Nodal Discontinuous Galerkin Method For Maxwell's Equations In Transverse Magnetic Field And Perfectly Matched Layers

In this paper, we mainly use a nodal discontinuous Galerkin method (NDG) for solving the two-dimensional time-dependent Maxwell's equations in transverse magnetic field and perfectly matched layers control model.First of all, this paper analyzes stability the problem. Our fully discrete schemes uses the k order discontinuous piecewise polynomial in space, and the leap-frog scheme in time discretization. We also proved the stability of the fully dis-crete schemes under the condition of CFL, and proved in the L2 under norm have O(h~k+?~2) order of convergence.All in all, this paper select the base functions with k=1 and k=2, numerical results are presented to demonstrate that the correctness of the theory and method is efficient.