A one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method for lossy media is presented. Different from the method provided by others, the proposed method is originated from the conventional ADI-FDTD method instead of considering the leapfrog ADI-FDTD method as a perturbation of the conventional explicit FDTD method. Its unconditional stability is analytically proven through a method that combines the von Neumann method with the Jury criterion. In addition, its unconditional stability and computational efficiency are verified through numerical experiments.
2. Namiki, T., "A new FDTD algorithm based on alternating-direction implicit method," IEEE Trans. Microw. Theory Tech., Vol. 47, No. 10, 2003-2007, Oct. 1999.
3. Zheng, F., Z. Chen, and J. Zhang, "Toward the development of a three dimensional unconditionally stable finite-different time-domain method," IEEE Trans. Microwave Theory Tech., Vol. 48, No. 9, 1550-1558, Sep. 2000.
4. Cooke, S. J., M. Botton, T. M. Antonsen, and B. Levush, "A leapfrog formulation of the 3D ADI-FDTD algorithm," Int. J. Numer. Model,, Vol. 22, No. 2, 187-200, 2009.
5. Yang, S. C., Z. Chen, Y. Yu, and W. Y. Yin, "An unconditionally stable one-step arbitrary-order leapfrog ADI-FDTD method and its numerical properties," IEEE Trans. Antennas Propag.,, Vol. 60, No. 4, 1995-2003, Apr. 2012.
6. Gan, T. H. and E. L. Tan, "Stability and dispersion analysis for three-dimensional (3-D) leapfrog ADI-FDTD method," Progress In Electromagnetics Research M, Vol. 23, 1-12, Jan. 2012.
7. Heh, D. Y. and E. L. Tan, "Dispersion analysis of FDTD schemes for doubly lossy media," Progress In Electromagnetics Research B, Vol. 14, 177-192, 2010.
8. Velarde, L. F., J. A. Pereda, A. Vegas, and O. Gonzalez, "A weighted-average scheme for accurate FDTD modeling of electromagnetic wave propagation in conductive media," IEEE Antennas Wireless Propag. Lett., Vol. 3, 302-305, 2004.
9. Pereda, J. A., A. Grande, O. Gonzalez, and A. Vegas, "The 1D ADI-FDTD method in lossy media," IEEE Antennas Wireless Propag. Lett., Vol. 7, 477-480, 2008.
10. Heh, D. Y. and E. L. Tan, "Unified efficient fundamental ADI-FDTD schemes for lossy media," Progress In Electromagnetics Research B, Vol. 32, 217-242, 2011.
11. Gan, T. H. and E. L. Tan, "Unconditionally stable leapfrog ADI-FDTD method for lossy media," Progress In Electromagnetics Research M, Vol. 26, 173-186, 2012.
12. Xiao, F. and X. H. Tang, "Stability and numerical dispersion analysis of a fourth-order accurate FDTD method," IEEE Trans. Antennas Propag., Vol. 54, No. 9, 2525-2530, Sep. 2006.
Submit
