Nodal Discontinuous Galerkin Methods For Time-domain Cloak Model

In this paper,two different types of time-domain cloak model are discussed.Under nodal discontinuous Galerkin method and Leap-frog time discretization method,the numerical simulation results are obtained and the governing equations is wellposed analyzed.In this paper,the nodal discontinuous Galerkin method for two-dimensional elliptical cloak model and carpet cloak model is studied.We first establish mathematical models according to the electromagnetism,and then derive the governing equations of time-domain elliptical cloaks model and time-domain carpet cloak model.On this basis,we analyse the well-posedness of the model for the governing equation,and a concise stability analysis is given.Then,according to the governing equation,we use the nodal discontinuous Galerkin method in space,and the leap-frog scheme in time discretization.Similarly,the discrete schemes of the same method are established for PML in of the solution regions.Finally,for the established discrete format,the relevant algorithm is realized by Matlab,and several numerical experiments are carried out to compare.According to the final numerical test results,we can intuitively observe how the electromagnetic wave propagates in the physical region,and finally we obtain the cloak effect of the material,and verify the correctness and effectiveness of the mathematical theory and numerical scheme.