[Nouvelles constructions de méthodes de décomposition de domaine pour des systèmes d'équations aux dérivées partielles]
Nous proposons de nouvelles méthodes de décomposition de domaine pour des systèmes d'équations aux dérivées partielles en dimensions 2 et 3. Elles sont obtenues à l'aide de la factorisation de Smith. Des résultats numériques illustrent l'approche.
We propose new domain decomposition methods for systems of partial differential equations in two and three dimensions. The algorithms are derived with the help of the Smith factorization. This could also be validated by numerical experiments.
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@article{CRMATH_2005__340_9_693_0,
author = {Dolean, Victorita and Nataf, Fr\'ed\'eric and Rapin, Gerd},
title = {New constructions of domain decomposition methods for systems of {PDEs}},
journal = {Comptes Rendus. Math\'ematique},
pages = {693--696},
publisher = {Elsevier},
volume = {340},
number = {9},
year = {2005},
doi = {10.1016/j.crma.2005.03.026},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.03.026/}
}
TY - JOUR AU - Dolean, Victorita AU - Nataf, Frédéric AU - Rapin, Gerd TI - New constructions of domain decomposition methods for systems of PDEs JO - Comptes Rendus. Mathématique PY - 2005 SP - 693 EP - 696 VL - 340 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.03.026/ DO - 10.1016/j.crma.2005.03.026 LA - en ID - CRMATH_2005__340_9_693_0 ER -
%0 Journal Article %A Dolean, Victorita %A Nataf, Frédéric %A Rapin, Gerd %T New constructions of domain decomposition methods for systems of PDEs %J Comptes Rendus. Mathématique %D 2005 %P 693-696 %V 340 %N 9 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.03.026/ %R 10.1016/j.crma.2005.03.026 %G en %F CRMATH_2005__340_9_693_0
Dolean, Victorita; Nataf, Frédéric; Rapin, Gerd. New constructions of domain decomposition methods for systems of PDEs. Comptes Rendus. Mathématique, Tome 340 (2005) no. 9, pp. 693-696. doi : 10.1016/j.crma.2005.03.026. http://archive.numdam.org/articles/10.1016/j.crma.2005.03.026/
[1] Proceedings of the 15th International Domain Decomposition Conference, 2003
[2] A robin–robin preconditioner for an advection–diffusion problem, C. R. Acad. Sci. Paris, Ser. I, Volume 325 (1997), pp. 1211-1216
[3] A domain decomposition preconditioner for an advection–diffusion problem, Comput. Methods Appl. Mech. Engrg., Volume 184 (2000), pp. 145-170
[4] Variational formulation and algorithm for trace operator in domain decomposition calculations (Chan, T.; Glowinski, R.; Périaux, J.; Widlund, O., eds.), Domain Decomposition Methods, SIAM, Philadelphia, PA, 1989, pp. 3-16
[5] V. Dolean, F. Nataf, A new domain decomposition method for the compressible Euler equations, Technical report, CMAP, CNRS UMR 7641, Ecole Polytechnique, 2005. http://www.cmap.polytechnique.fr/preprint/repository/567.pdf, http://hal.ccsd.cnrs.fr/ccsd-00004319, submitted for publication
[6] F. Nataf, A new construction of perfectly matched layers for the linearized Euler equations, http://www.cmap.polytechnique.fr/preprint/repository/566.pdf, http://hal.ccsd.cnrs.fr/ccsd-00004155, submitted for publication
[7] F. Nataf, G. Rapin, A new domain decomposition method for the Stokes and Oseen systems, submitted for publication
[8] Balancing Neumann–Neumann methods for incompressible stokes equations, Comm. Pure Appl. Math., Volume 55 (2002), pp. 302-335
[9] Non-overlapping domain decomposition methods for adaptive hp approximations of the Stokes problem with discontinuous pressure fields, Comput. Methods Appl. Mech Engrg., Volume 145 (1997), pp. 361-379
[10] Boundary Value Problems for Elliptic Systems, Cambridge University Press, Cambridge, 1995
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