Solving metamaterial Maxwell's equations via a vector wave integro-differential equation

Authors:
Yunqing Huang;Jichun Li;Wei Yang
Affiliations:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, China;Department of Mathematical Sciences, University of Nevada Las Vegas, NV 89154-4020, USA;Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, China
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

In this paper, we discuss the time-domain metamaterial Maxwell's equations. One major contribution of this paper is that after some effort we find that the metamaterial Maxwell's equations can be beautifully reduced to a vector wave integro-differential equation involving just one unknown, which is quite similar to that obtained from the standard Maxwell's equations in vacuum. Then we study the existence and uniqueness of this new modeling equations, and propose a fully-discrete finite element method to solve this model. Numerical results justifying our analysis are presented. This discovery shall make simulation of metamaterials much more efficient than the previous works.