[Méthodes FETI dual-primal pour approximations aux éléments finis d'arête en dimension trois.]
Nous considérons des algorithmes FETI pour des approximations en éléments finis d'arête en dimension trois. Nous montrons d'abord qu'il existe un couplage fort entre les degrés de liberté tangentiels associés aux arêtes et aux faces des sous-domaines. Nous proposons ensuite un algorithme FETI dual-primal qui utilise un changement de base et un choix particulier pour le solveur grossier. Nous donnons une borne logarithmique pour le nombre de conditionnement de l'algorithme. Les tests numériques confirment cette borne et la nécessité du changement de base.
We consider domain decomposition algorithms of FETI type for edge element approximations in three dimensions. We first show that a strong coupling exists between tangential degrees of freedom associated to the subdomain edges and faces. We then propose a dual-primal FETI algorithm that relies on a change of basis and on a suitable choice of a coarse space. We give a logarithmic bound for the condition number of the resulting preconditioned operator. Numerical results confirm this bound and the necessity of performing a change of basis.
Accepté le :
Publié le :
@article{CRMATH_2004__339_9_673_0,
author = {Toselli, Andrea},
title = {Domain decomposition methods of dual-primal {FETI} type for edge element approximations in three dimensions},
journal = {Comptes Rendus. Math\'ematique},
pages = {673--678},
publisher = {Elsevier},
volume = {339},
number = {9},
year = {2004},
doi = {10.1016/j.crma.2004.09.021},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.09.021/}
}
TY - JOUR AU - Toselli, Andrea TI - Domain decomposition methods of dual-primal FETI type for edge element approximations in three dimensions JO - Comptes Rendus. Mathématique PY - 2004 SP - 673 EP - 678 VL - 339 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.09.021/ DO - 10.1016/j.crma.2004.09.021 LA - en ID - CRMATH_2004__339_9_673_0 ER -
%0 Journal Article %A Toselli, Andrea %T Domain decomposition methods of dual-primal FETI type for edge element approximations in three dimensions %J Comptes Rendus. Mathématique %D 2004 %P 673-678 %V 339 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.09.021/ %R 10.1016/j.crma.2004.09.021 %G en %F CRMATH_2004__339_9_673_0
Toselli, Andrea. Domain decomposition methods of dual-primal FETI type for edge element approximations in three dimensions. Comptes Rendus. Mathématique, Tome 339 (2004) no. 9, pp. 673-678. doi : 10.1016/j.crma.2004.09.021. http://www.numdam.org/articles/10.1016/j.crma.2004.09.021/
[1] Salinas: A scalable software for high-performance structural and solid mechanics simulations, Proceedings of the IEEE/ACM SC2002 Conference, Baltimore, MD, November 16–22, 2002
[2] Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions, SIAM J. Numer. Anal., Volume 31 (1994) no. 6, pp. 1662-1694
[3] FETI-DP: a dual-primal unified FETI method. I. A faster alternative to the two-level FETI method, Int. J. Numer. Methods Engrg., Volume 50 (2001) no. 7, pp. 1523-1544
[4] Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients, SIAM J. Numer. Anal., Volume 40 (2002) no. 1, pp. 159-179
[5] Finite Element Methods for Maxwell's Equations, Numerical Mathematics and Scientific Computation, The Clarendon Press, Oxford University Press, New York, 2003
[6] Mixed finite elements in , Numer. Math., Volume 35 (1980), pp. 315-341
[7] A. Toselli, X. Vasseur, Dual-primal FETI algorithms for edge element approximations: two-dimensional h and p finite elements on shape-regular meshes, Tech. Report 04-01, Seminar for Applied Mathematics, ETH Zürich, 2004, SIAM J. Numer. Anal., in press
Cité par Sources :
