Publications in Scientific Journals:
A. Arnold, C. Negulescu:
"Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions";
Numerische Mathematik,
138
(2018),
2;
501
- 536.
English 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.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1007/s00211-017-0913-7
Created from the Publication Database of the Vienna University of Technology.