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WEAKLY CONDITIONALLY STABLE AND UNCONDITIONALLY STABLE FDTD SCHEMES FOR 3D MAXWELL'S EQUATIONS

By J. Chen and J. Wang

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Abstract:
To overcome the Courant limit on the time step size of the conventional finite-difference time-domain (FDTD) method, some weakly conditionally stable and unconditionally stable FDTD methods have been developed recently. To analyze the relations between these methods theoretically, they are all viewed as approximations of the conventional FDTD scheme in present discussion. The errors between these methods and the conventional FDTD method are presented analytically, and the numerical performances, including computation accuracy, efficiency, and memory requirements, are discussed, by comparing with those of the conventional FDTD method.

Citation:
J. Chen and J. Wang, "Weakly Conditionally Stable and Unconditionally Stable FDTD Schemes for 3D Maxwell's Equations," Progress In Electromagnetics Research B, Vol. 19, 329-366, 2010.
doi:10.2528/PIERB09110502

References:
1. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propagat., Vol. 14, No. 3, 302-307, May 1966.
doi:10.1109/TAP.1966.1138693

2. Yang, S., Y. Chen, and Z. P. Nie, "Simulation of time modulated linear antenna arrays using the FDTD method," Progress In Electromagnetics Research, Vol. 98, 175-190, 2009.
doi:10.2528/PIER09092507

3. Swillam, M. A., R. H. Gohary, M. H. Bakr, and X. Li, "Efficient approach for sensitivity analysis of lossy and leaky structures using FDTD," Progress In Electromagnetics Research, Vol. 94, 197-212, 2009.
doi:10.2528/PIER09061708

4. Huang, C. H., C. C. Chiu, C. L. Li, and Y.-H. Li, "Image reconstruction of the buried metallic cylinder using FDTD method and SSGA," Progress In Electromagnetics Research, Vol. 85, 195-210, 2008.
doi:10.2528/PIER08072901

5. Taflove, A., Computational Electrodynamics, Artech House, Norwood, MA, 1995.

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

7. Namiki, T., "3-D ADI-FDTD scheme-unconditionally stable time-domain algorithm for solving full vector Maxwell's equations," IEEE Trans. Microwave Theory Tech., Vol. 48, No. 10, 1743-1748, Oct. 2000.
doi:10.1109/22.873904

8. Chen, J. and J. Wang, "PEC condition implementation for the ADI-FDTD method," Microwave Opt. Technol. Lett., Vol. 49, No. 3, 526-530, Mar. 2007.
doi:10.1002/mop.22185

9. Sun, G. and C. W. Trueman, "Some fundamental characteristics of the one-dimensional alternate-direction-implicit finite-difference timedomain method," IEEE Trans. Microawave Theory Tech., Vol. 52, No. 1, 46-52, Jan. 2004.
doi:10.1109/TMTT.2003.821230

10. Ahmed, I. and Z. Chen, "Error reduced ADI-FDTD methods," IEEE Antennas Wireless Propag. Lett., Vol. 4, 323-325, 2005.

11. Sun, G. and C. W. Trueman, "Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-domain method," IEEE Trans. Antennas Propag., Vol. 54, No. 5, 2275-2284, May 2006.
doi:10.1049/el:20040420

12. Sun, G. and C. W. Trueman, "An unconditionally-stable FDTD method based on the Crank-Nicolson scheme for solving the three-dimensional Maxwell's equations," Electron. Lett., Vol. 40, No. 10, 589-590, 2004.
doi:10.1049/el:20030416

13. Sun, G. and C. W. Trueman, "Unconditionally stable Crank-Nicolson scheme for solving two-dimensional Maxwell's equations," Electron. Lett., Vol. 39, No. 7, 595-596.
doi:10.1002/mop.11089

14. Zhao, A. P., "A novel implementation for two-dimensional unconditionally stable FDTD method," Microwave Opt. Technol. Lett., Vol. 38, No. 6, 457-462, Sep. 2003.
doi:10.1002/mop.21684

15. Yang, Y., R. S. Chen, and E. K. N. Yung, "The unconditionally stable Crank-Nicolson FDTD method for three-dimensional Maxwell's equations," Microwave Opt. Technol. Lett., Vol. 48, No. 8, 1619-1622, Aug. 2006.
doi:10.1109/TAP.2009.2029377

