We proposed a provably stable FDTD subgridding method for accurate and efficient transient electromagnetic analysis. In the proposed method, several field components are properly added to the boundaries of Yee's grid to make sure that the discrete operators meet the summation-by-parts (SBP) property. Then, by incorporating the simultaneous approximation terms (SATs) into the finite-difference time-domain (FDTD) method, the proposed FDTD subgridding method mimics the energy estimate of the continuous Maxwell's equations at the semi-discrete level to guarantee its stability. Further, to couple multiple mesh blocks with different mesh sizes, the interpolation matrices are also derived. The proposed FDTD subgridding method is accurate, efficient, easy to implement and be integrated into the existing FDTD codes with only simple modifications. At last, three numerical examples with fine structures are carried out to validate the effectiveness of the proposed method.
翻译：我们提出了准确和高效瞬时电磁分析的可实现稳定的FDTD子网格方法。在拟议方法中,在Yee网格的界限中适当增加了几个字段部件,以确保离散操作员符合按部分列的总和特性。然后,通过将同步近似条件(SATs)纳入有限差分时间范围(FDTD)方法,拟议的FDTD子网格方法模仿了半分层连续马克斯韦尔方程式的能量估计,以保证其稳定性。此外,将多个网格块和不同网格大小的网格组合也得出了内插矩阵。拟议的FDTD子网格方法准确、高效、易于执行,并仅作简单修改后纳入现有的FDTD代码。最后,采用了三个带有精细结构的数字示例,以验证拟议方法的有效性。
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