Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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By E. Tonti

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The objective of this paper is to present an approach to electromagnetic field simulation based on the systematic use of the global (i.e. integral) quantities. In this approach, the equations of electromagnetism are obtained directly in a finite form starting from experimental laws without resortingto the differential formulation. This finite formulation is the natural extension of the network theory to electromagnetic field and it is suitable for computational electromagnetics.

Citation: (See works that cites this article)
E. Tonti, "Finite Formulation of the Electromagnetic Field," Progress In Electromagnetics Research, Vol. 32, 1-44, 2001.

1. Bossavit, A. and J. C. Verite, "A mixed FEM-BIEM method to solve eddy-currents problems," IEEE Trans.on Magnetics, Vol. 18, 431-435, 1982.

2. Bossavit, A., "A rationale for ‘edge-elements’ in 3-D fields computations," IEEE Trans.on Magnetics, Vol. 24, No. 1, 74-79, 1988.

3. Bossavit, A., C. Emson, and I. D. Mayergoyz, Methodes Numeriques en Electromagnetisme, Eyrolles, 1991.

4. Bossavit, A. and C. Emson, Computational Electromagnetism, Academic Press, 1998.

5. Deschamps, G. A., "Electromagnetics and differential forms," Proceedings of the IEEE, Vol. 69, No. 6, 676-696, 1981.

6. Deschamps, G. A. and R. W. Ziolkowski, "Comparison of Clifford and Grassmann algebras in applications to electromagnetism," Clifford algebras and their Applications in Mathematical Physics, J. S. R. Chisholm and A. K. Common (eds.), 501–515, Reidel Publ Comp., 1986.

7. Fleury, P. and J. P. Mathieu, Elettrostatica, Corrente Continua, Magnetismo, Zanichelli, Vol. 6, 1970.

8. Fouille, A., Electrotecnique a L’usage des Ingenieurs, Dunod, 1961.

9. Hallen, E., Electromagnetic Theory, Chapman & Hall, 1962.

10. Ingarden, R. S. and A. Jamiolkowsky, Classical Electrodynamics, Elsevier, 1985.

11. Jiang, B., J. Wu, and L. A. Povinelli, "The origin of spurious solutions in computational electromagnetics," Journal of Computational Physics, Vol. 125, 104-123, 1996.

12. Jefimenko, O. D., Electricity and Magnetism, Appleton-Century-Crofts, 1966.

13. Kotiuga, P. R., "Hodge decomposition and computational electromagnetics," Thesis, Department of Electrical Engineering, McGill University, Montreal, 1984.

14. Kron, G., "Equivalent circuits of the field equations of Maxwell," Proc. IRE, Vol. 32, 289-299, 1944.

15. Kron, G., "The frustratingsearc h for a geometrical model of electrodynamic networks," Tensor, Vol. 13, 111-128, 1963.

16. Langevin, P., "Sur la nature des grandeurs et les choix d’un systeme d’unites electriques," Bull. Soc.Francaise de Physique, Vol. 164, 9, 1922. Reprinted in Oeuvres Scientifiques de Paul Langevin, 493–505, Centre Nationale de la Recerque Scientifique, 1950.

17. Marrone, M., "Computational aspects of cell method in electrodynamics,", this volume.

18. Maxwell, J. C., Traite Elementaire d’electricite, Gauthier Villars, 1884.

19. Meixner, J., "The behaviour of electromagnetic fields at edges," IEEE Trans.A ntennas Propag., Vol. 20, No. 4, 442-446, 1972.

20. Pauli, W., Elettrodinamica, translation of Vorlesung Elektrodynamik, Boringhieri, 1964.

21. Penfield, P. and H. Haus, Electrodynamics of Moving Media, M.I.T. Press, 1967.

22. Perucca, E., Fisica Generale e Sperimentale, IV edizione, Vol. 2, Unione Tipografica Editrice Torinese, 1945.

23. Pohl, R. W., Physical Principles of Electricity and Magnetism, Blackie and Son, 1930.

24. Post, E. J., Geometry and Physics: A Global Approach, Burge, (ed.), Problems in the Foundation of Physics, Vol. 4, Springer-Verlag, 1971.

25. Rojansky, V., Electromagnetic Fields and Waves, Dover, 1979.

26. Schelkunoff, S. A., Electromagnetic Fields, Blaisdell, 1963.

27. Silvester, P., "Finite element solution of homogeneous waveguides problems," Alta Frequenza, Vol. 38, 313-317, 1969.

28. Sun, D. K., J. Manges, X Yuan, and Z. Cendes, "Spurious modes in finite-elements methods," IEEE Trans.A nt.Pr opag., Vol. 37, No. 5, 12-24, 1995.

29. Tonti, E., "On the mathematical structure of a large class of physical theories," Rend.A cc.Linc ei, Vol. LII, 48-56, 1972.

30. Tonti, E., "A mathematical model for physical theories," Rend. Acc.Lincei, Vol. LII, Part I, 175–181, Part II, 350–356, 1972.

31. Tonti, E., "On the formal structure of physical theories,", Preprint of the Italian National Research Council, 1975 (unpublished).

32. Tonti, E., "The algebraic-topological structure of physical theories," Conference on Symmetry, Similarity and Group Theoretic Methods in Mechanics, 441-467, Calgary, Canada, 1974.

33. Tonti, E., "The reasons for analogies between physical theories," Appl.Mat.Mo delling, Vol. I, 37-50, 1976.

34. Tonti, E., "On the geometrical structure of electromagnetism," Gravitation, Electromagnetism and Geometrical Structures, for the 80th Birthday of A.Lichner owicz, Edited by G. Ferrarese. Pitagora Editrice Bologna, 281–308, 1995.

35. Tonti, E., "Algebraic topology and computational electromagnetism," Fourth International Workshop on the Electric and Magnetic Fields: from Numerical Models to Industrial Applications, 284-294, Marseille, 1998.

36. Truesdell, C. and R. Toupin, The Classical Field Theories Handbuck der Physik, Band III/1, Springer, 1960.

37. Van Dantzig, D., "Electromagnetism, independent of metrical geometry," Proc.A msterdam Acad., Vol. 37, 521-525, 526–531, 643–652, 825–836, 1934.

38. Veblen, O. and J. H. C. Whitehead, The Foundations of Differential Geometry, Vol. 29, 55-56, Cambr. Tracts, 1932.

39. Weiland, T., "Eine methode zur Losungder Maxwellschen Gleichungen fur sechskomponentige felder auf diskreter basis," AEU, Band 31, Heft 3, 1977.

40. Weiland, T., "On the numerical solution of Maxwell’s equations and applications in the field of accelerator physics," Particle Accelerators, 245-292, 1984.

41. Weiland, T., "On the unique numerical solution of maxwellian eigenvalue problems in three dimensions," Particle Accelerators, 227-242, 1985.

42. Weiland, T., "Time domain electromagnetic field computation with finite difference methods," Int.J.of Num.Mo delling, Vol. 9, 295-319, 1996.

43. Yee, K. S., "Numerical solution of initial boundary value problems involvingMaxw ell’s equations in isotropic media," IEEE Trans. Antennas Propag., Vol. 14, 302-307, 1966.

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