A three-dimensional spatially filtered FDTD with controllable stability beyond the courant limit

It has been recently shown that the stability limit of the Finite-Difference Time-Domain (FDTD) method can be controlled by iterative spatial filtering and extended beyond the conventional Courant-Friedrichs-Lewy limit. However, the trade-off associated with this approach comes from the fact that while the relaxed stability limit allows for the use of a larger time step, spatial filtering is implemented through additional numerical operations. This trade-off manifests itself most significantly in three-dimensional simulations. This paper contributes the algorithmic developments needed for the efficient extension of the spatially filtered FDTD to three-dimensional applications and further demonstrates a three-dimensional late-time stable subgridding scheme based on spatial filtering.