Overcoming the FDTD stability limit via model order reduction and eigenvalue perturbation

Abstract

In the Finite Difference Time Domain (FDTD) method, the time-step is constrained by the Courant-Friedrichs-Lewy (CFL) limit. The CFL limit is particularly restrictive in the presence of fine geometrical details, since it imposes a very small time-step. We propose an efficient method for overcoming this constraint via model order reduction, coupled with an eigenvalue perturbation method that ensures stability even for time-steps beyond the CFL limit. Two numerical examples demonstrate that the proposed method is faster than FDTD as well as existing alternative techniques for overcoming the CFL barrier.