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W. Auzinger, H. Hofstätter, O. Koch, K. Kropielnicka, P. Singh:
"Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime";
Talk: ParNum 2019, Dubrovnik; 2019-10-28 - 2019-10-30.

Time dependent Schrödinger equations with conservative force eld commonly
constitute a major challenge in the numerical approximation, especially when
they are analysed in the semiclassical regime. Extremely high oscillations originate
from the semiclassical parameter, and call for appropriate methods. We propose
to employ a combination of asymptotic Zassenhaus splitting with time adaptivity.
While the former turns the disadvantage of the semiclassical parameter into an
advantage, leading to highly e cient methods with low error constants, the latter
enables to choose an optimal time step and to speed up the calculations when the
oscillations subside. We support the results with numerical examples.