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Progress In Electromagnetics Research
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Physical Spline Finite Element (PSFEM) Solutions to One Dimensional Electromagnetic Problems

By X. Zhou

Full Article PDF (667 KB)

Abstract:
In this paper, a new computational technique is presented for the first time. In this method, physical differential equations are incorporatedin to interpolations of basic element in finite element methods. This is named physical spline finite element method (PSFEM). Theoretically, the physical spline interpolation introduces many new features. First, physical equations can be usedin the interpolations to make the interpolations problem-associated. The algorithm converges much faster than any general interpolation while keeping the simplicity of the first order Lagrange interpolation. Second, the concept of basis functions may need to be re-examined. Thirdly, basis functions could be complex without simple geometric explanations. The applications to typical one-dimensional electromagnetic problems show the great improvements of the newly developed PSFEM on accuracy, convergence andstabilit y. It can be extendedto other applications. Extension to two- andthree-d imensional problems is briefly discussed in the final section.

Citation:
X. Zhou, "Physical Spline Finite Element (PSFEM) Solutions to One Dimensional Electromagnetic Problems," Progress In Electromagnetics Research, Vol. 40, 271-294, 2003.
doi:10.2528/PIER02121801
http://www.jpier.org/PIER/pier.php?paper=0212181

References:
1. Zienkiewicz, O. C., The Finite Element Method in Structural and Continuum Mechanics, McGraw-Hill, New York, 1967.

2. Kwon, Y. W. and H. Bang, The Finite Element Method Using MATLAB, CRC Press, Boca Raton, 1997.

3. Silvester, P. P., Finite Elements for Electrical Engineers, Cambridge University Press, New York, 1996.
doi:10.1017/CBO9781139170611

4. Jin, J., The Finite Element Method in Electromagnetics, John Wiley & Sons, New York, 1993.

5. Volakis, J. L., A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications, IEEE Press, New York, 1998.
doi:10.1109/9780470544655

6. Silvester, P. P. and G. Pelosi, Finite Elements for Wave Electromagnetics: Method and Techniques, IEEE Press, New York, 1994.

7. Babuska, I. and M. Suri, "The p andhp versions of the finite element methods, basic principles and properties," SIAM Rev., Vol. 36, 578-632, 1994.
doi:10.1137/1036141

8. Melenk, J., K. Gerdes, and C. Schwab, "Fully discrete hp-finite elements: fast quadrature," Compu. Methods Appli. Mech. Engrg., Vol. 190, 4339-4364, October 2001.
doi:10.1016/S0045-7825(00)00322-4

9. Noor, A. K. and W. D. Pilkey, State-of the Art Surveys on Finite Element Technology, American Society of Mechanical Engineers, New York, 1983.

10. Cheney, W. and D. Kincaid, Numerical Mathematics and Computing, Brooks/Cole Publishing Company, Pacific Grove, 1994.

11. Castillo, L. E. G., T. K. Sarkar, and M. S. Palma, "An efficient finite element methodemplo ying wavelet type basis functions (waveguide analysis)," COMPEL — The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 13, 278-292, May 1994.

12. Mitchell, A. R., "Variational principles andthe finite element method," J. Inst. Maths. Applications, Vol. 9, 378-389, 1972.
doi:10.1093/imamat/9.3.378

13. Benjeddou, A., "Vibrations of complex shells of revolution using B-spline finite elements," Computer & Structures, Vol. 74, 429-440, April 2000.
doi:10.1016/S0045-7949(99)00060-7

14. Ahlberg, J. H., E. N. Nilson, and J. L. Walsh, The Theory of Splines and Their Applications, Academic Press, New York, 1967.

15. Prenter, P. M., Splines and Variational Methods, Wiley, New York, 1975.

16. de Boor, C., A Practical Guide to Spline, Springer-Verlag, New York, 1978.
doi:10.1007/978-1-4612-6333-3

17. Liang, X., B. Jian, and G. Ni, "The B-spline finite element methodin electromagnetic fieldn umerical analysis," IEEE Trans. on Magnetics, Vol. 23, 2641-2643, Sept. 1987.
doi:10.1109/TMAG.1987.1065516

18. Legault, S. R., T. B. A. Senior, and J. L. Volakis, "Design of planar absorbing layers for domain truncation in FEM applications," Electromagnetics, Vol. 16, 451-464, July 1996.
doi:10.1080/02726349608908490

19. Liang, X., B. Jian, and G. Ni, "B-spline finite element method applied to axi-symmetrical and nonlinear field problems," IEEE Trans. on Magnetics, Vol. 24, 27-30, Jan. 1988.
doi:10.1109/20.43850

20. Press, W. H. and S. A. Tewkdsky, Numerical Recipes in C, The Art of Scientific Computing, Cambridge University Press, New York, 1992.

21. Allen, M. B. and E. L. Isaacson, Numerical Analysis for Applied Science, Wiley, 1997.
doi:10.1002/9781118033128

22. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Teinhold, New York, 1990.

23. Zhou, X., "Physical spline finite element methodin microwave engineering,", Ph.D. thesis, Arizona State University, May 2001.

24. Zhou, X. and G. Pan, "Application of physical spline FEM to waveguide problems," PIERS 2000 Progress in Electromagnetics Research Symposium, 77, Boston, USA, July 2002.


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