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,
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.