In this paper we propose a finite element time-domain method for modeling the optical black holes (OBHs) coupled with the perfectly matched layer (PML) technique. Stability analysis is carried out for the proposed scheme. Simulations of cylindrical, elliptical and square black holes demonstrate that our method is quite effective in modeling OBHs in time domain. To our best knowledge, this is the first OBHs simulation realized by the finite element time-domain method.

Since the development of Yee scheme back in 1966, it has become one of the most popular simulation tools for modeling electromagnetic wave propagation in various situations.However, its rigorous error analysis on nonuniform rectangular type gridswas carried out until 1994 by Monk and Süli. They showed that theYee scheme is still second-order convergent on a nonuniform mesh even though the local truncation error is only of first order. In this paper, we extend their results to Maxwell’s equations in metamaterials by a simpler proof, and show the second-order superconvergence in space for the trueYee scheme instead of the only semi-discrete form discussed in Monk and Süli’s original work. Numerical results supporting our analysis are presented.

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