A new stable hybrid three-dimensional generalized finite difference time domain algorithm for analyzing complex structures

In this paper, we propose a new stable hybrid, three-dimensional (3-D), generalized finite difference time domain algorithm-formulated by using of the cell method (CM) (a finite volumes type method)-designed to analyze objects with fine details without using very small time steps dictated by the Courant condition. The new algorithm is an extension to the 3-D cases of an analogous hybrid two-dimensional algorithm, also formulated by the CM, and presented earlier by the authors in a previous publication. We carry out a detailed analysis of the stability of the proposed algorithm, paying special attention to the phenomenon of late time instabilities. Finally, the results of some numerical tests are provided to show the absence of instabilities and the efficiency of the hybrid algorithm.