three dimensions (Invited Paper)," in the Commemorative Collection on the 150-Year Anniversary of Maxwell's Equations, Progress In Electromagnetics Research, Vol. 153, 33-55, 2015.

2. Jin, J.-M., The Finite Element Method in Electromagnetics, 3rd Ed., Wiley, Hoboken, NJ, 2014.

3. Jiles, D. C. and D. L. Atherton, "Theory of the magnetisation process in ferromagnetics and its application to the magnetomechanical effect," J. Phys. D: Appl. Phys., Vol. 17, No. 6, 1265-1281, Jun. 1984.
doi:10.1088/0022-3727/17/6/023

4. Jiles, D. C. and D. L. Atherton, "Theory of ferromagnetic hysteresis," Journal of Magnetism and Magnetic Materials, Vol. 61, 48-60, Sep. 1986.
doi:10.1016/0304-8853(86)90066-1

5. Bergqvist, A. J., "A simple vector generalization of the Jiles-Atherton model of hysteresis," IEEE Trans. Magn., Vol. 32, No. 5, 4213-4215, Sep. 1996.
doi:10.1109/20.539337

6. Leite, J. V., N. Sadowski, P. Kuo-Peng, N. J. Batistela, J. P. A. Bastos, and A. A. de Espindola, "Inverse Jiles-Atherton vector hysteresis model," IEEE Trans. Magn., Vol. 40, No. 4, 1769-1775, Jul. 2004.
doi:10.1109/TMAG.2004.830998

7. Broyden, C. G., "A class of methods for solving nonlinear simultaneous equations," Math. Comp., Vol. 19, 577-593, 1965.
doi:10.1090/S0025-5718-1965-0198670-6

8. Zienkiewicz, O. C., "A new look at the Newmark, Houboult and other time stepping formulas: A weighted residual approach," Earthquake Engineering and Structural Dynamics, Vol. 5, 413-418, 1977.
doi:10.1002/eqe.4290050407

9. Ren, Z., "Influence of the R.H.S. on the convergence behaviour of the curl-curl equation," IEEE Trans. Magn., Vol. 32, No. 3, 655-658, May 1996.
doi:10.1109/20.497323

10. Whitney, H., Geometric Integration Theory, Princeton University Press, Princeton, NJ, 1957.

11. Nédélec, J. C., "Mixed finite elements in R3," Numer. Meth., Vol. 35, 315-341, 1980.
doi:10.1007/BF01396415

12. Webb, J. P., "Hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements," IEEE Trans. Antennas Propag., Vol. 47, No. 8, 1244-1253, Aug. 1999.
doi:10.1109/8.791939

13. Newmark, N. M., "A method of computation for structural dynamics," J. Engineering Mechanics Division. ASCE, Vol. 85, 67-94, Jul. 1959.

14. Gedney, S. D. and U. Navsariwala, "An unconditionally stable finite element time-domain solution of the vector wave equation," IEEE Microw. Guided Wave Lett., Vol. 5, No. 10, 332-334, Oct. 1995.
doi:10.1109/75.465046

15. Peterson, A. F., "Absorbing boundary conditions for the vector wave equation," Microw. Opt. Tech. Lett., Vol. 1, No. 2, 62-64, 1988.
doi:10.1002/mop.4650010206

16. Webb, J. P. and V. N. Kanellopoulos, "Absorbing boundary conditions for the finite element solution of the vector wave equation," Microw. Opt. Tech. Lett., Vol. 2, No. 10, 370-372, 1989.
doi:10.1002/mop.4650021010

17. Testing electromagnetic analysis methods (T.E.A.M.), http://www.compumag.org/jsite/team.html, International Compumag Society.

18. Albanese, R. and G. Rubinacci, "Solution of three dimensional eddy current problems by integral and differential methods," IEEE Trans. Magn., Vol. 24, 98-101, Jan. 1998.

19. Lee, S. H., "Efficient finite element electromagnetic analysis for high-frequency/high-speed circuits and multiconductor transmission line,", Ph.D. dissertation, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 2009.

20. Jorgensen, E., J. L. Volakis, P. Meincke, and O. Breinbjerg, "Higher order hierarchical Legendre basis functions for electromagnetic modeling," IEEE Trans. Antennas Propag., Vol. 52, No. 11, 2985-2995, Nov. 2004.
doi:10.1109/TAP.2004.835279

21. Nakata, T., T. Takahashi, K. Fujiwara, and P. Olszewski, "Analysis of magnetic fields of 3-D nonlinear magnetostatic model (problem 13)," Proc. of the European TEAM Workshop and Int. Sem. on Elecmagn. Field Anal., Oxford, England, Apr. 1990.

22. Nakata, T., N. Takahashi, and K. Fujiwara, "Summary of results for benchmark problem 10 (steel plates around a coil)," Compel., Vol. 14, No. 2/3, 103-112, Sep. 1995.
doi:10.1108/eb010141

23. Bottauscio, O., M. Chiampi, C. Ragusa, L. Rege, and M. Repetto, "A test-case for validation of magnetic field analysis with vector hysteresis," IEEE Trans. Magn., Vol. 38, No. 2, 893-896, Mar. 2002.
doi:10.1109/20.996230

24. Yamada, S., K. Bessho, and J. Lu, "Harmonic balance finite element method applied to nonlinear AC magnetic analysis," IEEE Trans. Magn., Vol. 24, No. 4, 2971-2973, Jul. 1989.