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Journal of Scientific Computing

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28-11-2015

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

Authors: Wei Yang, Yunqing Huang, Jichun Li

Published in: Journal of Scientific Computing | Issue 2/2016

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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 \(L^2\) 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.

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Title: Developing a Time-Domain Finite Element Method for the Lorentz Metamaterial Model and Applications
Authors: Wei Yang
Yunqing Huang
Jichun Li
Publication date: 28-11-2015
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0144-y

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