Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties

Philippe Chartier 1, 2, * Norbert J. Mauser 3 Florian Méhats 1, 2 Yong Zhang 3
* Auteur correspondant
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : In this paper, we present the Stroboscopic Averaging Method (SAM), recently introduced in [7,8,10,12], which aims at numerically solving highly-oscillatory differential equations. More specifically, we first apply SAM to the Schrödinger equation on the 1-dimensional torus and on the real line with harmonic potential, with the aim of assessing its efficiency: as compared to the well-established standard splitting schemes, the stiffer the problem is, the larger the speed-up grows (up to a factor 100 in our tests). The geometric properties of SAM are also explored: on very long time intervals, symmetric implementations of the method show a very good preservation of the mass invariant and of the energy. In a second series of experiments on 2-dimensional equations, we demonstrate the ability of SAM to capture qualitatively the long-time evolution of the solution (without spurring high oscillations).
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Article dans une revue
Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2016, 9 (5), pp.1327-1349. 〈10.3934/dcdss.2016053〉
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https://hal.archives-ouvertes.fr/hal-00850513
Contributeur : Florian Méhats <>
Soumis le : mercredi 7 août 2013 - 09:16:08
Dernière modification le : jeudi 7 février 2019 - 17:34:23

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Philippe Chartier, Norbert J. Mauser, Florian Méhats, Yong Zhang. Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties. Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2016, 9 (5), pp.1327-1349. 〈10.3934/dcdss.2016053〉. 〈hal-00850513〉

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