[Méthodes parallèles de directions simultanées pour des équations elliptiques et paraboliques.]
On utilise des méthodes parallèles de type directions simultanées pour résoudre des équations linéaires elliptiques et paraboliques du second ordre. On adapte quelques idées de Lu, Neittaanmäki and Tai, ce qui conduit à une (grande) famille de systèmes différentiels ordinaires qui sont indépendants. Quelques résultats de convergence et stabilité sont indiqués. On présente aussi quelques expériences numériques.
Adapting some previous ideas by Lu, Neittaanmäki and Tai, we use simultaneous directions methods to solve linear second-order elliptic and parabolic equations. The task is reduced to solving a (large) family of independent one-dimensional linear systems. We indicate some convergence results. We also present some numerical experiments.
Accepté le :
Publié le :
@article{CRMATH_2004__339_2_145_0,
author = {Galo, Jos\'e R. and Albarreal, Isidoro I. and Calzada, M. Carmen and Cruz, Jos\'e Luis and Fern\'andez-Cara, Enrique and Mar{\'\i}n, Mercedes},
title = {Simultaneous directions parallel methods for elliptic and parabolic systems},
journal = {Comptes Rendus. Math\'ematique},
pages = {145--150},
publisher = {Elsevier},
volume = {339},
number = {2},
year = {2004},
doi = {10.1016/j.crma.2004.05.007},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.05.007/}
}
TY - JOUR AU - Galo, José R. AU - Albarreal, Isidoro I. AU - Calzada, M. Carmen AU - Cruz, José Luis AU - Fernández-Cara, Enrique AU - Marín, Mercedes TI - Simultaneous directions parallel methods for elliptic and parabolic systems JO - Comptes Rendus. Mathématique PY - 2004 SP - 145 EP - 150 VL - 339 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.05.007/ DO - 10.1016/j.crma.2004.05.007 LA - en ID - CRMATH_2004__339_2_145_0 ER -
%0 Journal Article %A Galo, José R. %A Albarreal, Isidoro I. %A Calzada, M. Carmen %A Cruz, José Luis %A Fernández-Cara, Enrique %A Marín, Mercedes %T Simultaneous directions parallel methods for elliptic and parabolic systems %J Comptes Rendus. Mathématique %D 2004 %P 145-150 %V 339 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.05.007/ %R 10.1016/j.crma.2004.05.007 %G en %F CRMATH_2004__339_2_145_0
Galo, José R.; Albarreal, Isidoro I.; Calzada, M. Carmen; Cruz, José Luis; Fernández-Cara, Enrique; Marín, Mercedes. Simultaneous directions parallel methods for elliptic and parabolic systems. Comptes Rendus. Mathématique, Tome 339 (2004) no. 2, pp. 145-150. doi : 10.1016/j.crma.2004.05.007. http://www.numdam.org/articles/10.1016/j.crma.2004.05.007/
[1] Convergence analysis and error estimates for a parallel algorithm for solving the Navier–Stokes equations, Numer. Math., Volume 93 (2002), pp. 201-221
[2] J.R. Galo, PhD Thesis, Univ. de Sevilla, 2002
[3] J.R. Galo, I. Albarreal, M.C. Calzada, J.L. Cruz, E. Fernández-Cara, M. Marín, Convergence and optimization of the parallel method of simultaneous directions for the solution of elliptic problems, in press
[4] J.R. Galo, I. Albarreal, M.C. Calzada, J.L. Cruz, E. Fernández-Cara, M. Marín, Stability and convergence of a parallel fractional step method for the solution of linear parabolic problems, in press
[5] A parallel splitting-up method for partial differential equations and its applications to Navier–Stokes equations, RAIRO–Math. Model. Num., Volume 26 (1992) no. 6, pp. 673-708
[6] Splitting and alternating direction methods, Handbook of Numerical Analysis, I, North-Holland, 1990, pp. 197-462
Cité par Sources :
