Fourier analysis of numerical algorithms for the Maxwell equations
Journal of Computational Physics
High accuracy solution of Maxwell's equations using nonstandard finite differences
Computers in Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
The Immersed Interface/Multigrid Methods for Interface Problems
SIAM Journal on Scientific Computing
Staggered Time Integrators for Wave Equations
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Numerical treatment of two-dimensional interfaces for acoustic and elastic waves
Journal of Computational Physics
DSC time-domain solution of Maxwell's equations
Journal of Computational Physics
Journal of Computational Physics
High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
Journal of Computational Physics
Multidimensional optimization of finite difference schemes for Computational Aeroacoustics
Journal of Computational Physics
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The finite difference time domain (FDTD) method is an important tool in numerical electromagnetic simulation. There are many ways to construct a finite difference approximation such as the Taylor series expansion theorem, the filtering theory, etc. This paper aims to provide the comparison between the Taylor finite difference (TFD) scheme based on the Taylor series expansion theorem and the window finite difference (WFD) scheme based on the filtering theory. Their properties have been examined in detail, separately. In addition, the formula of the generalized finite difference (GFD) scheme is presented, which can include both the TFD scheme and the WFD scheme. Furthermore, their application in the numerical solution of Maxwell's equations is presented. The formulas for the stability criterion and the numerical dispersion relation are derived and analyzed. In order to evaluate their performance more accurately, a new definition of error is presented. Upon it, the effect of several factors including the grid resolution, the Courant number and the aspect ratio of the cell on the performance of the numerical dispersion is examined.