论文标题
SBP-SAT FDTD子生产方法使用交错的YEE网格而不修改字段组件
A SBP-SAT FDTD Subgridding Method Using Staggered Yee's Grids Without Modifying Field Components
论文作者
论文摘要
提出了同时逐个近似项（SBP-SAT）有限差分时间域（FDTD）子生产方法的求和，以模拟本文中的几何结构。与我们以前的工作相比，提出的SBP-SAT FDTD方法使用交错的YEE网格，而无需通过在边界上的字段外推添加或修改任何字段组件，以使离散操作员满足SBP属性。外推的准确性与边界附近的二阶有限差分方案保持一致。另外，SATS用于薄弱地强制具有不同网格尺寸的多个网格块之间的切向边界条件。使用精心设计的插值矩阵和SAT的选定自由参数，整个计算域中没有发生耗散。因此，从理论上讲，它的长期稳定性是可以保证的。进行了三个数值示例以验证其有效性。结果表明，提出的SBP-SAT FDTD子生产方法是稳定，准确，高效且易于实现的，并且基于现有的FDTD代码仅具有一些修改。
A summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-domain (FDTD) subgridding method is proposed to model geometrically fine structures in this paper. Compared with our previous work, the proposed SBP-SAT FDTD method uses the staggered Yee's grid without adding or modifying any field components through field extrapolation on the boundaries to make the discrete operators satisfy the SBP property. The accuracy of extrapolation keeps consistency with that of the second-order finite-difference scheme near the boundaries. In addition, the SATs are used to weakly enforce the tangential boundary conditions between multiple mesh blocks with different mesh sizes. With carefully designed interpolation matrices and selected free parameters of the SATs, no dissipation occurs in the whole computational domain. Therefore, its long-time stability is theoretically guaranteed. Three numerical examples are carried out to validate its effectiveness. Results show that the proposed SBP-SAT FDTD subgridding method is stable, accurate, efficient, and easy to implement based on existing FDTD codes with only a few modifications.
