Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime

Winfried Auzinger, Harald Hofstätter, Othmar Koch, Karolina Kropielnicka, Pranav Singh

Research output: Contribution to journalArticle

Abstract

Time dependent Schrödinger equations with conservative force field 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 efficient 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.

Original languageEnglish
Article number124550
JournalApplied Mathematics and Computation
Volume362
Early online date9 Jul 2019
DOIs
Publication statusPublished - 1 Dec 2019

Keywords

  • Asymptotic splittings
  • Numerical time integration
  • Splitting schemes
  • Time adaptivity

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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