A Practical Fourth Order Finite-Difference Time-Domain Algorithm for the Solution of Maxwell’s Equations
Keywords:FDTD, finite difference time domain, fourth order approximation, higher order
Implementing a practical fourth order accurate in time and second order accurate in space finite difference time domain simulation using MATLAB is the goal of this paper. The formulation presented for the fourth order approximation is simple to integrate into an existing second order accurate in time and second order accurate in space formulation and wellestablished code. The fourth order formulation has been verified and simulation accuracy is confirmed through the application of radiation from a single and an array of dipole antennas.
A. Z. Elsherbeni and V. Demir, The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB® Simulations. 2nd edition, Edison, New Jersey: SciTech Publishing, 2015.
M. 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, Feb. 1997.
J. Fang, “Time-Domain Finite Difference Computations for Maxwell's Equations,” Ph.D. dissertation, EECS Dept., Univ. California, Berkeley, 1989.
K. Hwang and A. C. Cangellaris, “Computational efficiency of Fang’s fourth-order FDTD schemes,” Electromagnetics, vol. 23, 2003.
N. V. Kantartzis and T. D. Tsiboukis, Higher Order FDTD Schemes for Waveguide and Antenna Structures. 1st edition, Morgan & Claypool Publishers, 2006.
C. A. Balanis, Antenna Theory Analysis and Design. 3rd edition, Hoboken, New Jersey: A John Wiley & Sons, Inc., 2005.