A theoretical study of the stability criteria for hybridized FDTD algorithms for multiscale analysis

In this paper, we propose two new hybrid, two-dimensional, generalized finite-difference time-domain algorithms-formulated by using the cell method-and designed to analyze objects with fine details, without using very small time steps dictated by the Courant condition. A detailed analysis of the stability of the proposed algorithms is presented, with special attention devoted to the phenomenon of late time instabilities. Finally, some rules are provided that would ensure the stability of the proposed algorithms.