A stable three-dimensional subgridding method for both spatial and temporal spaces

In this paper we detailed a new three-dimensional Subgridding or Multigrid-FDTD method based on our recently proposed method in two-dimensions. First a 3D spatial subgridding method based on Monk´s two-dimensional method is described. Then by using conservation principle we showed the spatial subgridding method is stable, as well as the temporal subgridding method used. Finally, by separating the temporal and spatial perimeter interfaces for subgridding to different positions - the “temporal-spatial” coupled problem is decoupled into two separate independent problems. This decoupling makes the new 3D subgridding method naturally stable for electromagnetic wave propagation problems in both spatial and temporal spaces. Numerical results obtained show no late-time instability after ten million time steps.