Contributions to Books:

A. Arnold, C. Negulescu:
"Stationary Schrödinger equation in the semiclassical limit: Numerical coupling of oscillatory and evanscent regions";
in: "ASC Report 12/2016", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2016, ISBN: 978-3-902627-09-4, 1 - 32.

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 effcient 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.

Schrödinger equation, highly oscillating wave functions, evanescent wave functions, higher order WKB-approximation, domain decomposition method, numerical analysis, stiffness-independent error estimates, asymptotic analysis, tunnelling structures.

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.