<div class="csl-bib-body">
<div class="csl-entry">Arnold, A., & Negulescu, C. (2018). Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions. <i>Numerische Mathematik</i>. https://doi.org/10.1007/s00211-017-0913-7</div>
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This paper is concerned with a 1D Schrödinger scattering problem involving both oscillatory and evanescent regimes, separated by jump discontinuities in the potential function, to avoid “turning points”. We derive a non-overlapping domain decomposition method to split the original problem into sub-problems on these regions, both for the continuous and afterwards for the discrete problem. Further, a hybrid WKB-based numerical method is designed for its efficient and accurate solution in the semi-classical limit: a WKB-marching method for the oscillatory regions and a FEM with WKB-basis functions in the evanescent regions. We provide a complete error analysis of this hybrid method and illustrate our convergence results by numerical tests.
en
dc.language
English
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dc.language.iso
en
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dc.publisher
Springer
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dc.relation.ispartof
Numerische Mathematik
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.title
Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions
en
dc.type
Article
en
dc.type
Artikel
de
dc.rights.license
Creative Commons Namensnennung 4.0 International
de
dc.rights.license
Creative Commons Attribution 4.0 International
en
dc.contributor.affiliation
Université de Toulouse, France
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dcterms.dateSubmitted
2016-06-06
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dc.rights.holder
The Author(s) 2017
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dc.type.category
Original Research Article
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tuw.journal.peerreviewed
true
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tuw.peerreviewed
true
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tuw.version
vor
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wb.publication.intCoWork
International Co-publication
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dcterms.isPartOf.title
Numerische Mathematik
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tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing