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Progress In Electromagnetics Research
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DISCRETE ELECTROMAGNETISM WITH THE FINITE INTEGRATION TECHNIQUE

By M. Clemens and T. Weiland

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Abstract:
The Finite Integration Technique (FIT) is a consistent discretization scheme for Maxwell's equations in their integral form. The resulting matrix equations of the discretized fields can be used for efficient numerical simulations on modern computers. In addition, the basic algebraic properties of this discrete electromagnetic field theory allow to analytically and algebraically prove conservation properties with respect to energy and charge of the discrete formulation and gives an explanation of the stability properties of numerical formulations in the time domain.

Citation: (See works that cites this article)
M. Clemens and T. Weiland, "Discrete Electromagnetism with the Finite Integration Technique," Progress In Electromagnetics Research, Vol. 32, 65-87, 2001.
doi:10.2528/PIER00080103
http://www.jpier.org/PIER/pier.php?paper=00080103

References:
1. Weiland, T., "A discretization method for the solution of Maxwell’s equations for six-component fields," Electronics and Communications AEU, Vol. 31, No. 3, 116-120, 1977.

2. Tonti, E., "On the geometrical structure of electromagnetism," Gravitation, Electromagnetism and Geometrical Structures, G. Ferraese (ed.), 281–308, Pitagora, Bologna, 1996.

3. Bossavit, A., L. Kettunen, and T. Tarhassaari, "Some realizations of a discrete Hodge operator: A reinterpretation of the finite element technique," IEEE Transactions on Magnetics, Vol. 35, 1494-1497, May 1999.
doi:10.1109/20.767212

4. Teixeira, F. L. and W. C. Chew, "Lattice electromagnetic theory from a topological viewpoint," Journal of Mathematical Physics, Vol. 40, No. 1, 169-187, 1999.
doi:10.1063/1.532767

5. Nedelec, J. C., "Mixed finite elements in R3," Numerische Mathematik, No. 35, 315-341, 1980.
doi:10.1007/BF01396415

6. van Rienen, U. and T. Weiland, "Triangular discretization method for the evaluation of RF-fields in cylindrically symmetric cavities," IEEE Transactions on Magnetics, Vol. 21, No. 6, 2317-2320, 1985.
doi:10.1109/TMAG.1985.1064183

7. Schuhmann, R. and T. Weiland, "A stable interpolation technique for FDTD on nonorthogonal grids," International Journal on Numerical Modelling, Vol. 11, 299-306, May 1998.
doi:10.1002/(SICI)1099-1204(199811/12)11:6<299::AID-JNM314>3.0.CO;2-A

8. Thoma, P. and T. Weiland, "A consistent subgridding scheme for the finite difference time domain method," International Journal of Numerical Modelling, Vol. 9, 359-374, 1996.
doi:10.1002/(SICI)1099-1204(199609)9:5<359::AID-JNM245>3.0.CO;2-A

9. Chen, W. K., Graph Theory and It’s Engineering Applications, Vol. 5, Advanced Series in Electrical and Computer Engineering, World Scientific, Singapor, 1996.

10. Weiland, T., "Time domain electromagnetic field computation with finite difference methods," International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 9, 259-319, 1996.

11. Clemens, M., "Zur numerischen Berechnung zeitlich langsamver ¨anderlicher elektromagnetischer Felder mit der Finiten- Integrations-Methode,", Ph.D. thesis, Technische Universitat Darmstadt, 1998.

12. Weiland, T., "Lossy waveguides with arbitrary boundary contour and distribution of material," Electronics and Communications AEU, Vol. 33, 170, 1979.

13. Muller, W. and W. Wolff, "Ein Beitrag zur numerischen Berechnung von Magnetfeldern," Elektrotechnische Zeitung, Vol. 96, 269-273, 1975.

14. Muller, W., J. Kr¨uger, A. Jacobus, R. Winz, T.Weiland, H. Euler, U. Kamm, and W. R. Novender, "Numerical solution of 2- and 3- dimensional nonlinear field problems by means of the computer program PROFI," Archiv fur Elektrotechnik, Vol. 65, 299-307, 1982.
doi:10.1007/BF01452154

15. Krietenstein, B., P. Thoma, R. Schuhmann, and T. Weiland, "The perfect boundary approximation technique facing the big challenge of high precision computation," Proceedings of the 19th LINAC Conference, Chicago, August 1998.

