Study Of Numerical Calculation Of Time Harmonic Scattering Problem

In this paper, we mainly study the numerical calculation method of the scattering problem, including the time harmonic acoustic scattering problem and the scattering problem of the double layer medium. In this paper, an optimization method for the perfect matched layer(PML) is presented, and the convergence of the PML method is analyzed.In this paper, first the use of acoustic wave and electromagnetic wave scattering problems, basic definition and development status at home and abroad to give brief introduction; secondly for acoustic time harmonic scattering problems, to construct an optimal PML method and algorithm gives the well posedness and Convergence: the third, the double-layer dielectric scattering problems, given the when the wave number for the piecewise constant when a numerical calculation method, namely uniaxial optimal PML method, and discusses the convergence of the algorithm.In the acoustic harmonic scattering problems of optimization of the perfect matching layer(PML) method, the introduction of a with a small parameter of the absorption function, not only makes the scattering problem of numerical calculation does not rely on the PML layer thickness, and to the problem of the convergence analysis of convenience. It is proved that as long as is sufficiently small, the optimal PML solution of exponential convergence to the solution of sub problems.In the solution of double-layer dielectric scattering problems optimal perfectly matched layer(PML) method. We also in the absorption function is introduced in a small parameter. And it is proved that the as long as the parameters are small enough, the optimal PML solution of exponential convergence to the solution of the original double-layer dielectric scattering problems.