M. Ehrhardt (TU Berlin)

"A Review of Transparent and Artificial Boundary Conditions Techniques
for Linear and Nonlinear Schrödinger Equations"

(joint work with X. Antoine, A. Arnold, C. Besse, A. Schädle)

Abstract:

In this talk we discuss different techniques to solve numerically the
time-dependent Schrödinger equation on unbounded domains.
We present and compare several approaches to implement the classical
transparent boundary condition into finite difference and finite element discretizations. 
We present in detail the most recent approaches and describe briefly alternative ideas 
pointing out the relations between these works.

Finally, we conclude with several numerical examples from
different application areas to compare the presented techniques. 
We mainly focus on
the one-dimensional problem but also touch upon the situation in two space dimensions
and the cubic nonlinear case.

Reference:

   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. Vol. 4, Number 4, (2008), 729-796. (open-access article)
   http://www.global-sci.com/openaccess/v4_729.pdf