We address the electromagnetic problem involving small structures, and put forward an improved, explicit finite-difference time-domain (FDTD) algorithm based on the Newmark discretization with subgridding technique. This algorithm achieves a stable, low-reflection, and straightforward subgridding with an arbitrary grid refinement ratio by adopting hanging variables. The Newmark method is employed to discretize the numerical system generated by the subgridding method. Besides, the Neumann series is used to obtain the inverse of the coefficient matrix. It makes the time-marching explicit and stable with a uniform large time step only determined by the coarse grid size in the whole computational domain. The series expansion avoids the matrix inversion operation, which largely enhances the calculation efficiency compared to the traditional Newmark-FDTD method. Numerical results prove the reliability and robustness of the proposed method.

中文翻译：

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一种具有子网格技术的显式 Newmark-FDTD 算法

我们解决了涉及小结构的电磁问题，并提出了一种改进的、基于 Newmark 离散化和子网格技术的显式有限差分时域 (FDTD) 算法。该算法通过采用悬挂变量实现了具有任意网格细化率的稳定、低反射和直接的子网格化。Newmark 方法用于离散化由子网格化方法生成的数值系统。此外，使用诺依曼级数来获得系数矩阵的逆。它使时间推进明确且稳定，具有统一的大时间步长，仅由整个计算域中的粗网格大小决定。级数展开避免了矩阵求逆运算，与传统的Newmark-FDTD方法相比，大大提高了计算效率。数值结果证明了所提出方法的可靠性和鲁棒性。