Search search
Publication Date
to
Vol. 36
Latest Volume
All Volumes
PIERB 118 PIERB 117 PIERB 116 PIERB 115 PIERB 114 PIERB 113 PIERB 112 PIERB 111 PIERB 110 PIERB 109 PIERB 108 PIERB 107 PIERB 106 PIERB 105 PIERB 104 PIERB 103 PIERB 102 PIERB 101 PIERB 100 PIERB 99 PIERB 98 PIERB 97 PIERB 96 PIERB 95 PIERB 94 PIERB 93 PIERB 92 PIERB 91 PIERB 90 PIERB 89 PIERB 88 PIERB 87 PIERB 86 PIERB 85 PIERB 84 PIERB 83 PIERB 82 PIERB 81 PIERB 80 PIERB 79 PIERB 78 PIERB 77 PIERB 76 PIERB 75 PIERB 74 PIERB 73 PIERB 72 PIERB 71 PIERB 70 PIERB 69 PIERB 68 PIERB 67 PIERB 66 PIERB 65 PIERB 64 PIERB 63 PIERB 62 PIERB 61 PIERB 60 PIERB 59 PIERB 58 PIERB 57 PIERB 56 PIERB 55 PIERB 54 PIERB 53 PIERB 52 PIERB 51 PIERB 50 PIERB 49 PIERB 48 PIERB 47 PIERB 46 PIERB 45 PIERB 44 PIERB 43 PIERB 42 PIERB 41 PIERB 40 PIERB 39 PIERB 38 PIERB 37 PIERB 36 PIERB 35 PIERB 34 PIERB 33 PIERB 32 PIERB 31 PIERB 30 PIERB 29 PIERB 28 PIERB 27 PIERB 26 PIERB 25 PIERB 24 PIERB 23 PIERB 22 PIERB 21 PIERB 20 PIERB 19 PIERB 18 PIERB 17 PIERB 16 PIERB 15 PIERB 14 PIERB 13 PIERB 12 PIERB 11 PIERB 10 PIERB 9 PIERB 8 PIERB 7 PIERB 6 PIERB 5 PIERB 4 PIERB 3 PIERB 2 PIERB 1
All Journals
PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2011-11-10
A New Element-Oriented Model for Computational Electromagnetics
By
Hamid Magrez,

    Prof. Hamid Magrez

    Physic

    Mohammed First University

    Morocco

    Homepage

Abdelhak Ziyyat

    Dr. Abdelhak Ziyyat

    Faculty of Sciences

    Mohammed First University

    Morocco

    Homepage

Progress In Electromagnetics Research B, Vol. 36, 193-220, 2012
doi:10.2528/PIERB11050102 | Google Scholar

Abstract
In this paper, we present a new model using a Four-dimensional (4D) Element-Oriented physical concepts based on a topological approach in electromagnetism. Its general finite formulation on dual staggered grids reveals a flexible Finite-Difference Time-Domain (FDTD) method with reasonable local approximating functions. This flexible FDTD method is developed without recourse to the traditional Taylor based forms of the individual differential operators. This new formulation generalizes both the standard FDTD (S-FDTD) and the nonstandard FDTD (NS-FDTD) methods. Moreover, it can be used to generate new numerical methods. As proof, we deduce a new nonstandard scheme more accurate than the S-FDTD and the known nonstandard NS-FDTD methods. Through some numerical examples, we validate this proposal, and we show the power and the advantage of this Element-Oriented Model.
Download Full Article (746) View Full Article volume
Citation
Hamid Magrez, and Abdelhak Ziyyat, "A New Element-Oriented Model for Computational Electromagnetics," Progress In Electromagnetics Research B, Vol. 36, 193-220, 2012.
doi:10.2528/PIERB11050102
References

1. Sadiku, M. N. O., Numerical Techniques in Electromagnetics, 2nd Ed., CRC Press, 2001.

2. Salon, S. and M. V. K. Chari, Numerical Methods in Electromagnetism, Academic Press, 1999.

3. Rjasanow, S. and O. Steinbach, The Fast Solution of Boundary Integral Equations, Springer, 2007.

4. Baranger, J., J. F. Maitre, and F. Oudin, "Connection between finite volume and mixed finite element methods," RAIRO, Modelisation Math. Anal. Numer., Vol. 30, 445-465, 1996.        Google Scholar

5. De La Bourdonnay, A. and S. Lala, "Duality between finite elements and finite volumes and Hodge operator," Numerical Methods in Engineering'96, 557-561, Wiley & Sons, Paris, 1996.        Google Scholar

6. Bossavit, A. and L. Kettunen, "Yee-like schemes on staggered cellular grids: A synthesis between FIT and FEM approaches," IEEE Trans. Magn., Vol. 36, No. 4, 861-867, 2000.
doi:10.1109/20.877580        Google Scholar

7. Teixeira, F. L., "Geometric aspects of the simplicial discretization of Maxwell's equations," Progress In Electromagnetics Research, Vol. 32, 171-188, 2001.
doi:10.2528/PIER00080107        Google Scholar

8. Tonti, E., "Finite formulation of the electromagnetic field," Progress In Electromagnetics Research, Vol. 32, 1-44, 2001.
doi:10.2528/PIER00080101        Google Scholar

9. Mattiussi, C., "An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology," J. Comp. Phys., Vol. 9, 295-319, 1997.        Google Scholar

10. Gross, P. W. and P. R. Kotiuga, Electromagnetic Theory and Computation: A Topological Approach, Cambridge University Press, 2004.
doi:10.1017/CBO9780511756337

