The PML method to solve a class of potential scattering problem with tapered wave incidence

This paper concerns about the two-dimensional direct scattering problem for Schrödinger equation with a class of decaying potential under the tapered wave incidence. We focus on the numerical solution of the problem by using the perfectly matched layer (PML) method. Based on the idea of complex coordinate stretching, the boundary value problem for the PML equation is formulated. Then the variational equation to the boundary value problem is proved to exist a unique solution except possibly for a set of values of wavenumber. The numerical experiments illustrate the influence of the thickness of PML layer, the absorption parameter, the wavenumber, the control bandwidth and even the incidence angle of the tapered wave on the effectiveness of this method.