Discontinuous Galerkin Discretizations And Analysis For The Cohen-Monk PML Model

In this thesis,we study the two-dimensional perfect matching layer(PML)model,which is reconstructed from the 3-D PML model established by Cohen and Monk in 1999.We propose a discontinuous Galerkin(DG)method for solving both two-dimensional transverse magnetic field(TMz)model and transverse electric field(TEz)model.Since the two-dimensional transverse electric field model can be obtained by the dual of the two-dimensional transverse magnetic field model,only the two-dimensional transverse magnetic field model is analyzed in this thesis.Firstly,the semi-discrete(spatial discrete)form of two-dimensional transverse magnetic field model is established,and the error analysis and stability analysis are carried out.Then,based on the semi-discrete(spatial discrete)model,the time discrete model is obtained,and its stability and error are analyzed.Finally,to illustrate the correctness and validity of the theory,this article has carried on the numerical experiments,numerical experiments were consists of two parts: the first part of the experiment using numerical solution and exact solution of the corresponding error and the rate of convergence and prove the validity of the theory,the second part of the experiment proves that the PML absorbing efficiency of the model,prove the validity of this method.