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首页> 外文期刊>Microwave and optical technology letters >The influence of the time step on the numerical dispersion error of an unconditionally stable 3-D ADI-FDTD method: a simple and unified approach to determine the maximum allowable time step required by a desired numerical dispersion accuracy
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The influence of the time step on the numerical dispersion error of an unconditionally stable 3-D ADI-FDTD method: a simple and unified approach to determine the maximum allowable time step required by a desired numerical dispersion accuracy

机译：时间步长对无条件稳定3-D ADI-FDTD方法数值离散误差的影响：一种简单且统一的方法来确定所需的数值离散精度所需的最大允许时间步长

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摘要

In this paper, by analyzing the numerical dispersion property of an unconditionally stable three-dimensional alternating direction implicit finite-difference time-domain (ADI-FDTD) method, the influence of the time steps on the numerical dispersion error of the method is investigated. It is demonstrated that, to keep the numerical dispersion error of the method within a certain level of accuracy, an upper limit for the time step allowed to be used in the method exists and it can be theoretically determined. Particularly, in order to systematically determine the upper limit for the computational domain meshed with arbitrary uniform and non-uniform grids, a special strategy used to divide Yee's cells into different categories is developed. Subsequently, a simple and unified approach for determining the maximum allowable time steps (i.e., the upper limits) from a desired numerical dispersion accuracy is proposed. Most importantly, with the help of the proposed approach, the maximum allowable time steps can be simply and easily determined once the meshing of structures (meshed with either uniform or non-uniform grids) is known, i.e., without carrying out any real ADI-FDTD simulations for the structures.
机译：通过分析无条件稳定的三维交变方向隐式有限差分时域方法（ADI-FDTD）的数值色散特性，研究了时间步长对该方法数值色散误差的影响。已经证明，为了将方法的数值分散误差保持在一定的精度水平内，存在允许在该方法中使用的时间步的上限，并且可以在理论上确定该上限。特别地，为了系统地确定与任意均匀和非均匀网格划分网格的计算域的上限，开发了一种用于将Yee的单元划分为不同类别的特殊策略。随后，提出了一种简单且统一的方法，用于根据所需的数值离散精度确定最大允许时间步长（即上限）。最重要的是，借助所提出的方法，一旦知道了结构的网格划分（用均匀或不均匀网格划分），即可简单，轻松地确定最大允许时间步长，即无需执行任何实际的ADI- FDTD结构仿真。

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