Commun. Comput. Phys., 9 (2011), pp. 147-179.


An Optimized Perfectly Matched Layer for the Schrodinger Equation

Anna Nissen 1*, Gunilla Kreiss 1

1 Department of Information Technology, Uppsala University, P.O. Box 337,

Received 1 September 2009; Accepted (in revised version) 1 April 2010
Available online 5 August 2010
doi:10.4208/cicp.010909.010410a

Abstract

We derive a perfectly matched layer (PML) for the Schrodinger equation using a modal ansatz. We derive approximate error formulas for the modeling error from the outer boundary of the PML and the error from the discretization in the layer and show how to choose layer parameters so that these errors are matched and optimal performance of the PML is obtained. Numerical computations in 1D and 2D demonstrate that the optimized PML works efficiently at a prescribed accuracy for the zero potential case, with a layer of width less than a third of the de Broglie wavelength corresponding to the dominating frequency.

AMS subject classifications: 35B65, 35P25, 35Q41, 65M06, 65M15

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Key words: Schrodinger equation, perfectly matched layer.

*Corresponding author.
Email: anna.nissen@it.uu.se (A. Nissen), gunilla.kreiss@it.uu.se (G. Kreiss)
 

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