The Fourth-Order One-Step Leapfrog HIE-FDTD Method
Keywords:
Computational efficiency, dispersive error, Finite-Difference Time-Domain (FDTD), fourth order, Hybrid Implicit- and Explicit-FDTD (HIEFDTD), one-step leapfrogAbstract
A new fourth-order one-step leapfrog hybrid implicit-explicit finite-difference time-domain (HIEFDTD) method has been proposed in this paper. This new method investigates the use of a second-order accurate in time and a fourth-order accurate in space. Because of the utilize of the one-step leapfrog theory, the proposed algorithm not only has the same formulation as that used for the traditional FDTD, but also require only one-step computations. The 2-D formulation of the method is presented and the time stability condition of the method is certified. Simulation results show that the proposed method is 6.8 times faster than the traditional second-order FDTD method and is 2.2 times faster than the second-order HIE-FDTD method, which shows that the proposed method has very high computational efficiency. On the other hand, the proposed method also has less dispersion error by comparing with traditional second-order FDTD method and the second-order HIEFDTD method.
Downloads
References
K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat., vol. AP-14, pp. 302-307, 1966.
A. Taflove, Computational Electrodynamics. Norwood, MA: Artech House, 1995.
Z. Chen, “A finite-difference time-domain method without the Courant stability conditions,” IEEE Microwave Guided Wave Lett., vol. 9, pp. 441- 443, 1999.
S. Staker, C. Holloway, A. Bhobe, and M. PiketMay, “ADI formulation of the FDTD method: Algorithm and material dispersion implementation,” IEEE Trans. Electromagn. Compat., vol. 45, no. 2, pp. 156-166, 2003.
N. V. Kantartzis, “Multi-frequency higher-order ADI-FDTD solvers for signal integrity predictions and interference modeling in general EMC applications.”
Y. Zhang, S. Lu, and J. Zhang, “Reduction of numerical dispersion of 3-D higher order ADIFDTD method with artificial anisotropy,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 10, pp. 2416-28, Oct. 2009. ACES Journal, vol. 25, no. 12, pp. 1046 1060, 2010.
H. Zheng and K. Leung, “A nonorthogonal ADIFDTD algorithm for solving 2-D scattering problems,” IEEE Trans. Antennas Propag., vol. 57, no. 12, pp. 3981-3902, Dec. 2009.
M. Darms, R. Schuhmann, H. Spachmann, and T. Weiland, “Dispersion and asymmetry effects of ADI-FDTD,” IEEE Microw. Wireless Compon. Lett., vol. 12, no. 12, pp. 491-493, Dec. 2002.
H. Zheng, L. Feng, and Q. Wu, “3-D nonorthogonal ADI-FDTD algorithm for the full-wave analysis of microwave circuit devices,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 1, pp. 128-135, Jan. 2010.
J. Chen and J. G. Wang, “Two approximate Crank– Nicolson finite-difference time-domain method for TE(z) waves,” IEEE Transactions on Antennas Propagation, vol. 57, pp. 3375-3378, 2009.
E. Li, I. Ahmed, and R. Vahldieck, “Numerical dispersion analysis with an improved LOD FDTD method,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 5, pp. 319-321, May 2007.
N. V. Kantartzis, T. Ohtani, and Y. Kanai, “Accuracy-adjustable nonstandard LOD-FDTD schemes for the design of carbon nanotube interconnects and nanocomposite EMC shields,” IEEE Trans. Magn., vol. 49, no. 5, pp. 1821 1824, 2013.
T. T. Zygiridis, N. V. Kantartzis, and T. D. Tsiboukis, “Parallel LOD-FDTD method with error-balancing properties,” IEEE Trans. Magn., vol. 51, no. 3, art. no. 7205804, 2015.
J. Shibayama, “Efficient implicit FDTD algorithm based on locally one-dimensional scheme,” Electron. Lett., vol. 44, pp. 1046-1047, 2005.
J. Chen and J. Wang, “A 3-D hybrid implicitexplicit FDTD scheme with weakly conditional stability,” Microwave Opt. Technol. Lett., vol. 48, pp. 2291-2294, 2006.
B. Huang and G. Wang, “A hybrid implicit-explicit FDTD scheme with weakly conditional stability,” Microwave Opt. Technol. Lett., vol. 39, pp. 97-101, 2003.
J. Chen and J. G. Wang, “A three-dimensional semi-implicit FDTD scheme for calculation of shielding effectiveness of enclosure with thin slots,” IEEE Transactions on Electromagnetic Compatibility, vol. 49, pp. 354-360, 2007.
J. Chen and J. G. Wang, “Numerical simulation using HIE–FDTD method to estimate various antennas with fine scale structures,” IEEE Transactions on Antennas Propagation, vol. 55, pp. 3603-3612, 2007
J. Fang, “Time domain finite difference computation for Maxwell’s equations,” Ph.D. Dissertation, Univ. of California at Berkeley, CA, 1989.
M. L. Ghrist, “High order difference methods for wave equations,” [D]. University of Colorado, 1997.
M. Fujii and W. J. R Hoefer, “A wavelet formulation of finite difference method: Full vector analysis of optical waveguide junctions,” IEEE J. Quantum Electron., vol. 37, pp. 1015-1029, Aug. 2011.
N. V. Kantartzis, “Hybrid unconditionally stable high-order nonstandard schemes with optimal error-controllable spectral resolution for complex microwave problems,” Int. J. Num. Modelling: Electronic Networks, Devices and Fields, vol. 25, no. 5, 6, pp. 621-644, 2012.
M. Krumpholz and L. P. B. Katehi, “MRTD: New time-domain schems based on multiresolution analysis,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 555-571, Apr. 1996.
T. Deveze, L. Beaulieu, and W. Tabbara, “A fourth order scheme for the fdtd algorithm applied to Maxwell’s equations,” IEEE APS Int. Symp. Proc., Chicago, IL, vol. 7, pp. 346-349, 1992.
S. J. Cooke, M. Botton, T. M. Antonsen, and B. Levush, “A leapfrog formulation of the 3D ADIFDTD algorithm,” Int. J. Numer. Model, vol. 22, no. 2, pp. 187-200, 2009.
