Development of three-dimensional unconditionally stable finite-difference time-domain methods
Development of three-dimensional unconditionally stable finite-difference time-domain methods
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DOI：
10.1109/mwsym.2000.863553
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发表时间：
2000-06
期刊：
影响因子：
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通讯作者：
Fenghua Zheng;Z. Chen;Jiazong Zhang
中科院分区：
文献类型：
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作者：
Fenghua Zheng;Z. Chen;Jiazong Zhang
时域有限差分法(FDTD)在求解电磁问题中得到了广泛的应用。然而，它处理电大尺寸或高Q结构问题的能力受到计算内存和时间要求的限制。这种要求是由于数值色散误差和CFL稳定性条件造成的。到目前为止，大多数研究工作都集中在开发诸如MRTD和PSTD的格式，这些格式具有低的数值色散，因此需要较低的计算内存。在本文中，我们将提出提高FDTD计算效率的另一个方向：消除CPL稳定性条件。换言之，我们将提出一种无条件稳定的三维有限差分方法，其中FDTD的时间步长不再受CPL稳定性条件的限制，而只受FDTD算法的建模精度的限制。从而减少了FDTD迭代次数和计算时间。为了进一步减小数值色散、各向异性和内存，还提出了一种高阶格式。理论研究和数值算例将被用来验证所提出的方案。
The finite-difference time-domain (FDTD) method has been widely applied in solving electromagnetic problems. Its capability of handling electrically large or high-Q structure problems is, however, limited by the requirements of large computation memory and time. Such requirements are due to the numerical dispersion errors and the CFL stability condition. So far, most of the research efforts have been focused in developing schemes such as MRTD and PSTD that possess low numerical dispersion and therefore require low computation memory. In this paper, we will present another direction in improving the FDTD computation efficiency: removal of the CPL stability condition. In other words, we will present an unconditionally stable 3D finite-difference time-domain method where the FDTD time step, is no longer restricted by the CPL stability condition but by the modelling accuracy of the FDTD algorithm only. As a result, FDTD iteration number and CPU time are reduced. To further reduce numerical dispersion, anisotropy and memory of the method, a high-order scheme is also presented. Theoretical studies and numerical examples will be presented to validate the proposed schemes.