Vol. 130
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2012-08-23
A Novel 3-D Weakly Conditionally Stable FDTD Algorithm
By
Progress In Electromagnetics Research, Vol. 130, 525-540, 2012
Abstract
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.
Citation
Jian-Bao Wang Bi-Hua Zhou Li-Hua Shi Cheng Gao Bin Chen , "A Novel 3-D Weakly Conditionally Stable FDTD Algorithm," Progress In Electromagnetics Research, Vol. 130, 525-540, 2012.
doi:10.2528/PIER12071904
http://www.jpier.org/PIER/pier.php?paper=12071904
References

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.