FDTD based second-order accurate local mesh refinement method for Maxwell's equations in two space dimensions

Abstract

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.