We perform stability analysis on the finite-difference time domain method (FDTD) when extended to incorporate local space-time adaptive mesh refinement (AMR). The neutrally stable Yee algorithm becomes extremely sensitive to perturbations introduced by the interpolation schemes employed at grid refinement interfaces. In this paper we investigate the stability of a range of interpolation schemes using Gustafsson-Kreiss-Sundstrom-Trefethen (GKS-T) mode and reflection/transmission coefficients analysis on the infinite domain with a single interface. This analysis allows detection of trapping instabilities, exponentially growing modes, mode resonances with the interface and mode-mode resonances. We also apply matrix stability analysis for more complicated computational domains containing multiple grid refinement interfaces.
"Stability of 2D FDTD algorithms with local mesh refinement for Maxwell's equations." Commun. Math. Sci. 4 (2) 345 - 374, June 2006.