Absorbing boundary conditions for the two-dimensional schr?dinger equation with an exterior potential part I: Construction and a priori estimates

摘要

The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schr?dinger equation with a time and space varying exterior potential and for general convex smooth boundaries. The construction is based on asymptotics of the inhomogeneous pseudodifferential operators defining the related Dirichlet-to-Neumann operator. Furthermore, a priori estimates are developed for the truncated problems with various increasing order boundary conditions. The effective numerical approximation will be treated in a second paper.