[Intégrateurs symplectiques pour des systèmes Hamiltoniens hautement oscillants avec fréquences rapides variables]
Nous dérivons des intégrateurs symplectiques pour une classe de systèmes Hamiltoniens hautement oscillants. L'approche est basée sur un développement à deux échelles de la solution de l'équation de Hamilton–Jacobi associée à la dynamique originale. Cette Note présente une extension des techniques précédemment introduites dans Le Bris et Legoll (2007, 2010) [10,11] au cas où les fréquences rapides du système ne sont plus constantes, mais dépendent des variables lentes.
We derive symplectic integrators for a class of highly oscillatory Hamiltonian systems. Our approach is based upon a two-scale expansion of the solution to the Hamilton–Jacobi equation associated to the original dynamics. This Note presents an extension of the approach previously introduced in Le Bris and Legoll (2007, 2010) [10,11] to the case where the fast frequencies of the system, instead of being constant, explicitly depend on the slow degrees of freedom.
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@article{CRMATH_2010__348_17-18_1033_0,
author = {Dobson, Matthew and Le Bris, Claude and Legoll, Fr\'ed\'eric},
title = {Symplectic schemes for highly oscillatory {Hamiltonian} systems with varying fast frequencies},
journal = {Comptes Rendus. Math\'ematique},
pages = {1033--1038},
publisher = {Elsevier},
volume = {348},
number = {17-18},
year = {2010},
doi = {10.1016/j.crma.2010.08.005},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.08.005/}
}
TY - JOUR AU - Dobson, Matthew AU - Le Bris, Claude AU - Legoll, Frédéric TI - Symplectic schemes for highly oscillatory Hamiltonian systems with varying fast frequencies JO - Comptes Rendus. Mathématique PY - 2010 SP - 1033 EP - 1038 VL - 348 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.08.005/ DO - 10.1016/j.crma.2010.08.005 LA - en ID - CRMATH_2010__348_17-18_1033_0 ER -
%0 Journal Article %A Dobson, Matthew %A Le Bris, Claude %A Legoll, Frédéric %T Symplectic schemes for highly oscillatory Hamiltonian systems with varying fast frequencies %J Comptes Rendus. Mathématique %D 2010 %P 1033-1038 %V 348 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.08.005/ %R 10.1016/j.crma.2010.08.005 %G en %F CRMATH_2010__348_17-18_1033_0
Dobson, Matthew; Le Bris, Claude; Legoll, Frédéric. Symplectic schemes for highly oscillatory Hamiltonian systems with varying fast frequencies. Comptes Rendus. Mathématique, Tome 348 (2010) no. 17-18, pp. 1033-1038. doi : 10.1016/j.crma.2010.08.005. http://www.numdam.org/articles/10.1016/j.crma.2010.08.005/
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☆ This work was supported in part by the NSF Mathematical Sciences Postdoctoral Research Fellowship, by the INRIA under the grant “Action de Recherche Collaborative” HYBRID, and by the Agence Nationale de la Recherche, under grant ANR-09-BLAN-0216-01 (MEGAS).
