A stable FDTD subgridding method for both spatial and temporal spaces

Abstract

The proposed FDTD subgridding method is stable in both spatial and temporal spaces. Late-time instability has been resolved by separating the space and time interpolation interfaces from conventional collocated to same position. Numerical experiments conducted in 2D of 10 million time steps have no instability problem after a minimum gap distance for various refinement factors. Compare to existing subgridding methods the new method is not restricted to a single refinement factor and need no special treatment at material interfaces. This should open the FDTD subgridding method to more applications.

Explicit and provably stable spatiotemporal FDTD refinement

“…In this paper we introduce an explicit spatiotemporal FDTD refinement scheme, which lets us update the refined regions with a locally smaller time step. We are not the first to attempt this [25,23,1,13,4,5,12,3,6], but to our knowledge this scheme is the first that is explicit, provably conditionally stable, and recursively applicable (i.e. the refined region can be further refined).…”

“…where E is the electric field, B the magnetic field, c the speed of light, and µ r , ε r the relative magnetic permeability and electric permittivity. We choose in this paper to use Gaussian units, since they make the symmetry of Maxwell's equations more readily apparent: note the factor 1/c in both (2) and (3).…”