An Unsymmetric FDTD Subgridding Algorithm With Unconditional Stability
An Unsymmetric FDTD Subgridding Algorithm With Unconditional Stability
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DOI：
10.1109/tap.2018.2835561
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发表时间：
2018-08
影响因子：
5.7
通讯作者：
Jin Yan;D. Jiao
中科院分区：
文献类型：
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作者：
Jin Yan;D. Jiao
为了保持具有任意子网格的网格的精度，时域有限差分 (FDTD) 子网格方案通常会导致不对称的数值系统。这样的数值系统可能具有复值特征值，这将使 FDTD 的传统显式时间推进变得绝对不稳定。在本文中，我们开发了一种精确的 FDTD 子网格算法，适用于普通网格和子网格之间具有任意对比度的任意子网格设置。尽管最终的系统矩阵也是不对称的，但我们开发了一种时间推进方法来克服稳定性问题，而不会牺牲原始 FDTD 的无矩阵优点。该方法具有通用性，也适用于其他底层数值系统不对称的子网格化算法。然后，所提出的 FDTD 子网格算法进一步变得无条件稳定，从而允许使用独立于空间步长的时间步长。涉及具有各种对比度的 2 维和 3 维子网格的大量数值实验证明了所提出的子网格算法的准确性、稳定性和效率。
To preserve accuracy in a grid with arbitrary subgrids, a finite-difference time-domain (FDTD) subgridding scheme, in general, would result in an unsymmetric numerical system. Such a numerical system can have complex-valued eigenvalues, which will render a traditional explicit time marching of FDTD absolutely unstable. In this paper, we develop an accurate FDTD subgridding algorithm suitable for arbitrary subgridding settings with arbitrary contrast ratios between the normal grid and the subgrid. Although the resulting system matrix is also unsymmetric, we develop a time-marching method to overcome the stability problem without sacrificing the matrix-free merit of the original FDTD. This method is general, which is also applicable to other subgridding algorithms whose underlying numerical systems are unsymmetric. The proposed FDTD subgridding algorithm is then further made unconditionally stable, thus permitting the use of a time step independent of space step. Extensive numerical experiments involving both 2- and 3-D subgrids with various contrast ratios have demonstrated the accuracy, stability, and efficiency of the proposed subgridding algorithm.