On the accuracy of some absorbing boundary conditions for the Schrödinger equation

Abstract

A detailed analysis of absorbing boundary conditions for the linear Schrodinger equation is presented in this paper. It is focused on absorbing boundary conditions that are obtained by using rational functions to approximate the exact transparent boundary conditions. Different strategies are investigated for the optimal selection of the coefcients of these rational functions, including the Pade approximation, the L2 norm approximations of the Fourier symbol, L2 minimization of a reection coeficient, and two error minimization techniques for the chosen benchmark problems with known exact solutions. The results of computational experiments are given and a detailed comparison of the eficiency of these techniques is presented.