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2008, Volume 1, Issue 1: 101-125. Doi: 10.3934/krm.2008.1.101
This issue Previous Article Self-averaging of kinetic models for waves in random media Next Article Fast-reaction limit for the inhomogeneous Aizenman-Bak model

Discrete transparent boundary conditions for the Schrodinger equation -- a compact higher order scheme

  • 1.

    Institut für Angewandte und Numerische Mathematik, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, 48149 Münster

  • 2.

    Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstr. 8, 1040 Wien

Received:  September 2007
Revised:  October 2007
Published:  March 2008
Abstract / Introduction Related Papers Cited by
    Abstract
  • We consider the two-dimensional time-dependent Schrödinger equation with the new compact nine-point scheme in space and the Crank-Nicolson difference scheme in time. For the resulting difference equation we derive discrete transparent boundary conditions in order to get highly accurate solutions for open boundary problems. Numerical experiments illustrate the perfect absorption of outgoing wave independently of their impact angle at the boundary. Finally, we apply inhomogeneous discrete transparent boundary conditions to the transient simulation of quantum waveguides.
    Mathematics Subject Classification: Primary: 65M06, 65M12; Secondary: 35Q40.

    Citation:
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