New Methods For The Study Of Electromagnetic Field In Metamaterials

In this paper, nonconforming mixed finite element method is proposed to simu-late a perfectly matched layer model for the three-dimensional time-dependent Maxwell’s equations. First of all, we give the basic introduction of the model. Then we have a semi-discrete and full discrete error estimation to the model. The error estimate of the semi-discrete scheme is given by convergence order O(ha) and the Crank-Nicolson full dis-crete scheme is also presented with O(T3/2+ha). Finally, the numerical simulation of the PML phenomenon is given and the results are very good.Nodal discontinuous Galerkin method is presented to approximate the time-domain Lorentz model equations in meta-materials. The upwind flux is chosen in spatial discrete scheme. Low-storage five-stage fourth-order explicit Runge-Kutta method is employed in time discrete scheme. An error estimate of accuracy O(T4+hσ-1) is proved under the L2-norm, where σ= min(N+1,p). Numerical experiments for transverse electric case and transverse magnetic case are demonstrated to verify the stability and the efficiency of the method in lower and higher wave frequency.