11. Maxwell, J. C., A Treaties on Electricity and Magnetism, Clarendon Press, 1892, Reprinted in 2002.

12. Stern, A., Y. Tong, M. Desbrun, and J. E. Marsden, "Computational electromagnetism with variational integrators and discrete differential forms," arXiv: 0707.4470 [math.NA], 2007.        Google Scholar

13. Hiptmair, R., "Discrete Hodge-operators: An algebraic perspective," Progress In Electromagnetics Research, Vol. 32, 247-269, 2001.
doi:10.2528/PIER00080110        Google Scholar

14. Hiptmair, R., "Discrete Hodge operators," Numer. Math., Vol. 90, No. 2, 65-289, 2001.
doi:10.1007/s002110100295        Google Scholar

15. Auchmann, B. and S. Kurz, "A geometrically defined discrete Hodge operator on simplicial cells," IEEE Trans. Magn., Vol. 42, No. 4, 643-646, 2006.
doi:10.1109/TMAG.2006.870932        Google Scholar

16. Mickens, R. E., Applications of Nonstandard Finite Difference Schemes, World Scientific, 2000.
doi:10.1142/9789812813251

17. Marrone, M., "Computational aspects of the cell method in electrodynamics," Progress In Electromagnetics Research, Vol. 32, 317-356, 2001.
doi:10.2528/PIER00080113        Google Scholar

18. Garcia, S. G. and T.-W. Lee, "On the accuracy of the ADI-FDTD method," IEEE Antennas and Wireless Propagation Letters, Vol. 1, No. 1, 2002.        Google Scholar

19. Ahmed, I., E. K. Chua, E. P. Li, and Z. Chen, "Development of the three dimensional unconditionally stable LOD-FDTD method," IEEE Trans. Antennas Propag., Vol. 56, No. 11, 3596-3600, 2008.
doi:10.1109/TAP.2008.2005544        Google Scholar

20. Zheng, F., Z. Chen, and J. Zhang, "A finite-difference time-domain method without the Courant stability conditions," IEEE Microw. Guided Wave Lett., Vol. 9, No. 11, 441-443, 1999.
doi:10.1109/75.808026        Google Scholar

21. Anguelov, R. and S. Lubuma, "On non-standard finite difference models of reaction-diffusion equations," Journal of Applied Mathematics, Vol. 175, No. 1, 2005.        Google Scholar

22. Bossavit, A., "Generalized finite differences' in computational electromagnetics," Progress In Electromagnetics Research, Vol. 32, 45-64, 2001.
doi:10.2528/PIER00080102        Google Scholar

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

24. Alotto, P., F. Freschi, and M. Repetto, "Multiphysics problems via the cell method: The role of Tonti diagrams," IEEE Trans. Magn., 2959-2962, Aug. 2010.
doi:10.1109/TMAG.2010.2044487        Google Scholar

25. Tarhasaari, T., L. Kettunen, and A. Bossavit, "Some realizations of a discrete Hodge operator: A reinterpretation of finite element techniques," IEEE Trans. Magn., Vol. 35, No. 3, 1494-1497, 1999.
doi:10.1109/20.767250        Google Scholar

26. Tarhasaari, T. and L. Kettunen, "Topological approach to computational electromagnetism," Progress In Electromagnetics Research, Vol. 32, 189-206, 2001.
doi:10.2528/PIER00080108        Google Scholar

27. Truesdell, C. and R. A. Toupin, The Classical Field Theories, Harrdbuch der Physik, Vol. 311, 226-793, edited by S. Flugge, 1960.

28. Tarhasaari, T. and L. Kettunen, "Topological approach to computational electromagnetism," Progress In Electromagnetic Research, Vol. 32, 189-206, 2001.
doi:10.2528/PIER00080108        Google Scholar

29. Kirawanich, P., et al. "Methodology for interference analysis using electromagnetic topology techniques," Applied Physics Letters, Vol. 84, 2004.        Google Scholar

30. Lindel, I. V., Differential Forms in Electromagnetics, IEEE Press, 2004.
doi:10.1002/0471723096

31. Lindel, I. V., "Electromagnetic wave equation in differential-form representation," Progress In Electromagnetics Research, Vol. 54, 321-333, 2005.
doi:10.2528/PIER05021002        Google Scholar

32. Lindell, I. V., "Electromagnetic fields in self-dual media in differential-form representation," Progress In Electromagnetics Research, Vol. 58, 319-333, 2006.
doi:10.2528/PIER05072201        Google Scholar

33. Mattiussi, C., "The geometry of time-stepping," Progress In Electromagnetics Research, Vol. 32, 123-149, 2001.
doi:10.2528/PIER00080105        Google Scholar

34. Anguelov, R. and S. Lubuma, "Nonstandard dfinite-difference methods by nonlocal approwimations," Mathematics and Computer in Simulation, 2003.        Google Scholar

35. Magrez, H. and A. Ziyyat, "Modélisation orientée objet en electromagntisme," Congrés Méditerranen des Télécommunications CMT, Casablanca, 2010.

36. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, 1989.

37. Pinheiro, H., J. P. Webb, and I. Tsukerman, "Flexible local approximation models for wave scattering in photonic crystal devices," IEEE Trans. Magn., Vol. 43, No. 4, 1321-1324, 2007.
doi:10.1109/TMAG.2006.891004        Google Scholar

38. Tsukerman, I., "A class of difference schemes with flexible local approximation," The Journal of Computational Physics, Vol. 211, No. 2, 659-699, 2006.
doi:10.1016/j.jcp.2005.06.011        Google Scholar

Download Full Article (746) View Full Article volume


The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.