Research On The Calculation Method Of Perfectly Matched Layer In The Scattering Problem

In this paper, numerical calculation method is studied for the scattering problem, which includes the bounded scattering body and the unbounded scattering body. In this paper, we give a brief introduction on each part of knowledge and the corresponding optimization of the perfect matching layer (PML) method, and the correctness and validity of the optimized PML are illustrated by examples. The main contents of this paper are as follows:In the first chapter, the development status of the use of acoustic wave and electromagnetic wave, the basic definitions and the development status of domestic and abroad are introduced briefly. In the second chapter, for the scattering problem of diffraction grating problem, we give the variable separation of solutions in cylindrical coordinates. PML methods for the optimization satisfying Helmholtz equations for the scattering problem of are introduced. The mathematical model is given for the bounded scattering problem, and the optimization method of PML is introduced in this circumstance. At the end of this chapter, the PML method to optimize the time harmonic scattering problems is introduced. In the third chapter, for the bounded scattering problem, we get the convergence estimates, and give some theorems and their proofs of convergence. At the end of this chapter, some examples are illustrated and compared for the bounded scattering problem. Finally, we get the optimal results. In the fourth chapter, we first introduce the development of the unbounded scattering problem, and give a narrative for rough surface scattering problem. And we give some related theorems. An important condition-upward propagating radiation condition (UPRC) is specified and an important theorem-limiting absorption principle is given. In the last chapter of this thesis, we give a brief summary a brief summary.The paper uses the optimization PML method for the computation in scattering problem. The optimal PML method is:selects the PML medium parameters in the PML layer of the generalized integral of unbounded function. The chosen parameters can guarantee the PML calculation and the thickness of the PML layer are almost independent, and thus save the computation. And if we choose a small parameter for ε0, the PML layer can achieve enough good of the absorption effect. So, as long as we chose a small enough ε0, the accuracy of computation is not dependent on the thickness of the PML layer. For small thickness, the finite element mesh node is relatively small, and it can save the amount of calculation in a certain extent.