Developing a Time-Domain Finite Element Method for the Lorentz Metamaterial Model and Applications

Document Type

Article

Publication Date

1-1-2016

Publication Title

Journal of Scientific Computing

Volume

68

Issue

2

First page number:

438

Last page number:

463

Abstract

In this paper, we propose a new time-domain finite element method for solving the time dependent Maxwell’s equations coupled with the Lorentz metamaterial model. The Lorentz metamaterial Maxwell’s equations are much more complicated than the standard Maxwell’s equations in free space. Our fully discrete scheme uses edge elements to approximate the unknowns in space, and uses the leap-frog scheme in time discretization. Numerical stability and the optimal error estimate in the L2 norm are proved for our proposed scheme. Extensive numerical results are presented to confirm the theoretical analysis and applications of our scheme to model many interesting phenomena happened when wave propagates in the Lorentz metamaterials. Examples include the convergence effect happened in the concave lenses formed by the negative refraction index metamatrials, and total reflection and total transmission observed in the zero index metamaterials. © 2015, Springer Science+Business Media New York.

Keywords

Edge elements; Finite element method; Lorentz metamaterial model; Maxwell’s equations; Total reflection; Total transmission

Language

English

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