Stability of Explicit–Implicit Hybrid Time-Stepping Schemes for Maxwellʹs Equations

An improved version of the stable FEM–FDTD hybrid method [T. Rylander and A. Bondeson, Comput. Phys. Commun.125, 75 (2000)] for Maxwellʹs equations is presented. The new formulation has a modified time-stepping scheme and is rigorously proven to be stable for time steps up to the stability limit for the FDTD. The new scheme gives less reflection at the boundary between the structured and unstructured grids than the original formulation. The hybrid method is compared to the FDTD, with staircasing for scattering from a conducting sphere. The discretization errors of the hybrid show quadratic dependence on mesh size, while the scaling is less clear for the FDTD. The FDTD gives errors that are 5–60 times higher than that of the hybrid, depending on resolution and staircasing strategy.