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Reduced-order modeling in FDTD subgridding with complexity independent of the grid refinement ratio

The Finite Difference Time Domain (FDTD) method can become quite inefficient for multiscale problems, where finely-featured objects are present in a large computational domain. We present a model order reduction approach to accelerate multiscale FDTD simulations. Complex objects are first meshed with a refined grid. The obtained FDTD equations are then compressed with model reduction and finally instantiated into the coarse grid that is used in the rest of the domain. The novelty of this work is that the reduced model size is lower than in previous approaches. Moreover, the model complexity is independent of the refinement ratio between coarse and fine grid. The proposed method is provably stable and can lead to significant computational savings in multiscale scenarios, as shown by the numerical example.