Finite element simulation of three dimensional cloaks

Abstract

The investigation of scattering characteristics of complex electromagnetic (EM) problems are of great interest in the computational electromagnetics domain in the past decades due to their extensive applications. Complex electromagnetic (EM) problems include electriclarge or complicated electromagnetic structures and complex materials, such as cloaks, perfect lens, ferrites and meta materials, etc‥ For the first case, the problem can be solved efficiently with the method of moment (MoM)-based techniques, such as the multilevel fast multipole algorithm (MLFMA), the conjugate gradient method and fast Fourier transform (CG-FFT) if only the perfectly electrical conducting (PEC) objects or homogeneous dielectric objects are included in the scattering objects. While for the second case, the MoM-based methods are not so powerful. For problems containing complex media, the finite element method and the finite-difference time-domain (FDTD) method are the most suitable methods. In this paper, the three-dimensional (3D) tangential vector finite element method (TVFEM) is investigated to simulate the scattering characteristics of complex materials. In our investigation, the scattering objects are illuminated by the plane wave. The control equation to be solved is selected to be the three-dimensional electric wave equation. The computation domain is truncated with perfectly matched layers and is discretized with tetrahedrons. In each tetrahedron, the involved integration is computed with Gauss integration to form the FEM linear system. The generated linear system is solved with the preconditioned Krylov subspace method. In the final, an elliptical cloak is designed and analyzed with the finite element method. The efficiency and accuracy of the method is investigated and compared, which showed that the three-dimensional tangential vector finite element method is rather accurate in simulating complex electromagnetic problems containing anisotropic materials.