Reduction of numerical dispersion by optimizing second-order cross product derivative term in the ADI-FDTD method

2007 ◽  
Vol 50 (1) ◽  
pp. 123-127
Author(s):  
Ki-Bok Kong ◽  
Jong-Sung Kim ◽  
Seong-Ook Park
Keyword(s):  
Fdtd Method ◽  
Cross Product ◽  
Second Order ◽  
Numerical Dispersion ◽  
Derivative Term

scholarly journals Modified Splitting FDTD Methods for Two-Dimensional Maxwell’s Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Liping Gao ◽  
Shouhui Zhai
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Scattering Problem ◽  
Fdtd Method ◽  
Second Order ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Fourier Methods ◽  
Fdtd Methods

In this paper, we develop a new method to reduce the error in the splitting finite-difference method of Maxwell’s equations. By this method two modified splitting FDTD methods (MS-FDTDI, MS-FDTDII) for the two-dimensional Maxwell equations are proposed. It is shown that the two methods are second-order accurate in time and space and unconditionally stable by Fourier methods. By energy method, it is proved that MS-FDTDI is second-order convergent. By deriving the numerical dispersion (ND) relations, we prove rigorously that MS-FDTDI has less ND errors than the ADI-FDTD method and the ND errors of ADI-FDTD are less than those of MS-FDTDII. Numerical experiments for computing ND errors and simulating a wave guide problem and a scattering problem are carried out and the efficiency of the MS-FDTDI and MS-FDTDII methods is confirmed.

A New Unconditionally Stable Time Integration Method for Analysis of Nonlinear Structural Dynamics

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Ali Akbar Gholampour ◽  
Mehdi Ghassemieh ◽  
Mahdi Karimi-Rad
Keyword(s):  
Time Integration ◽  
Second Order ◽  
Numerical Dispersion ◽  
Computational Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Similar Time ◽  
Unconditionally Stable ◽  
Average Acceleration

A new time integration scheme is presented for solving the differential equation of motion with nonlinear stiffness. In this new implicit method, it is assumed that the acceleration varies quadratically within each time step. By increasing the order of acceleration, more terms of the Taylor series are used, which are expected to have responses with better accuracy than the classical methods. By considering this assumption and employing two parameters δ and α, a new family of unconditionally stable schemes is obtained. The order of accuracy, numerical dissipation, and numerical dispersion are used to measure the accuracy of the proposed method. Second order accuracy is achieved for all values of δ and α. The proposed method presents less dissipation at the lower modes in comparison with Newmark's average acceleration, Wilson-θ, and generalized-α methods. Moreover, this second order accurate method can control numerical damping in the higher modes. The numerical dispersion of the proposed method is compared with three unconditionally stable methods, namely, Newmark's average acceleration, Wilson-θ, and generalized-α methods. Furthermore, the overshooting effect of the proposed method is compared with these methods. By evaluating the computational time for analysis with similar time step duration, the proposed method is shown to be faster in comparison with the other methods.

scholarly journals An Artificial Anisotropy Four-Step HIE-FDTD Method With Lower Numerical Dispersion Error

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 199016-199024
Author(s):  
Yong-Dan Kong ◽  
Chu-Bin Zhang ◽  
Hong-Yu Zhang ◽  
Qing-Xin Chu
Keyword(s):  
Fdtd Method ◽  
Numerical Dispersion ◽  
Dispersion Error
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