High-Order Unconditionally Stable Two-Step Leapfrog ADI-FDTD Methods and Numerical Analysis
High-Order Unconditionally Stable Two-Step Leapfrog ADI-FDTD Methods and Numerical Analysis
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DOI：
10.1109/tap.2013.2274634
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发表时间：
2013-07
影响因子：
5.7
通讯作者：
Yong-Dan Kong;Q. Chu;Ronglin Li
中科院分区：
文献类型：
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作者：
Yong-Dan Kong;Q. Chu;Ronglin Li
提出了三维高阶无条件稳定两步跳变方向隐式时域有限差分（ADI-FDTD）方法。基于指数演化算子（EEO），将矩阵形式的麦克斯韦方程组分解为4个子过程，然后采用跳越格式生成2个子过程。随后，从理论上证明了所提出的高阶方法具有无条件稳定性，并解析导出了数值色散。有几个因素会影响色散：例如，方案的顺序，传播角度，时间步长和网格大小。本文对这四个因素进行了全面的阐述。具体而言，所提方案的归一化数值相速度误差（NNPVE）低于一步跳越ADI-FDTD方法。最后通过数值实验验证了所提方法的有效性。结果表明，二阶方法的相对误差与四步ADI-FDTD方法相同，但计算效率更高。
High-order unconditionally stable two-step leapfrog alternating direction implicit-finite-difference time-domain (ADI-FDTD) methods in three-dimensional (3-D) domains are presented. Based on the exponential evolution operator (EEO), the Maxwell's equations in a matrix form can be split into four subprocedures first, and then two subprocedures are generated by using the leapfrog scheme. Subsequently, the proposed high-order methods are theoretically proven for unconditional stability, and the numerical dispersion is derived analytically. There are several factors to effect the dispersion: for example, the order of schemes, propagation angle, time step, and mesh size. These four factors are illustrated comprehensively in this paper. Specifically, the normalized numerical phase velocity error (NNPVE) of the proposed schemes is lower than that of the one-step leapfrog ADI-FDTD method. Finally, numerical experiments are presented to demonstrate the validity of the proposed methods. It was found that the proposed second-order method has the same level of relative error as that of the four-step ADI-FDTD method, but it has a higher computational efficiency.