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.
翻译:与我们先前的工作相比,拟议的SBP-SAT FDTD方法使用错开的 Yee 网格,而不通过实地外推法增加或修改任何实地组成部分,以使离散操作员能够满足SBP特性。外推法的准确性与边界附近第二等级的有限差异计划相一致。此外,还利用卫星在不同的网格大小的多个网格区块之间薄弱地执行相近边界条件。经过精心设计的内插矩阵和选定的SAT自由参数,整个计算域不会出现分解现象。因此,其长期稳定性在理论上是有保证的。进行了三个数字实例,以证实其有效性。结果显示,拟议的SBP-SAT的FDTD子网格化方法稳定、准确、高效、容易以现有的FDTD代码为基础执行,但只有少量修改。