Numerical Study of the Plasma-Lorentz Model in Metamaterials

Authors:
Jichun Li;Yunqing Huang;Wei Yang
Affiliations:
Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, USA 89154-4020;Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, China 411105;Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, China 411105
Venue:
Journal of Scientific Computing
Year:
2013

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Abstract

Since 2000, the study of metamaterial has been a very hot topic due to its potential applications in many areas such as design of invisibility cloak and sub-wavelength imaging. Although several metamaterial models are often used by physicists and engineers, the study of their mathematical properties has lagged behind. In this paper, we initiate our investigation in the plasma-Lorentz model. More specifically, we first discuss the well-posedness of this model, then develop two fully-discrete finite element methods for solving it. Detailed stability and error analysis are carried out, and 3-D numerical results justifying our theoretical analysis are presented.