16. Schuhmann, R. and T. Weiland, "FDTD on nonorthogonal grids with triangular fillings," IEEE Transactions on Magnetics, Vol. 35, 1470-1473, May 1999.
doi:10.1109/20.767244

17. Clemens, M., M. Hilgner, R. Schuhmann, and T. Weiland, "Transient eddy current simulation using the nonorthogonal finite integration technique," Conference Records of the CEFC 2000, Milwaukee, 385, 2000. Full paper submitted to IEEE Transactions on Magnetics.

18. Gutschling, S., "Zeitbereichsverfahren zur simulation elektromagnetischer felder in dispersiven materialien," Ph.D. thesis, Technische Universitat Darmstadt, 1998.

19. Gutschling, S., H. Kruger, H. Spachmann, and T. Weiland, "FIT-formulation for nonlinear dispersive media," International Journal on Numerical Modelling, Vol. 12, 81-92, 1999.

20. Kruger, H., H. Spachmann, and T. Weiland, "FIT-formulation for gyrotropic media," Proceedings of the ICCEA1999, Torino, Italy, 1999.

21. Clemens, M., S. Drobny, and T. Weiland, "Time integration of slowly-varying electromagnetic field problems using the finite integration technique," Proceedings of the ENUMATH 97, 246-253, Heidelberg, 1999.

22. Bossavit, A. and L. Kettunen, "Yee-like schemes on a tetrahedral mesh, with diagonal lumping," International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 12, No. 1/2, 129-142, 1999.
doi:10.1002/(SICI)1099-1204(199901/04)12:1/2<129::AID-JNM327>3.0.CO;2-G

23. Janich, K., Vektoranalysis, 191-222, Springer Lehrbuch, Springer, 1993.
doi:10.1007/978-3-662-10752-2

24. Weiland, T., "On the unique numerical solution of Maxwellian eigenvalue problems in three dimensions," Particle Accelerators, Vol. 17, 227-242, 1985.

25. Tonti, E., "Discrete formulation of the electromagnetic field,", University Trieste, 34127 Trieste, Italy, 1998.

26. Thoma, P. and T. Weiland, "Numerical stability of finite difference time domain methods," IEEE Transactions on Magnetics, Vol. 34, No. 5, 2740-2743, 1998.
doi:10.1109/20.717636

27. Schmitt, D., "Zur numerischen berechnung von resonatoren und wellenleitern,", Ph.D. thesis, Technische Hochschule Darmstadt, 1994.

28. Hahne, P., "Zur numerischen berechnung zeitharmonischer elektromagnetischer felder,", Ph.D. thesis, Technische Hochschule Darmstadt, 1992.

29. Bossavit, A., "`stiff’ problems in eddy-current theory and the regularization of Maxell’s equations," Conference Records of the CEFC 2000, Milwaukee, 497, 1997. Full paper submitted to IEEE Transactions on Magnetics.

30. Grosmann, C. and H.-G. Roos, Numerik partieller Differentialgleichungen, B. G. Teubner Verlag, Stuttgart, 1994.
doi:10.1007/978-3-322-96752-7

31. Schuhmann, R. and T. Weiland, "Conservation of discrete energy and related laws in the finite integration technique,", this volume.

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

33. Zienkiewicz, O. C., W. L. Wood, N. H. Hine, and R. L. Taylor, "A unified set of single step algorithms; part 1," Int. J. for Num. Meth. in Eng., Vol. 20, 1529-1552, 1984.
doi:10.1002/nme.1620200814

34. Monk, P., "A mixed method for approximating Maxwell’s equations," SIAM J. Numer. Anal., Vol. 28, 1610-1634, December 1991.
doi:10.1137/0728081

35. Clemens, M. and T. Weiland, "Transient eddy current calculation with the FI-method," IEEE Transactions on Magnetics, Vol. 35, 1163-1166, May 1999.
doi:10.1109/20.767155

36. Clemens, M. and T. Weiland, "Numerical algorithms for the FDiTD and FDFD simulation of slowly-varying electromagnetic fields," Int. J. Numerical Modelling, Special Issue on Finite Difference Time Domain and Frequency Domain Methods, Vol. 12, No. 1/2, 3-22, 1999.

37. Drobny, S., M. Clemens, and T. Weiland, "Dual nonlinear magnetostatic formulations using the finite integration technique," Conference Records of the CEFC 2000, Milwaukee, 392, 2000. Full paper submitted to IEEE Transactions on Magnetics.


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