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An Optimized Perfectly Matched Layer for the Schrödinger Equation

Published online by Cambridge University Press:  20 August 2015

Anna Nissen  and
Gunilla Kreiss
Anna Nissen*
Affiliation:
Department of Information Technology, Uppsala University, P.O. Box 337, SE-75105 Uppsala, Sweden
Gunilla Kreiss*
Affiliation:
Department of Information Technology, Uppsala University, P.O. Box 337, SE-75105 Uppsala, Sweden
*
Corresponding author.Email:anna.nissen@it.uu.se
Email:gunilla.kreiss@it.uu.se
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Abstract

We derive a perfectly matched layer (PML) for the Schrödinger 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.

Keywords

35B6535P2535Q4165M0665M15Schrödinger equationperfectly matched layer
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 1 , January 2011 , pp. 147 - 179
Copyright
Copyright © Global Science Press Limited 2011

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