Absorbing Boundary conditions using Titchmarsh-Weyl theory joint work with C. Zheng, Tsinghua University, Beijing, China

Summary

A new approach for simulating the solution of the time-dependent Schrödinger equation with a general variable potential will be proposed. The key idea is to approximate the Titchmarsh-Weyl m-function (exact Dirichlet-to-Neumann operator) by a rational function with respect to the spectral parameter. With the proposed method we can overcome the usual high-frequency restriction for absorbing boundary conditions of general variable potential problems. We end up with a fast computational algorithm for absorbing boundary conditions that are accurate for the full frequency band.

Application Partners

References

1. X. Antoine, A. Arnold, C. Besse, M. Ehrhardt and A. Schädle, A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations, Commun. Comput. Phys. 4 (2008), 729-796. (open-access article)
   supplementary material (Matlab codes):
   • MATLAB GUI
   • Talks from the ICIAM07 Minisymposium
2. M. Ehrhardt and C. Zheng, Implementing exact absorbing boundary condition for the linear one-dimensional Schrödinger problem with variable potential by Titchmarsh-Weyl theory, WIAS Preprint No. 1426, July 2009 (submitted to: Journal of Computational Physics)

ehrhardt@wias-berlin.de