Explicit 3D FDTD subgridding with provable stability and conservative properties

The development of a non-conforming local refinement (subgridding) technique that is provably stable and free of spurious modes is considered by many to be the "holy grail" of FDTD. Here the implicit FE geometric multigrid approach is combined with a new mass lumping procedure. The result is a remarkable subgridding method that is both explicit (efficient) and backed by strong statements of (i) electro-dynamic energy conservation, (ii) electrostatic/magnetostatic charge conservation and (iii) proof of nonexistence of late-time instabilities. These improvements carve the trail for the next generation of robust auto-adaptive time-domain simulators.