Conservative and Provably Stable FDTD Subgridding

The finite difference time domain (FDTD) method is a common, robust simulation technique for transient electromagnetic interactions with complicated structures. However, the standard FDTD method is limited to cartesian grids everywhere in the computational grid. Many practitioners have extended FDTD to handle multiresolution problems by using finer grids near structures with small geometrical features abutted to coarse grids in regions of empty space. Unfortunately, subgridding implementations based on interpolation or extrapolation of neighboring field values can exhibit late time instabilities. Herein, a subgridding method based on multigrid finite element principles will be developed and its stability proven. Numerical results will assess its performance in 2-D and 3-D.