Integrators for highly oscillatory Hamiltonian systems: an homogenization approach

Claude Le Bris 1 Frédéric Legoll 1, 2
1 MICMAC - Methods and engineering of multiscale computing from atom to continuum
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
2 Multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes
NAVIER UMR 8205 - Laboratoire Navier
Abstract : We introduce a systematic way to construct symplectic schemes for the numerical integration of a large class of highly oscillatory Hamiltonian systems. The bottom line of our construction is to consider the Hamilton-Jacobi form of the Newton equations of motion, and to perform a two-scale expansion of the solution, for small times and high frequencies. The approximation obtained for the solution is then used as a generating function, from which the numerical scheme is derived. Several options for the derivation are presented, some of them also giving rise to non symplectic variants. The various integrators obtained are tested and compared to several existing algorithms. The numerical results demonstrate their efficiency.
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Article dans une revue
Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2010, 13 (2), pp.347-373
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https://hal.inria.fr/inria-00165293
Contributeur : Frederic Legoll <>
Soumis le : lundi 30 juillet 2007 - 21:17:20
Dernière modification le : vendredi 25 mai 2018 - 12:02:03
Document(s) archivé(s) le : mardi 21 septembre 2010 - 13:42:44

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Claude Le Bris, Frédéric Legoll. Integrators for highly oscillatory Hamiltonian systems: an homogenization approach. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2010, 13 (2), pp.347-373. 〈inria-00165293v2〉

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