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, the void space domain decomposition (VSDD) method. It features solve speeds comparable to those of the finite-difference time domain (FDTD) method, but enables domains 10 times larger or more with typical compute configurations. With VSDD, there is no need to solve a matrix equation that spans the entire problem domain. The network bandwidth requirement, a key limitation of FDTD, is reduced by about a factor of 35 or more, even though both algorithms require comparable numbers of voxel operations.
Thomas Baehr-Jones (Wed,) studied this question.