Accelerating multiscale finite-difference time-domain simulations through model order reduction and CFL limit extension

The Finite-Difference Time-Domain (FDTD) method is widely use to solve Maxwell´s equations numerically. FDTD has a low computational cost per timestep due to its explicit nature. However, the FDTD timestep cannot exceed the Courant-Friedrichs-Lewy (CFL) stability limit. This condition makes FDTD quite inefficient for multiscale problems, since the presence of small geometrical details imposes a fine grid and, because of the CFL limit, a very small timestep. Since multiscale problems occur frequently in practice, over-coming the CFL limit of FDTD is a major research topic. Examples of multiscale problems are the prediction of electromagnetic compatibility issues in printed circuit boards, and the simulation of electromagnetic propagation in indoor/outdoor environments.