The Finite-Difference Time-Domain method (FDTD) is a popular technique
to solve Maxwell equations. Since FDTD is an explicit scheme, its
timestep is constrained by the Courant-Friedrichs-Lewy (CFL) stability
condition. As a result, FDTD simulations can be time-consuming for
multiscale problems. Several methods have been proposed in the
literature to extend the CFL limit, including implicit FDTD methods and
filtering techniques. In this talk, we present a novel approach based on
model order reduction and a perturbation scheme to extend the CFL limit.
First, the order of the FDTD equations is reduced using a Krylov method.
Then, the method is made stable above the CFL limit using a perturbation
approach.
The proposed technique preserves the structure of the FDTD equations,
leads to substantial speed-ups with respect to FDTD, and provides
results which agree with standard FDTD within 1-2% error. Several
numerical examples related to high-frequency circuits, waveguides and
focusing devices will be presented.