High-Accurate Non-Uniform Grids for System-Combined ADI-FDTD Method in Near-Field Scattering with Proper CFL Factor

In this paper, a high-accurate technique with non-uniform grids is introduced into a system-combined alternative-direction-implicit finite-difference time-domain (SC-ADI-FDTD) algorithm, and then successfully used to analyze electromagnetic propagations. To our knowledge, the conventional FDTD with non-uniform grids can be effectively deal with some edges of the three-dimensional cubes and complicated structures of the tiny objects by modulating the local grid scales, which to the extent improves its reliability and accuracy. However, due to existing the finer grids in the local computational region and the inevitable Courant-Friedrichs-Lewy (CFL) limit in the conventional FDTD, the temporal interval must be determined by the minimum fine spatial grid, resulting in much larger temporal sampling density required during the whole computation process. As the advantage of circumventing the repeated variables, the non-uniform SC-ADI-FDTD (NUSC-ADI-FDTD) cannot only break through the CFL limit to implement the high-efficient computation, but also further save more CPU time in the local microstructure cases. Furthermore, the empirical formula between the spatial sampling density and the CFL factors can be obtained from the numerical fitting method after errors analysis. The numerical simulations of the electromagnetic scattering have been executed to illustrate feasibility and validity of our proposed method.