Approximate Crank-Nicolson schemes for the 2-D finite-difference time-domain method for TEz waves

IEEE Transactions on Antennas and Propagation

Volumn 52, Issue 11, 2004, Pages 2963-2972

  Sun, Guilin ^a   Trueman, Christopher W ^a  

^a Dept of Electrical and Computer Engineering   (Canada)

Author keywords

Computational electromagnetics; Crank Nicolson (CN) scheme; Finite difference time domain (FDTD); Numerical dispersion; Unconditional stability

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; TIME DOMAIN ANALYSIS;

COMPUTATIONAL ELECTROMAGNETICS; CRANK-NICOLSON SCHEME; NUMERICAL DISPERSION; UNCONDITIONAL STABILITY;

ELECTROMAGNETIC WAVES;

EID: 9744231463     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2004.835142     Document Type: Article

References (17)

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. A. Taflove and S. C. Hagness, Computational Electrodynamics - the Finite-Difference Time-Domain Method, 2nd ed. Boston, MA: Artech House, 2000.
3. T. Namiki, "A new FDTD algorithm based on alternating-direction implicit method," IEEE Trans. Microwave Theory Tech., vol. 47, pp. 2003-2007, Oct. 1999.
4. F. Zheng, Z. Chen, and J. Zhang, "Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method," IEEE Trans. Microwave Theory Tech., vol. 48, pp. 1550-1558, Sept. 2000.
5. G. Sun and C. W. Trueman, "Analysis and numerical experiments on the numerical dispersion of two-dimensional ADI-FDTD," IEEE Antennas Wireless Propagat. Lett., vol. 2, pp. 78-81, 2003.
6. S. G. Garcia, T.-W. Lee, and S. C. Hagness, "On the accuracy of the ADI-FDTD method," IEEE Antennas Wireless Propagat. Lett., vol. 1, pp. 31-34, 2002.
7. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 2nd ed. New York: Springer-Verlag, 1993. Translated by R. Bartels, W. Gautschi and C. Witzgall.
8. J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations. Pacific Grove, CA: Wadawoth & Brooks/Cole Advanced Books & Software, 1989.
9. A. Fijany, M. A. Jensen, Y. Rahmat-Samii, and J. Barhen, "A massively parallel computation strategy for FDTD: Time and space parallelism applied to electromagnetics problems," IEEE Trans. Antennas Propagat., vol. 43, pp. 1441-1449, Dec. 1995.
10. G. Sun and C. W. Trueman, "Unconditionally stable solution for wave equations of the second order," in Proc. ISAPE'03, Beijing, China, Oct. 28-31, 2003.
11. G. Sun, and C. W. Trueman "Unconditionally stable Crank-Nicolson scheme for solving the two-dimensional Maxwell's equations," IEE Electron. Lett., vol. 39, pp. 595-597, Apr. 2003.
12. A. Zhao, "A novel implementation for two-dimensional unconditionally stable FDTD method," Microwave Opt. Tech. Lett., vol. 38, no. 6, pp. 457-462, Sept. 2003.
13. G. Sun and C. W. Trueman, "Quantification of the truncation errors in finite-difference time-domain methods," in Proc. Canadian Conf. Electrical and Computer Engineering and Humane Technology CCECE 2003, Montreal, Canada, May 4-7, 2003.
14. G. Sun, and C. W. Trueman "Solutions of the Crank-Nicolson scheme in the finite-difference time-domain method," Internal Report, Concordia Univ., ECE Dept., Aug. 2003.
15. G. Sun, and C. W. Trueman "Accuracy of three unconditionally-stable FDTD schemes for solving Maxwell's equations," Applied Computational Electromagn. Soc. J., vol. 18, pp. 41-47, Nov. 2003.
16. J. W. Nehrbass, J. O. Jevtic, and R. Lee, "Reducing the phase error for finite-difference methods without increasing the order," IEEE Trans. Antennas Propagat., vol. 46, pp. 1194-1201, 1998.
17. G. Sun and C. W. Trueman, "Numerical validation of dispersion relations using a cylindrical wave for 2-D FDTD methods," Microwave Opt. Technol. Lett., vol. 43, no. 2, pp. 138-142, Oct. 2004.