2012-10-17
Unconditionally Stable Leapfrog Adi-FDTD Method for Lossy Media
By
Progress In Electromagnetics Research M, Vol. 26, 173-786, 2012
Abstract
This paper presents an unconditionally stable threedimensional (3-D) leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method for lossy media. Conductivity terms of lossy media are incorporated into the leapfrog ADI-FDTD method in an analogous manner as the conventional explicit FDTD method since the leapfrog ADI-FDTD method is a perturbation of the conventional explicit FDTD method. Implementation of the leapfrog ADI-FDTD method for lossy media with special consideration for boundary condition is provided. Numerical results and examples are presented to validate the formulation.
Citation
Theng Huat Gan, and Eng Leong Tan, "Unconditionally Stable Leapfrog Adi-FDTD Method for Lossy Media," Progress In Electromagnetics Research M, Vol. 26, 173-786, 2012.
doi:10.2528/PIERM12090307
References

1. 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.
doi:10.1002/jnm.707        Google Scholar

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.
doi:10.1109/22.795075        Google Scholar

3. Zheng, F., Z. Chen, and J. Zhang, "Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method," IEEE Trans. Microw. Theory Tech., Vol. 48, No. 9, 1550-1558, Sep. 2000.
doi:10.1109/22.869007        Google Scholar

4. Tan, E. L., "Fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain methods," IEEE Trans. Antennas Propagat., Vol. 56, No. 1, 170-177, Jan. 2008.
doi:10.1109/TAP.2007.913089        Google Scholar

5. 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.
doi:10.2528/PIERM11111803        Google Scholar

6. Yang, S. C., Z. Chen, Y. Yu, and W. Y. Yin, "The unconditionally stable one-step leapfrog ADI-FDTD method and its comparisons with other FDTD methods," IEEE Microw. Wireless Comp. Lett., Vol. 21, 640-642, Dec. 2011.
doi:10.1109/LMWC.2011.2173182        Google Scholar

7. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media," IEEE Trans. Antennas Propagat., Vol. 14, No. 3, 302-307, May 1966.        Google Scholar

8. Taflove, A. and K. R. Umashankar, "The finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures," Progress In Electromagnetics Research, Vol. 2, 287-373, 1990.        Google Scholar

9. 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.
doi:10.2528/PIERB11051801        Google Scholar

10. Chen, J. and J. Wang, "PEC condition implementation for the ADI-FDTD method," Microwave Opt. Technol. Lett., Vol. 49, 526-530, Mar. 2007.
doi:10.1002/mop.22185        Google Scholar

11. Jolani, F., Y. Yu, and Z. Chen, "A hybrid FDTD and leapfrog ADI-FDTD method with PML implementation," IEEE MTT-S International Microwave Symposium Digest (MTT), 2011.        Google Scholar

12. Namiki, T., "3-D ADI-FDTD method --- Unconditionally stable time-domain algorithm for solving full vector Maxwells equations," IEEE Trans. Microw. Theory Tech., Vol. 48, No. 10, 1743-1748, Oct. 2000.
doi:10.1109/22.873904        Google Scholar

13. Chen, C. C. P., T. W. Lee, N. Murugesan, and S. C. Hagness, "Generalized FDTD-ADI: An unconditionally stable full-wave Maxwell's equations solver for VLSI interconnect modeling," IEEE/ACM Int. Conf. on Computer Aided Design, ICCAD, 156-163, 2000.        Google Scholar

14. Gan, T. H. and E. L. Tan, "Mur absorbing boundary conditions Mur absorbing boundary conditions," IEEE Asia Pacific Conference on Antenna and Propagation, Singapore, Aug. 2012.        Google Scholar

15. 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.        Google Scholar

16. Tay, W. C. and E. L. Tan, "Implementation of PMC and PEC boundary conditions for efficient fundamental ADI and LOD FDTD," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 4, 563-573, 2010.        Google Scholar

17. Tay, W. C, D. Y. Heh, and E. L. Tan, "GPU-accelerated fundamental ADI-FDTD with complex frequency shifted convolutional perfectly matched layer," Progress In Electromagnetics Research M, Vol. 14, 177-192, 2010.
doi:10.2528/PIERM10090605        Google Scholar

18. Benford, J., J A. Swegle, and E. Schamiloglu, High Power Microwaves, 2nd Ed., Taylor and Francis Group, CRC Press, 2007.
doi:10.1201/9781420012064

19. Hippel, A., Dielectric Materials and Applications, 2nd Ed., Artech House, 1995.

20. Wang, X. H, W. Y. Yin, Y. Yu, Z. Chen, J.Wang, and Y. Guo, "A convolutional perfect matched layer (CPML) for one-step leapfrog ADI-FDTD method and its applications to EMC problems," IEEE Trans. Electromagn. Compat., 2012.        Google Scholar

21. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed., Artech House, Boston, MA, 2005.