[Préconditionnements analytiques en paramètres et applications aux méthodes de collocation réduites]
On étend dans cette note la méthode de collocation réduite récemment introduite dans [3] au cas non linéaire et on propose deux stratégies de préconditionnement dont une est indépendante des paramètres et facile a mettre en oeuvre et l'autre possède la propriété classique de décomposition affine en les paramètres qui permet une mise en oeuvre rapide en ligne/hors ligne. Ces stratégies améliorent la qualité de l'approximation et la vitesse de convergence.
In this paper, we extend the recently developed reduced collocation method [3] to the nonlinear case, and propose two analytical preconditioning strategies. One is parameter independent and easy to implement, the other one has the traditional affinity with respect to the parameters, which allows an efficient implementation through an offline–online decomposition. Overall, preconditioning improves the quality of the error estimation uniformly on the parameter domain, and speeds up the convergence of the reduced solution to the truth approximation.
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@article{CRMATH_2014__352_7-8_661_0,
author = {Chen, Yanlai and Gottlieb, Sigal and Maday, Yvon},
title = {Parametric analytical preconditioning and its applications to the reduced collocation methods},
journal = {Comptes Rendus. Math\'ematique},
pages = {661--666},
publisher = {Elsevier},
volume = {352},
number = {7-8},
year = {2014},
doi = {10.1016/j.crma.2014.06.001},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.06.001/}
}
TY - JOUR AU - Chen, Yanlai AU - Gottlieb, Sigal AU - Maday, Yvon TI - Parametric analytical preconditioning and its applications to the reduced collocation methods JO - Comptes Rendus. Mathématique PY - 2014 SP - 661 EP - 666 VL - 352 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.06.001/ DO - 10.1016/j.crma.2014.06.001 LA - en ID - CRMATH_2014__352_7-8_661_0 ER -
%0 Journal Article %A Chen, Yanlai %A Gottlieb, Sigal %A Maday, Yvon %T Parametric analytical preconditioning and its applications to the reduced collocation methods %J Comptes Rendus. Mathématique %D 2014 %P 661-666 %V 352 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.06.001/ %R 10.1016/j.crma.2014.06.001 %G en %F CRMATH_2014__352_7-8_661_0
Chen, Yanlai; Gottlieb, Sigal; Maday, Yvon. Parametric analytical preconditioning and its applications to the reduced collocation methods. Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 661-666. doi : 10.1016/j.crma.2014.06.001. http://www.numdam.org/articles/10.1016/j.crma.2014.06.001/
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