For analyzing the electromagnetic problems with the fine structures in one or two directions, a novel weakly conditionally stable finite-difference time-domain (WCS-FDTD) algorithm is proposed. By dividing the 3-D Maxwell's equations into two parts, and applying the Crank-Nicolson (CN) scheme to each part, a four sub-step implicit procedures can be obtained. Then by adjusting the operational order of four sub-steps, a novel 3-D WCS-FDTD algorithm is derived. The proposed method only needs to solve four implicit equations, and the Courant-Friedrich-Levy (CFL) stability condition of the proposed algorithm is more relaxed and only determined by one space discretisation. In addition, numerical dispersion analysis demonstrates the numerical phase velocity error of the weakly conditionally stable scheme is less than that of the 3-D ADI-FDTD scheme.
"A Novel 3-d
Weakly Conditionally Stable FDTD Algorithm," Progress In Electromagnetics Research,
Vol. 130, 525-540, 2012. doi:10.2528/PIER12071904
1. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag., Vol. 14, No. 3, 302-307, 1966. doi:10.1109/TAP.1966.1138693
2. Lei, J.-Z., C.-H. Liang, and Y. Zhang, "Study on shielding effectiveness of metallic cavities with apertures by combining parallel FDTD method with windowing technique," Progress In Electromagnetics Research, Vol. 74, 85-112, 2007. doi:10.2528/PIER07041905
3. 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
4. Hadi, M. F. and S. F. Mahmoud, "Optimizing the compact-FDTD algorithm for electrically large waveguiding structures," Progress In Electromagnetics Research, Vol. 75, 253-269, 2007. doi:10.2528/PIER07060703
5. Xiao, S.-Q., Z. Shao, and B.-Z. Wang, "Application of the improved matrix type FDTD method for active antenna analysis," Progress In Electromagnetics Research, Vol. 100, 245-263, 2010. doi:10.2528/PIER09112204
6. Li, J., L.-X. Guo, and H. Zeng, "FDTD method investigation on the polarimetric scattering from 2-D rough surface," Progress In Electromagnetics Research, Vol. 101, 173-188, 2010. doi:10.2528/PIER09120104
7. Vaccari, A., A. Cala' Lesina, L. Cristoforetti, and R. Pontalti, "Parallel implementation of a 3D subgridding FDTD algorithm for large simulations ," Progress In Electromagnetics Research, Vol. 120, 263-292, 2011.
8. Izadi, M., M. Z. A. Ab Kadir, and C. Gomes, "Evaluation of electromagnetic fields associated with inclined lightning channel using second order FDTD-hybrid methods," Progress In Electromagnetics Research, Vol. 117, 209-236, 2011.
9. Sirenko, K., V. Pazynin, Y. K. Sirenko, and H. Ba·gci, "An FFT-accelerated FDTD scheme with exact absorbing conditions for characterizing axially symmetric resonant structures," Progress In Electromagnetics Research, Vol. 111, 331-364, 2011. doi:10.2528/PIER10102707
10. Lee, K. H., I. Ahmed, R. S. M. Goh, E. H. Khoo, E. P. Li, and T. G. G. Hung, "Implementation of the FDTD method based on lorentz-Drude dispersive model on gpu for plasmonics applications," Progress In Electromagnetics Research, Vol. 116, 441-456, 2011.
11. Kong, Y.-D. and Q.-X. Chu, "Reduction of numerical dispersion of the six-stages split-step unconditionally-stable FDTD method with controlling parameters ," Progress In Electromagnetics Research, Vol. 122, 175-196, 2012. doi:10.2528/PIER11082512
12. Sun, G. and C. W. Trueman, "Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-domain method," IEEE Trans. Microwave Theory Tech., Vol. 54, No. 5, 2275-2284, 2006. doi:10.1109/TMTT.2006.873639
13. Xu, K., Z. Fan, D.-Z. Ding, and R.-S. Chen, "GPU accelerated unconditionally stable Crank-Nicolson FDTD method for the analysis of three-dimensional microwave circuits," Progress In Electromagnetics Research, Vol. 102, 381-395, 2010. doi:10.2528/PIER10020606
14. Rouf, H. K., F. Costen, S. G. Garcia, and S. Fujino, "On the solution of 3-D frequency dependent crank-nicolson FDTD scheme," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 16, 2163-2175, 2009. doi:10.1163/156939309790109261
15. 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, 2000. doi:10.1109/22.869007
16. Namiki, T., "3-D ADI-FDTD method-unconditionally stable time-domain algorithm for solving full vector Maxwell's equations," IEEE Trans. Microwave Theory Tech., Vol. 48, No. 10, 1743-1748, 2000. doi:10.1109/22.873904
17. Tay, W. C. and E. L. Tan, "Implementations of PMC and PEC boundary conditions for efficient fundamental ADI and LOD-FDTD," Journal of Electromagnetic Waves and Application, Vol. 24, No. 4, 565-573, 2010.
18. Shi, Y., L. Li, and C.-H. Liang, "The ADI multi-domain pseudospectral time-domain algorithm for 2-D arbitrary inhomogeneous media," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 4, 543-558, 2005. doi:10.1163/1569393053303929
19. Huang, B. K., G. Wang, Y. S. Jiang, and W. B. Wang, "A hybrid implicit-explicit FDTD scheme with weakly conditional stability," Microw. Opt. Tech. Lett., Vol. 39, 97-101, 2003. doi:10.1002/mop.11138
20. Chen, J. and J. G. Wang, "A novel WCS-FDTD method with weakly conditional stability," IEEE Trans. Electomag. Compat., Vol. 49, No. 2, 419-429, 2007. doi:10.1109/TEMC.2007.897130
21. Thomas, J. W., Numerical Partial Differential Equations: Finite Difference Methods, Springer Verlag, Berlin, Germany, 1995.
22. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd Ed., Artech House, Norwood, MA, 2000.