Title: Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions
Language: English
Authors: Arnold, Anton 
Negulescu, Claudia 
Category: Research Article
Issue Date: 2018
Journal: Numerische Mathematik
ISSN: 0945-3245
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.
DOI: 10.1007/s00211-017-0913-7
Library ID: AC15188651
URN: urn:nbn:at:at-ubtuw:3-4336
Organisation: E101 - Institut für Analysis und Scientific Computing 
Publication Type: Article
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