Liu Guo-sheng, Zhang Guo-ji. Study for the Numerical Properties of the Higher-Order LOD-FDTD Methods[J]. Journal of Electronics & Information Technology, 2010, 32(6): 1384-1388. doi: 10.3724/SP.J.1146.2009.00881
Citation:
Liu Guo-sheng, Zhang Guo-ji. Study for the Numerical Properties of the Higher-Order LOD-FDTD Methods[J]. Journal of Electronics & Information Technology, 2010, 32(6): 1384-1388. doi: 10.3724/SP.J.1146.2009.00881
Liu Guo-sheng, Zhang Guo-ji. Study for the Numerical Properties of the Higher-Order LOD-FDTD Methods[J]. Journal of Electronics & Information Technology, 2010, 32(6): 1384-1388. doi: 10.3724/SP.J.1146.2009.00881
Citation:
Liu Guo-sheng, Zhang Guo-ji. Study for the Numerical Properties of the Higher-Order LOD-FDTD Methods[J]. Journal of Electronics & Information Technology, 2010, 32(6): 1384-1388. doi: 10.3724/SP.J.1146.2009.00881
In this paper, the numerical properties of higher-order Locally One Dimensionally Finite-Difference Time-Domain (LOD-FDTD) are investigated, i.e. stability, numerical dispersion, and convergence. The universal formulas of the amplitude factor and the numerical dispersion relationship are derived for 3D varying-order LOD-FDTD, and their unconditional stability is analytically proved. Based on this universal formula, the numerical convergence of this class of methods is discussed, and the convergence condition is presented for the first time. Numerical results in calculating the resonant frequency show that, higher-order methods can achieve better performance while not dramatically increasing computational time.
葛德彪, 闫玉波. 电磁波时域有限差分方法. 第二版, 西安: 西安电子科技大学出版社, 2005: 8-31.[2]Ge D B and Yan Y B. Finite-Difference Time-Domain Method for Electromagnetic Waves. Second Edition, Xian: the Press of Xidian University, 2005: 8-31.[3]Sun G and Trueman C W. Unconditionally stable Crank- Nicolson scheme for solving the two-dimensional Maxwells equations [J].Electronics Letters.2003, 39(7):595-597[4]Namiki T. A new FDTD algorithm based on alternating- direction implicit method [J].IEEE Transactions on Microwave and Theory Techniques.1999, 47(10):2003-2007[5]Liu G S, Zhang G J, and Hu B J. Numerical analysis for an improved ADI-FDTD method [J].IEEE Microwave and Wireless Components Letters.2008, 18(9):569-571[6]Fu W and Tan E L. Stability and dispersion analysis for higher order 3-D ADI-FDTD method [J].IEEE Transactions on Antennas and Propagation.2005, 53(11):3691-3696[7]Shibayama J, Muraki M, and Yamauchi J, et al.. Efficient implicit FDTD algorithm based on locally one-dimensional scheme [J].Electronics Letters.2005, 41(19):1046-1047[8]Ahmed I, Chua E K, and Li E P, et al.. Development of the three-dimensional unconditionally stable LOD-FDTD method [J].IEEE Transactions on Antennas and Propagation.2008, 56(11):3596-3600[9]Li E, Ahmed I, and Vahldieck R. Numerical dispersion analysis with an improved LOD-FDTD method [J].IEEE Microwave and Wireless Components Letters.2007, 17(5):319-321[10]Jung K Y and Teixeira F L. An iterative unconditionally stable LOD-FDTD method [J].IEEE Microwave and Wireless Components Letters.2008, 18(2):76-78