Improved Weakly Conditionally Stable Finite-Difference Time-Domain Method
Keywords:
FDTD method, perfect-electricconductor (PEC) condition, weakly conditionally stable FDTD methodAbstract
To circumvent the inaccuracy in the implementation of the perfect-electric-conductor (PEC) condition in the weakly conditionally stable finite-difference time-domain (WCS-FDTD) method, an improved weakly conditionally stable (IWCS) FDTD method is presented in this paper. In this method, the solving of the tridiagonal matrix for the magnetic field component is replaced by the solving of the tridiagonal matrix for the electric field components; thus, the perfectelectric- conductor (PEC) condition for the electric field components is implemented accurately. The formulations of the IWCS-FDTD method are given, and the stability condition of the IWCSFDTD scheme is presented analytically. Compared with the WCS-FDTD method, this new method has higher accuracy in the implantation of the PEC condition, which is demonstrated through numerical examples.
Downloads
References
K. S. Yee, “Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media,” IEEE Trans. Antennas Propagat., vol. 14, pp. 302-307, 1966.
A. Taflove, Computational Electrodynamics, Norwood, MA: Artech House, 1995.
F. Zheng, Z. Chen, and J. Zhang, “A FiniteDifference Time-Domain Method Without the Courant Stability Conditions,” IEEE Microwave Guided Wave Lett., vol. 9, pp. 441-443, 1999.
T. Namiki, “3-D ADI-FDTD MethodUnconditionally Stable Time-Domain Algorithm for Solving Full Vector Maxwell’s Equations,” IEEE Trans. Microwave Theory Tech., vol. 48, pp. 1743-1748, 2000.
G. Sun and C. W. Trueman, “Some Fundamental Characteristics of the One-Dimensional AlternateDirection-Implicit Finite-Difference Timedomain Method,” IEEE Trans. Microawave Theory Tech., vol. 52, pp. 46-52, 2004.
M. Darms, R. Schuhmann, H. Spachmann, and T. Weiland, “Dispersion and Asymmetric Effects of ADI-FDTD,” IEEE Microwave Wireless Components Lett, vol. 12, pp. 491-493, 2002.
N. V. Kantartzis, “Multi-Frequency Higher-Order ADI-FDTD Solvers for Signal Integrity Predictions and Interference Modeling in General EMC Applications,” Applied Computational Electromagnetic Society (ACES) Journal, vol. 25, pp. 1046-1060, 2010.
J. Chen and J. Wang, “An Unconditionally Stable Subcell Model for Thin Wires in the ADI-FDTD Method,” Applied Computational Electromagnetic Society (ACES) Journal, vol. 25, pp. 659-664, 2010.
G. Sun and C. W. Trueman, “Accuracy of Three Unconditionally-Stable FDTD Schemes for Solving Maxwell’s Equations,” Applied Computational Electromagnetic Society (ACES) Journal, vol. 18, pp. 41-47, 2003.
G. Sun and C. W. Trueman, “An UnconditionallyStable FDTD Method Based on the Crank–Nicolson Scheme for Solving the Three-Dimensional Maxwell’s Equations,” Electron. Lett., vol. 40, pp. 589-590, 2004.
J. Chen and J. Wang, “PEC Condition Implementation for the ADI-FDTD Method,” Microwave Opt. Technol. Lett., vol. 49, pp. 526- 530, 2007.
I. Ahmed and Z. Chen, “Error Reduced ADI-FDTD Methods,” IEEE Antennas Wireless Propag. Lett, vol. 4, pp. 323-325, 2005.
J. Chen and J. Wang, “Weakly Conditionally Stable Finite-Difference Time-Domain Method”, IET Microwaves, Antennas & Propagation, vol. 4, pp. 1927-1936, 2010.
J. Chen and J. Wang, “A Frequency-Dependent Weakly Conditionally Stable Finite-Difference Time-Domain Method for Dispersive Materials,” Applied Computational Electromagnetic Society (ACES) Journal, vol. 25, pp. 665-671, 2010.
