Reduction of model dimension in nonlinear finite element approximations of electromagnetic systems

Proceedings of the IEEE Workshop on Computers in Power Electronics, COMPEL

Volumn , Issue , 2004, Pages 20-27

  Rutenkroger, S ^a   Deken, B ^b   Pekarek, S ^b  

^a US NRC Region IV   (United States)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Empirical Eigenvectors; Finite Element Analysis; Nonlinear Analysis; Reduced Model Dimensions

Indexed keywords

EMPERICAL EIGENVECTORS; IRON-CORE; NONLINEAR ANALYSIS; REDUCED MODEL DIMENSIONS;

CURRENT DENSITY; EIGENVALUES AND EIGENFUNCTIONS; ELECTRIC INDUCTORS; ELECTRIC LOSSES; FINITE ELEMENT METHOD; MAGNETIC FLUX; MAXWELL EQUATIONS; NONLINEAR SYSTEMS; NUMERICAL ANALYSIS;

ELECTROMAGNETISM;

EID: 21644472598     PISSN: 10935142     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CIPE.2004.1428114     Document Type: Conference Paper

References (24)

1. Karhunen, K. "Zur Spektraltheorie Stochastischer Prozesse," Ann. Acad. Sci. Fennicae, Vol. 37, 1946.
2. Loève, M. Probability Theory. Van Nostrand, N.J., 1955.
3. Hotelling, H. "Analysis of Complex Statistical Variables in Principal Components," J. Exp. Psy., Vol. 24, 1953, pg 417.
4. Lorenz, E. "Empirical Orthogonal Eigenfunctions and Statistical Weather Prediction. Technical Report," MIT, Dept. of Meteorology, Statistical Forecasting Project, 1956.
5. Harman, H. Modern Factor Analysis. University of Chicago Press, 1960.
6. Lumley, J. "The Structure of Inhomogeneous Turbulent Flows," In Yaglom, A., and Tatarski, V., editors, Atmospheric Turbulence and Radio Wave Propagation, Nauka, Moscow, 1967, pp 166-178.
7. Golub, G., and van Loan, C. Matrix Computations. North Oxford Academic, Oxford, 1983.
8. Pearson, K. "On Lines and Planes of Closest Fit to Systems of Points in Space," Philo. Mag., Vol. 6, 1901, pg 559.
9. Schmidt, E. "Zur Theorie der Linearen und Nichtlinearen Integralgleichungen. I Teil: Zwicklung Willkürlicher Function nach Systemen Vorgeschriebener," Mathematische Annalen, Vol. 63, 1907, pp 433-476.
10. Holmes, P., J. Lumley, and G. Berkooz. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press, 1996.
11. Krysl, P., S. Lall, and J. Marsden. "Dimensional Model Reduction in Non-linear Finite Element Dynamics of Solids and Structures," International Journal for Numerical Methods in Engineering, vol. 51, 2001, pp 479-504.
12. Jin, J. The Finite Element Method in Electromagnetics. New York: Wiley, 1993.
13. nd Ed. McGraw-Hill, 1984
14. Demerdash, N., and Lau, N. "Flux Penetration and Losses in Solid Nonlinear Ferromagnetics using State Space Techniques Applied to Electrical Machines," IEEE Trans. MAG, Vol. 12, No. 6, Nov. 1976, pp 1039-1041.
15. Tandon, S., Armor, A., and Chari, M. "Nonlinear Transient Finite Element Field Computation for Electrical Machines and Devices," IEEE Trans. PAS, Vol. 102, No. 5, May 1983, pp 1089-1095.
16. Hannalla, A., and Macdonald, D. "Numerical Analysis of Transient Field Problems in Electrical Machines," Proc. IEEE, Vol. 123, No. 9, Sept. 1976, pp 893-898.
17. Foggia, A., Sabonnadiere, J., and Silvester, P. "Finite Element Solution of Saturated Traveling Magnetic Field Problems," IEEE Trans. PAS, Vol. 94, 1975, pp 886-871.
18. Chari, M. "Finite-Element Solution of Eddy-Current Problems in Magnetic Structures," IEEE Trans. PAS, Vol. 93, No. 1, 1974, pp 62-72.
19. Krefta, M., and O. Wasynczuk. "A finite element based state model of solid rotor synchronous machines," IEEE Transactions on Energy Conversion, vol. EC-2, 1987, pp. 21-30.
20. K. Fukunaga. Introduction to Statistical Pattern Recognition. Academic Press, Inc., 1972.
21. Sirovich, L. "Turbulence and the Dynamics of Coherent Structures," Pts I, II, and III. Quarterly of Applied Mathematics, vol. 45, 1987, pp 561-590.
22. Krysl, P., S. Lall, and J. Marsden. "Reduced-dimension Models in Nonlinear Finite Element Dynamics of Continuous Media," ICES'2K, August 2000, Los Angeles, California.
23. Owens, J., and P. Chapman. "Reduced FEA-state space modeling of stationary magnetic devices," IEEE 34th Annual Power Electronics Specialists Conference, vol. 1, 15-19 June 2003, pp 265-271.
24. nd Edition, Cambridge University Press, 1992.