Finite-difference frequency domain electromagnetics with the void space domain decomposition method

The finite-difference frequency domain (FDFD) method has received increasing interest, owing to its ability to provide useful information for inverse design. Here I introduce a new algorithm that provides FDFD solutions, which I name the void space domain decomposition (VSDD) method. It features solve speeds comparable to those achieved by the finite-difference time domain (FDTD) method, but enables domain sizes 10 times larger or more with typical compute configurations. The network bandwidth requirement, a key limitation for FDTD, is reduced by about a factor of 35 or more. I present an analysis showing that, independent of implementation, for some problems, both algorithms should exhibit comparable runtimes.