16. Chen, J. and J. Wang, "Two approximate Crank-Nicolson finite-difference time-domain method for waves," IEEE Trans. Antennas Propag., Vol. 57, No. 10, 3375-3378, Oct. 2009.
doi:10.1109/LAWP.2002.802583

17. Garcia, S. G., T.-W. Lee, and S. C. Hagness, "On the accuracy of the ADI-FDTD method," IEEE Antennas Wireless Propag. Lett., Vol. 1, No. 1, 31-34, 2002.
doi:10.1049/el:20062011

18. Chen, J. and J. Wang, "Error between unconditionally stable FDTD methods and conventional FDTD method," Electon. Lett., Vol. 42, No. 20, 1132-1133, Sep. 2006.
doi:10.1002/mop.11138

19. Huang, B., G. Wang, Y. S. Jiang, and W. B. Wang, "A hybrid implicit-explicit FDTD scheme with weakly conditional stability," Microwave Opt. Technol. Lett., Vol. 39, No. 2, 97-101, Oct. 2003.
doi:10.1002/mop.21898

20. Chen, J. and J. Wang, "A 3-D hybrid implicit-explicit FDTD scheme with weakly conditional stability," Microwave Opt. Technol. Lett., Vol. 48, No. 11, 2291-2294, Nov. 2006.
doi:10.1002/mop.22340

21. Chen, J. and J. Wang, "Comparison between HIE-FDTD method and ADI-FDTD method," Microwave Opt. Technol. Lett., Vol. 49, No. 5, 1001-1005, May 2007.
doi:10.1109/TEMC.2007.897130

22. Chen, J. and J. Wang, "A three-dimensional semi-implicit FDTD scheme for calculation of shielding effectiveness of enclosure with thin slots," IEEE Trans. Electromagn. Compat., Vol. 49, No. 2, 419-426, May 2007.
doi:10.1002/mop.22962

23. Ahmed, I. and E. Li, "Conventional perfectly matched layer for weakly conditionally stable hybrid implicit and explicit-FDTD method," Microwave Opt. Technol. Lett., Vol. 49, No. 12, 3106-3109, Dec. 2007.
doi:10.1109/TAP.2007.910338

24. Chen, J. and J. Wang, "Numerical simulation using HIE-FDTD method to estimate various antennas with fine scale structures," IEEE Trans. Antennas Propagat., Vol. 55, No. 12, 3603-3612, Dec. 2007.
doi:10.1002/mop.23390

25. Chen, J. and J. Wang, "Implementation of connection boundary for HIE-FDTD method," Microwave Opt. Technol. Lett., Vol. 50, No. 5, 1347-1352, May 2008.
doi:10.1109/TEMC.2008.922791

26. Chen, J. and J. Wang, "The body-of-revolution hybrid implicitexplicit finite-difference time-domain method with large time step size," IEEE Trans. Electromagn. Compat., Vol. 50, No. 2, 369-374, May 2008.
doi:10.1109/TAP.2008.929528

27. Xiao, F., X. Tang, and L. Wang, "Stability and numerical dispersion analysis of a 3D hybrid implicit-explicit FDTD method," IEEE Trans. Antennas Propag., Vol. 56, No. 10, 3346-3350, Oct. 2008.

28. Chen, J. and J. Wang, "3-D FDTD method with weakly conditional stability," Electon. Lett., Vol. 43, No. 1, Jan. 2-3, 2007.
doi:10.1109/TEMC.2007.897130

29. Chen, J. and J. Wang, "A novel WCS-FDTD method with weakly conditional stability," IEEE Trans. Electromagn. Compat., Vol. 49, No. 2, 419-426, May 2007.
doi:10.1109/TAP.2007.910346

30. Chen, J. and J. Wang, "A new method to avoid the reduction of the time step in CP-FDTD method," IEEE Trans. Antennas Propag., Vol. 55, No. 12, 3613-3619, Dec. 2007.
doi:10.1002/mop.22633

31. Chen, J. and J. Wang, "Using WCS-FDTD method to simulate various small aperture-coupled metallic enclosures," Microwave Opt. Technol. Lett., Vol. 49, No. 8, 1852-1858, Aug. 2007.
doi:10.1109/LMWC.2008.922574

32. Chen, J. and J. Wang, "A novel body-of-revolution finite-diĀ®erence time-domain method with weakly conditional stability," IEEE Microwave Wire Comp. Lett., Vol. 16, No. 6, 377-379, Jun. 2008.


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