Comparison between two stable hybridized generalized 2D FDTD algorithms for multiscale analysis

In many practical situations it is necessary to hybridize two algorithms, e.g., the FDTD and FETD, to improve the accuracy of the solution without placing an inordinately heavy burden on the CPU. In order to accomplish this task, without having to use a very small time step throughout the computational domain to satisfy the Courant condition (A. Taflove and S.C. Hagness, "Computational Electrodynamics: The Finite Difference Time-Domain Method", ed. Artech House, MA.,2000.) (which is associated with the smallest length of the mesh edges in the entire computational domain), we have recently proposed two stable hybridized FDTD algorithms in 2D. They have been developed by using the cell method (CM) (M. Marrone and R. Mittra, IEEE Trans. Antennas Prop.) that enabled us to address both the problems of instability and connectivity, when dealing with a combination of a coarse mesh FDTD in one domain and either a fine mesh or a triangular one in the other. In this paper we present the results of some numerical tests, which serve to compare the accuracy and the computational complexity of the proposed algorithms with the same for the classical FDTD method.