Numerical dispersion analysis of energy conserved splitting FDTD method for Maxwell's equations

2016 ◽  
Author(s):  
Lei Zhao ◽  
Wen Li ◽  
Wenhua Yu
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Fdtd Method ◽  
Dispersion Analysis ◽  
Numerical Dispersion

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.

Analyzing photonic space-time crystal with FDTD

2020 ◽  
Vol 34 (06) ◽  
pp. 2050082 ◽  
Author(s):  
Zheng Zhang ◽  
Wenjun Zhang ◽  
Lunwu Zeng
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Electromagnetic Wave Propagation ◽  
Fdtd Method ◽  
Space Time ◽  
Crystal Forms ◽  
Time Translation ◽  
Permittivity And Permeability ◽  
Translation Symmetry ◽  
Difference Time

When space (time) translation symmetry is spontaneously broken, the space crystal (time crystal) forms; when permittivity and permeability periodically vary with space (time), the photonic space crystal (photonic time crystal) forms. We rewrote Maxwell’s equations in photonic time crystal, and discretized Maxwell’s equations with finite difference time domain (FDTD) method, deduced the discretized electric and magnetic field, and simulated electromagnetic wave propagation in two-dimensional (2D) photonic space-time crystal and photonic space crystal (or photonic crystal), and discussed the effect of parameters on the band gap.

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