Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions

Arnold, Anton; Negulescu, Claudia

doi:10.1007/s00211-017-0913-7

Record link:

https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:3-4336
http://hdl.handle.net/20.500.12708/940

Title:

Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions

Citation:

Arnold, A., & Negulescu, C. (2018). Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions. Numerische Mathematik. https://doi.org/10.1007/s00211-017-0913-7

Publisher DOI:

10.1007/s00211-017-0913-7

CatalogPlus:

AC15188651

Publication Type:

Article - Original Research Article

Language:

English

Authors:

Arnold, Anton
Negulescu, Claudia

Organisational Unit:

E101 - Institut für Analysis und Scientific Computing

Journal:

Numerische Mathematik

ISSN:

0029-599X

Date (published):

Feb-2018

Publisher:

Springer

Peer reviewed:

Yes

Abstract:

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.

License:

CC BY 4.0