Truncation Error Analysis of a Pre-Asymptotic Higher-Order Finite Difference Scheme for Maxwell's Equations
Keywords:
FDTD, higher-order, preasymptotic, truncation errorAbstract
Pre-asymptotic higher-order methods are useful to the mitigation of numerical dispersion error in large-scale Finite-Difference Time-Domain (FDTD) simulations. Its truncation error is shown in this study to be 2 2 O O () () :: t s in general. In the limiting case where the CourantFriedrichs-Levy number approaches to zero, it becomes 2 4 O O () () :: t s .
Downloads
References
A. Taflove, “Advances in computational electrodynamics: the finite-difference timedomain method,” Boston: Artech, 1998.
J. Fang, “Time domain computation for Maxwell’s equations,” Ph.D. dissertation, Univ. California at Berkeley, 1989.
C. K. W. Tam and J. C. Webb, “Dispersionrelation-preserving finite difference schemes for computational acoustics,” J. Comp. Phys., vol. 107, pp. 262-281, 1993.
M. F. Hadi and M. Piket-May, “A modified FDTD (2,4) scheme for modeling electrically large structures with high-phase accuracy,” IEEE Trans. Antennas Propagat., vol. 45, no. 2, pp. 254-264, 1997.
J. B. Cole, “A high accuracy FDTD algorithm to solve microwave propagation and scattering problems on a coarse grid,” IEEE Trans. Microwave Theory Tech., vol. 43, no. 9, pp. 2053- 2058, 1995.
E. A. Forgy and W. C. Chew, “A new FDTD formulation with reduced dispersion for the simulation of wave propagation through inhomogeneous media,” IEEE AP-S Int. Symp. Proc., vol. 2, pp. 1316-1319, 1999.
S. Wang and F. L. Teixeira, “A finite-difference time-domain algorithm optimized for arbitrary propagation angles,” IEEE Trans. Antennas Propagat., vol. 51, no. 9, pp. 2456-2463, September 2003.
S. Wang and F. L. Teixeira, “A three-dimensional angle-optimized FDTD algorithm,” IEEE Trans. Microwave Theory & Tech., vol. 51, no. 3, pp. 811-817, March 2003.
S. Wang and F. L. Teixeira, “Grid-dispersion error reduction for broadband electromagnetic simulations,” IEEE Trans. Magnetics, vol. 40, no. 2, pp. 1440-1443, March 2004.
S. Wang and F. L. Teixeira, “Lattice models for large-scale simulations of coherent wave scattering,” Physical Review: E, vol. 69, 016701, January 2004.
S. Wang and F. L. Teixeira, “Dispersion-relationpreserving FDTD algorithms for large scale threedimensional problems,” IEEE Trans. Antennas Propagat., vol. 51, no. 8, pp. 1818-1828, August 2003.