An algorithm is presented for local space-time mesh refinement appropriate
for electromagnetic simulations based on the space-time staggered FDTD method.
The method is based on the adaptive mesh re.nement algorithm originally developed
for hyperbolic conservation laws. Analysis of the dispersion relation and of the numerical reflection
and transmission coefficients in one and two space dimensions shows that a scheme
based on linear interpolation at the grid interfaces is unstable due to reflection coefficient > 1
at frequencies above the cutoff frequency of the coarse grid.
A second-order accurate algorithm based on higher-order interpolations
that enforces conservation of the magnetic field circulation at the fine-coarse grid boundaries is constructed.
The new algorithm is shown to be stable and accurate for long time integration.
A numerical simulation of an optical ring microcavity resonator
using multilevel grid refinement in two space dimensions is presented.