Commun. Comput. Phys., 8 (2010), pp. 823-834.

Finite-Element Analysis of Three-Dimensional Axisymmetrical Invisibility Cloaks and Other Metamaterial Devices

Yong Bo Zhai 1, Xue Wei Ping 1, Wei Xiang Jiang 1, Tie Jun Cui 1*

1 State Key Laboratory of Millimeter Waves and the Institute of Target Characteristics and Identification, Department of Radio Engineering, Southeast University, Nanjing 210096, China.

Received 9 October 2009; Accepted (in revised version) 8 February 2010
Available online 17 May 2010


Accurate simulations of metamaterial devices are very important in the analysis of their electromagnetic properties. However, it is very difficult to make full-wave simulations of three-dimensional (3D) metamaterial devices due to the huge memory requirements and long computing time. In this paper, we present an efficient finite-element method (FEM) to analyze 3D axisymmetric electromagnetic devices designed by the transformation-optics approach, such as invisibility cloaks and concentrators. In the proposed method, we use the edge-based vector basis functions to expand the transverse field components, and the node-based scalar basis functions to expand the angular component. The FEM mesh is truncated with a cylindrical perfectly matched layer. We have applied the method to investigate the scattering from spherical and ellipsoidal invisibility cloaks and circularly cylindrical concentrators, in which the permittivity and permeability are both inhomogeneous and anisotropic. Numerical results are presented to show the validity and efficiency of the method.

AMS subject classifications: 52B10, 65D18, 68U05, 68U07

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Key words: Finite-element method, axisymmetrical scatterer, metamaterial devices.

*Corresponding author.
Email: (Y. B. Zhai), (X. W. Ping), (W. X. Jiang), (T. J. Cui)

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