A Synchronized SHSG-Based Combined FDTD–PITD Method for 3-D Multiscale Structures

Based on the switched-Huygens-subgridding (SHSG) technique and the precise integration time-domain (PITD) method, a combined method is presented for solving multiscale problems. In this method, the region containing small-scale structures is analyzed by the PITD method with fine cells, and the remaining region is analyzed by the finite difference time-domain (FDTD) method with coarse cells. Since PITD breaks the Courant-Friedrichs–Lewy (CFL) stability condition, the fields in the fine and coarse cells can be synchronously updated, reducing the number of updating steps in the fine cell region and improving the computational speed. The combined method has previously been used in the 1-D and 2-D cases. Here, the combined method is extended to the 3-D cases. Furthermore, the combined method is extended to arbitrary integer cell ratios to increase the flexibility in dealing with multiscale structures. Several numerical experiments are executed to demonstrate that the combined method is accurate and efficient for modeling 3-D multiscale structures.