Accelerating the Finite-Difference Time-Domain Method for Maxwell Equations through Model Order Reduction and CFL Limit Extension


Tuesday, 16 December, 2014 - 14:30

Speaker: Piero Triverio (University of Toronto - Department of Electrical and Computer Engineering)

Room: SISSA - Santorio A - room 133

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.