A general approach for the stability analysis of the time-domain finite-element method for electromagnetic simulations

IEEE Transactions on Antennas and Propagation

Volumn 50, Issue 11, 2002, Pages 1624-1632

  Jiao, Dan ^a   Jin, Jian Ming ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Finite element methods (FEM); Numerical analysis; Numerical stability; Time domain analysis; Transient analysis

Indexed keywords

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; NUMERICAL ANALYSIS; TIME DOMAIN ANALYSIS; TRANSIENTS;

ELECTROMAGNETIC SIMULATION; STABILITY ANALYSIS; TRANSIENT ANALYSIS;

ELECTROMAGNETIC WAVE PROPAGATION;

EID: 0036880343     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2002.803965     Document Type: Article

References (33)

1. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propagat., vol. 14, pp. 302-307, May 1966.
2. D. M. Sullivan, "Z-transform theory and the FDTD method," IEEE Trans. Antennas Propagat., vol. 44, pp. 28-34, Jan. 1996.
3. C. Hulse and A. Knoesen, "Dispersive models for the finite-difference time-domain method: Design, analysis and implementation." J. Opt. Soc. Amer., vol. 11, pp. 1802-1811, 1994.
4. P. G. Petropoulos, "Stability and phase error analysis of FDTD in dispersive dielectrics," IEEE Trans. Antennas Propagat., vol. 42, pp. 62-69, Jan. 1994.
5. W. H. Weedon and C. M. Rappaport, "A general method for FDTD modeling of wave propagation in arbitrary frequency-dispersive media," IEEE Trans. Antennas Propagat., vol. 45, pp. 401-410, Mar. 1997.
6. S. Gutschling, H. Kruger, and T. Weiland, "Time-domain simulation of dispersive media with the finite integration technique," Int. J. Numer. Model, vol. 13, pp. 329-348, 2000.
7. J. F. Lee, R. Lee, and A. C. Cangellaris, "Time-domain finite element methods," IEEE Trans. Antennas Propagat., vol. 45, pp. 430-442, Mar. 1997.
8. K. Choi, S. J. Salon, K. A. Connor, L. F. Libelo, and S. Y. Hahn, "Time domain finite analysis of high power microwave aperture antennas," IEEE Trans. Magn., vol. 31, pp. 1622-1625, May 1995.
9. M. Feliziani and F. Maradei, "An explicit-implicit solution scheme to analyze fast transients by finite elements," IEEE Trans. Magn., vol. 33, pp. 1452-1455, Mar. 1997.
10. G. Mur, "The finite-element modeling of three-dimensional time-domain electromagnetic fields in strongly inhomogeneous media," IEEE Trans. Magn., vol. 28, pp. 1130-1133, Mar. 1992.
11. J. F. Lee and Z. Sacks, "Whitney elements time domain (WETD) methods," IEEE Trans. Magn., vol. 31, pp. 1325-1329, May 1995.
12. S. D. Gedney and U. Navsariwala, "An unconditionally stable finite-element time-domain solution of the vector wave equation," IEEE Microwave Guided Wave Lett., vol. 5, pp. 332-334, May 1995.
13. W. P. Capers Jr, L. Pichon, and A. Razek, "A 3D finite element method for the modeling of bounded and unbounded electromagnetic problems in the time domain," Int. J. Numer. Model, vol. 13, pp. 527-540, 2000.
14. D. R. Lynch and K. D. Paulsen, "Time-domain integration of the Maxwell equations on finite elements," IEEE Trans. Antennas Propagat., vol. 38, pp. 1933-1942, Dec. 1990.
15. J. F. Lee, "WETD-a finite-element time-domain approach for solving Maxwell's equations," IEEE Microwave Guided Wave Lett., vol. 4, pp. 11-13, Jan. 1994.
16. Z. Sacks and J. F. Lee, "A finite-element time-domain method using prism elements for microwave cavities," IEEE Trans. Electromagn. Compat., vol. 37, pp. 519-527, Nov. 1995.
17. J. M. Jin, M. Zunoubi, K. C. Donepudi, and W. C. Chew, "Frequency-domain and time-domain finite-element solution of Maxwell's equations using spectral Lanczos decomposition method," Comput. Methods Appl. Mech. Eng., vol. 169, pp. 279-296, 1999.
18. D. A. White, "Orthogonal vector basis functions for time domain finite element solution of the vector wave equation," IEEE Trans. Magn., vol. 35, pp. 1458-1461, May 1999.
19. D. Jiao and J. M. Jin, "Three-dimensional orthogonal vector basis functions for time-domain finite element solution of vector wave equations," in Proc. IEEE APS Int. Symp. Dig., vol. 3, Boston, MA, July 2001, pp. 204-207.
20. ____, "Time-domain finite element modeling of dispersive media," in Proc. IEEE APS Int. Symp. Dig., vol. 3, Boston, MA, July 2001, pp. 180-183.
21. D. Jiao, M. Lu, E. Michielssen, and J. M. Jin, "A fast time-domain finite element-boundary integral method for electromagnetic analysis," IEEE Trans. Antennas Propagat., vol. 49, pp. 1453-1461, Oct. 2001.
22. D. Jiao, A. Ergin, B. Shanker, E. Michielssen, and J. M. Jin, "A fast time-domain higher-order finite element-boundary integral method for three-dimensional electromagnetic scattering analysis," IEEE Trans. Antennas Propagat., vol. 50, pp. 1192-1202, Sept. 2002.
23. R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems, 2nd ed. Melbourne, FL: Krieger, 1994.
24. J. Tuomela, "Fourth-order schemes for the wave equation, Maxwell equations, and linearized elastodynamic equations," Numer. Methods Partial Differential Equations, vol. 10, pp. 33-64, 1994.
25. R. E. Ziemer, W. H. Tranter, and D. R. Fannin, Signals and Systems: Continuous and Discrete. New York: Macmillan, 1989.
26. D. C. Sorensen, "Implicit application of polynomial filters in a κ-step Arnoldi method," SIAM J. Matrix Anal. Applicat., vol. 13, pp. 357-385, 1992.
27. ____, (1995) Implicitly Restarted Arnoldi Lanczos Methods for Large Scale Eigenvalue Calculations. [Online]. Available: ftp://ftp.caam.rice.edu/pub/software/ARPACK/DOCS/tutorial.ps.gz
28. R. J. Luebbers, F. P. Hunsberger, K. S. Kunz, R. B. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromagn. Compat., vol. 32, pp. 222-227, Aug. 1990.
29. O. P. Gandhi, B. Q. Gao, and J. Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microwave Theory Tech., vol. 41, pp. 658-665, Apr. 1993.
30. J. L. Young, "Propagation in linear dispersive media: Finite difference time-domain methodologies," IEEE Trans. Antennas Propagat., vol. 43, pp. 422-426, Apr. 1995.
31. D. M. Sullivan, "Frequency-dependent FDTD methods using Z transforms," IEEE Trans. Antennas Propagat., vol. 40, pp. 1223-1230, Oct. 1992.
32. J. M. Jin, The Finite Element Method in Electromagnetics. New York: Wiley, 1993.
33. T. Roy, T. K. Sarkar, A. R. Djordjevic, and M. Salazar-Palma, "Time-domain analysis of TM scattering from conducting cylinders using a hybrid method," IEEE Trans. Microwave Theory Tech., vol. 46, pp. 1471-1477, Oct. 1998.