A Stable 3-D FDTD Method with Multiple Embedded Reduced-Order Models

Abstract

The finite-difference time-domain (FDTD) method has been widely used for its versatility in solving electromagnetic problems. However, the computational efficiency of FDTD can be significantly reduced in subgridding schemes, where a locally refined grid is adopted in the spatial domain. An emerging approach to accelerate FDTD subgridding is model order reduction (MOR), which can be used to compress the update equations of the refined regions. However, reduced-order models can easily introduce instability when embedded into an FDTD grid. In this paper, we propose a systematic strategy to couple multiple reduced models to a 3-D FDTD grid with guaranteed stability under the Courant-Friedrichs-Lewy (CFL) limit of the fine grid. Furthermore, the CFL limit of the entire scheme can be extended with a perturbation of the reduced model coefficients, which can further improve computational efficiency. A numerical example with two reduced-order models indicates the potential of the proposed algorithm.