Studying and Analysis of a Novel RK-Sinc Scheme
Keywords:Convergence, dispersion, FDTD, Runge-Kutta, Sinc function, stability
In this paper, a novel high-order method, Runge-Kutta Sinc (RK-Sinc), is proposed. The RK-Sinc scheme employs the strong stability preserving Runge- Kutta (SSP-RK) algorithm to substitute time derivative and the Sinc function to replace spatial derivates. The computational efficiency, numerical dispersion and convergence of the RK-Sinc algorithm are addressed. The proposed method presents the better numerical dispersion and the faster convergence rate both in time and space domain. It is found that the computational memory of the RK-Sinc is more than two times of the FDTD for the same stencil size. Compared with the conventional FDTD, the new scheme provides more accuracy and great potential in computational electromagnetic field.
K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media,” IEEE Trans. Antennas Propagat., vol. AP-14, no. 3, pp. 302-307, May 1966.
J. Fang, “Time domain finite difference computation for Maxwell’s equation,” Ph.D. dissertation, Univ. of California at Berkeley, Berkeley, CA, 1989. 216 ACES JOURNAL, Vol. 36, No. 2, February 2021
C. W. Manry, S. L. Broschat, and J. B. Schneider, “High-order FDTD methods for large problems,” Applied Computational Electromagnetics Society Journal, vol. 10, no. 2, pp. 17-29, 1995.
D. W. Zingg, “Comparison of the high-accuracy finite difference methods for linear wave propagation,” SIAM J. Sci. Comput., vol. 22, no. 2, pp. 476-502, 2000.
M. Krumpholz and L. P. B. Katehi, “MRTD: New time-domain schemes based on multiresolution analysis,” IEEE Trans. Microw. Theory Tech., vol. 44, pp. 555-571, Apr. 1996.
S. Gottlieb, C.-W. Shu, and E. Tadmor, “Strong stability-preserving high-order time discretization methods,” SIAM Rev., vol. 43, no. 1, pp. 89-112, 2001.
M. H. Chen, B. Cockburn, and F. Reitich, “Highorder RKDG methods for computational electromagnetics,” J. Sci. Comput., vol. 22/23, no. 1-3, 205-226, June 2005.
J. Z. Zhang and Z. Z. Chen, “A higher-order FDTD using Sinc expansion function,” 2000 IEEE MTT-S International, pp. 113-116, 2000.
E. M. Tentzeris, R. L. Robertson, J. F. Harvey, and L. P. B. Katehi, “Stability and dispersion analysis of battle-Lemarie-based MRTD schemes,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 7, pp. 1004-1013, July 1999.
M. Fujii and W. J. R. Hoefer, “Dispersion of time-domain wavelet Galerkin method based on Daubechies compactly supported scaling functions with three and four vanishing moments,” IEEE Microwave Guided Wave Lett., vol. 10, no. 7, pp. 1752-1760, July 2002.
X. Chen and Q. S. Cao, “Analysis of characteristics of two-dimensional Runge-Kutta multiresolution time-domain scheme,” Progress in Electromagnetics Research M, vol. 13, pp. 217-227, 2010.
Q. S. Cao, R. Kanapady, and F. Reitich, “Highorder Runge-Kutta multiresolution time-domain methods for computational electromagnetics,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 8, pp. 3316-3326, Aug. 2006.
M. Zhu and Q. Cao, “Studying and analysis of the characteristic of the high-order and MRTD and RK-MRTD scheme,” Applied Computational Electromagnetics Society Journal, vol. 28, no. 5, pp. 380-389, May 2013.
M. Zhu and Q. S. Cao, “Analysis for threedimensional curved objects by Runge-Kutta high order time-domain method,” Applied Computational Electromagnetics Society Journal, vol. 30, no. 1, pp. 86-92, Jan. 2015.