Stable FDTD simulations with subgridding at the time step of the coarse grid: A model order reduction approach

Multiscale electromagnetic problems occur frequently in practical applications. Unfortunately, the Finite Difference Time Domain (FDTD) method can lose its remarkable efficiency when small and large geometrical features are present simultaneously. Small geometrical features impose a fine spatial grid, increasing memory consumption and CPU time. Moreover, because of the Courant-Friedrichs-Lewy (CFL) stability condition, time step has to be also reduced, further increasing the overall computational cost. We propose a new method to accelerate FDTD simulations with local grid refinements. The FDTD equations for the fine region are first compressed using model order reduction. The stability limit of the resulting equations is extended to match the stability limit of the coarse grid using a suitable perturbation approach. Finally, the reduced models of the fine regions are embedded into the main coarse grid. Owing to their enhanced stability, the whole simulation can be run at the large time step supported by the coarse grid. The proposed technique thus provides a way to perform stable FDTD simulations with subgridding at the CFL limit of the coarse grid. A numerical example demonstrates the remarkable speed-ups that can be obtained with the proposed method with respect to FDTD and spatial subgridding.