Non-reflecting boundary conditions for the two-dimensional Schrodinger equation

Non-reflecting boundary conditions are introduced for the two-dimensional Fresnel/Schrodinger equation. These are nonlocal in time and in space. Time discretization is done by the trapezoidal rule in the interior and by convolution quadrature on the boundary. A convergence estimate is given for the semidiscretization. Space discretization is done using the finite element method and coupling the boundary conditions by collocation. A numerical example is given. (C) 2002 Elsevier Science B.V. All rights reserved.