Four-Stage Split-Step 2D FDTD Method with Error-Cancellation Features
Keywords:
Finite-difference time-domain (FDTD) methods, numerical-dispersion relation, split-step approaches, unconditionally-stable methodsAbstract
We develop a methodology that enables the proper introduction of high-order spatial operators in an unconditionally-stable, split-step, finite-difference timedomain scheme. The proposed approach yields spatial approximations that guarantee better balancing of space-time errors, compared to standard fourth-order expressions. The latter are not as efficient as expected, due to their unmatched order with the scheme’s secondorder temporal accuracy. Our technique treats the dispersion relation as an error descriptor, derives spatial formulae that change with the cell shape and time-step size, and rectifies the performance over all frequencies.
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References
K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag., vol. AP-14, pp. 302-307, 1966.
A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference TimeDomain Method. Artech House, Norwood, MA, ed. 3, 2005.
G. Sun and C. W. Trueman, “Accuracy of three unconditionally-stable FDTD schemes,” ACES J., vol. 18, no. 4, pp. 41-47, Nov. 2003.
F. Zheng, Z. Chen, and J. Zhang, “A finitedifference time-domain method without the Courant stability conditions,” IEEE Microw. Guided Wave Lett., vol. 9, no. 11, pp. 441-443, Nov. 1999.
J. Shibayama, M. Muraki, J. Yamauchi, and H. Nakano, “Efficient implicit FDTD algorithm based on locally one-dimensional scheme,” Electron. Lett., vol. 41, no. 19, pp. 1046-1047, Sept. 2005.
J. Lee and B. Fornberg, “A split step approach for the 3-D Maxwell’s equations,” J. Comp. Appl. Math., vol. 158, no. 2, pp. 485-505, Sept. 2003.
W. Fu and E. L. Tan, “Development of split-step FDTD method with higher-order spatial accuracy,” Electron. Lett., vol. 40, no. 20, pp. 1252-1253, Sept. 2004.
M. Kusaf and A. Y. Oztoprak, “An unconditionally stable split-step FDTD method for low anisotropy,” IEEE Microw. Wireless Comp. Lett., vol. 18, no. 4, pp. 224-226, Apr. 2008.
A. Grande, J. A. Pereda, A. Serroukh, I. Barba, A. C. Cabeceira, and J. Represa, “Reinterpreting fourstage split-step FDTD methods as two-stage methods,” IEEE Trans. Antennas Propag., vol. 61, no. 11, pp. 5818-5821, Nov. 2013.
D. Y. Heh and E. L. Tan, “Further reinterpretation of multi-stage implicit FDTD schemes,” IEEE Trans. Antennas Propag., vol. 62, no. 8, pp. 4407- 4411, Aug. 2014.
W. Fu and E. L. Tan, “A parameter optimized ADIFDTD method based on the (2,4) stencil,” IEEE Trans. Antennas Propag., vol. 54, no. 6, pp. 1836- 1842, June 2006.
Q.-F. Liu, W.-Y. Yin, Z. Chen, and P.-G. Liu, “An efficient method to reduce the numerical dispersion in the LOD-FDTD method based on the (2,4) stencil,” IEEE Trans. Antennas Propag., vol. 58, no. 7, pp. 2384-2393, July 2010.
