Model Order Reduction and Stability Enforcement of Finite-difference Time-domain Equations Beyond the CFL Limit

The Finite-Difference Time Domain (FDTD) method is a versatile and popular method for solving Maxwell's equations. As a consequence of the explicit time integration, the maximum stable time-step of FDTD is constrained by the Courant-Friedrichs-Lewy (CFL) limit. This thesis focuses on two interdependent topics: model order reduction (MOR) of explicit FDTD equations and stability enforcement above the CFL limit. The combination of these two topics leads to the proposed CFL extension technique which has been demonstrated for 2D and 3D simulations. In addition, the proposed method has also been applied to the FDTD sub-gridding application. Comparisons have been made with existing implicit and explicit CFL extension techniques with respect to versatility, computational efficiency, and numerical dispersion errors. While there exist computation and memory limitations, the proposed method has demonstrated excellent versatility and accuracy for all test cases while having significant speed-ups over standard FDTD.M.A.S.2016-11-19 00:00:0