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Coupling of Gaussian Beam and Finite Difference Solvers for Semiclassical Schrodinger Equations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, Centres, SeRC - Swedish e-Science Research Centre.ORCID iD: 0000-0002-6321-8619
2015 (English)In: Advances in Applied Mathematics and Mechanics, ISSN 2070-0733, E-ISSN 2075-1354, Vol. 7, no 6, 687-714 p.Article in journal (Refereed) Published
Abstract [en]

In the semiclassical regime, solutions to the time-dependent Schrodinger equation for molecular dynamics are highly oscillatory. The number of grid points required for resolving the oscillations may become very large even for simple model problems, making solution on a grid intractable. Asymptotic methods like Gaussian beams can resolve the oscillations with little effort and yield good approximations when the atomic nuclei are heavy and the potential is smooth. However, when the potential has variations on a small length-scale, quantum phenomena become important. Then asymptotic methods are less accurate. The two classes of methods perform well in different parameter regimes. This opens for hybrid methods, using Gaussian beams where we can and finite differences where we have to. We propose a new method for treating the coupling between the finite difference method and Gaussian beams. The new method reduces the needed amount of overlap regions considerably compared to previous methods, which improves the efficiency.

Place, publisher, year, edition, pages
[Kieri, Emil; Kreiss, Gunilla] Uppsala Univ, Dept Informat Technol, Div Comp Sci, Uppsala, Sweden. [Runborg, Olof] KTH, Dept Math, Uppsala, Sweden. [Runborg, Olof] KTH, SeRC, Uppsala, Sweden., 2015. Vol. 7, no 6, 687-714 p.
Keyword [en]
Gaussian beams, semiclassical Schrodinger equation, hybrid methods
National Category
URN: urn:nbn:se:kth:diva-174200DOI: 10.4208/aamm.2013.m411ISI: 000361055400001ScopusID: 2-s2.0-84960871763OAI: diva2:860939

QC 20151014

Available from: 2015-10-14 Created: 2015-10-02 Last updated: 2015-10-14Bibliographically approved

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Runborg, Olof
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Numerical Analysis, NASeRC - Swedish e-Science Research Centre
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