Contributions to Books:
A. Arnold, M. Ehrhardt, M. Schulte, I. Sofronov:
"Discrete transparent boundary conditions for the Schrödinger equation on circular domains";
in: "ASC Report 31/2008",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
We propose transparent boundary conditions (TBCs) for the time-
dependent Schršodinger equation on a circular computational domain.
First we derive the two-dimensional discrete TBCs in conjunction with
a conservative Crank-Nicolson finite difference scheme. The presented
discrete initial boundary-value problem is unconditionally stable and
completely reflection-free at the boundary. Then, since the discrete
TBCs for the Schršodinger equation with a spatially dependent potential
include a convolution w.r.t. time with a weakly decaying kernel, we
construct approximate discrete TBCs with a kernel having the form of
a finite sum of exponentials, which can be efficiently evaluated by recursion.
In numerical tests we finally illustrate the accuracy, stability,
and efficiency of the proposed method.
two-dimensional Schršodinger equation, transparent boundary
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.