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Titel
Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions
Verfasser / Verfasserin Arnold, Anton ; Negulescu, Claudia
Erschienen in
Numerische Mathematik, 2018, Jg. 138, H. 2, S. 501-536
ErschienenSpringer Berlin Heidelberg, 2018
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
ISSN0945-3245
URNurn:nbn:at:at-ubtuw:3-4336 Persistent Identifier (URN)
DOI10.1007/s00211-017-0913-7 
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Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions [0.88 mb]
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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.

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