Structure-Preserving Reduction of Finite-Difference Time-Domain Equations with Controllable Stability Beyond the CFL Limit

Abstract: The timestep of the Finite-Difference Time-Domain method (FDTD) is constrained by the stability limit known as the Courant-Friedrichs-Lewy (CFL) condition. This limit can make FDTD simulations quite time consuming for structures containing small geometrical details. Several methods have been proposed in the literature to extend the CFL limit, including implicit FDTD methods and filtering techniques. In this paper, we propose a novel approach which combines model order reduction and a perturbation algorithm to accelerate FDTD simulations beyond the CFL barrier. We compare the proposed algorithm against existing implicit and explicit CFL extension techniques, demonstrating increased accuracy and performance on a large number of test cases, including resonant cavities, a waveguide structure, a focusing metascreen and a microstrip filter.