DG-method For Maxwell Equation In Double Negative Media

Double negative media can be generally defined as a class of "artificial" media, which cannot be found in natural ones. Since the permittivity and permeability of this material are both negative real values.it is also called as double-negative materials. When electromagnetic wave in double negative material, its refractive index is negative. Therefore this material is also known as negative index materials. When Electromagnetic wave propagates in it, the wave vector k, the electric field E and the magnetic field H satisfy the so called ’The Left Hand’s Law".Hence is sometimes called as "Left-handed materials" It has the negative refractive index, ideal image, the inverse Doppler effect. the anti-Cerenkov radiation and other exotic physical properties. Hence the Left-handed materials have a very great prospect.The main purpose of this paper is to chrestigate discontinuous Galerkin (DG) methods for Maxwell equation in double negative media. Inspired by [32] and [33]. both semi-discrete numerical scheme and space-time numerical scheme are proposed for solving Maxwell equations in double negative media. In our work, both lossy Drude polarization and magnetization models and Lorenz model are considered.A semi-discrete scheme is used to solve Maxwell equations in Double neg-ative media.We prove that this scheme is stable, and has a convergence rate of order O(hk+1/2). Numerical results in2-D and3-D are provided to validate the theoretical prediction.Besides,we also investigate a fully-discrete scheme to solve Maxwell equa-tion in double negative media. We prove that this scheme is stable,and have a convergence rate of order O(hk+1/2+τr+1). An ultra-convergence of order O(τ2r+1) in time step is observed for the numerical fluxes.