Comptes Rendus
no. 9
Numerical Analysis/Partial Differential Equations
New constructions of domain decomposition methods for systems of PDEs
[Nouvelles constructions de méthodes de décomposition de domaine pour des systèmes d'équations aux dérivées partielles]

Présenté par : Roland Glowinski

Victorita Dolean1 ; Frédéric Nataf1 ; Gerd Rapin2
1 CMAP, CNRS, UMR 7641, École polytechnique, 91128 Palaiseau cedex, France
2 Mathematics Department, NAM, University of Göttingen, 37083, Germany
Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 693-696.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.03.026
Victorita Dolean 1 ; Frédéric Nataf 1 ; Gerd Rapin 2

1 CMAP, CNRS, UMR 7641, École polytechnique, 91128 Palaiseau cedex, France
2 Mathematics Department, NAM, University of Göttingen, 37083, Germany 
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     author = {Victorita Dolean and Fr\'ed\'eric Nataf and Gerd Rapin},
     title = {New constructions of domain decomposition methods for systems of {PDEs}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {693--696},
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     doi = {10.1016/j.crma.2005.03.026},
     language = {en},
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Victorita Dolean; Frédéric Nataf; Gerd Rapin. New constructions of domain decomposition methods for systems of PDEs. Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 693-696. doi : 10.1016/j.crma.2005.03.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.03.026/

[1] Proceedings of the 15th International Domain Decomposition Conference, 2003

[2] Y. Achdou; F. Nataf A robin–robin preconditioner for an advection–diffusion problem, C. R. Acad. Sci. Paris, Ser. I, Volume 325 (1997), pp. 1211-1216

[3] Y. Achdou; P. Le Tallec; F. Nataf; M. Vidrascu A domain decomposition preconditioner for an advection–diffusion problem, Comput. Methods Appl. Mech. Engrg., Volume 184 (2000), pp. 145-170

[4] J.-F. Bourgat; R. Glowinski; P. Le Tallec; M. Vidrascu Variational formulation and algorithm for trace operator in domain decomposition calculations (T. Chan; R. Glowinski; J. Périaux; O. Widlund, 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] L.F. Pavarino; O.B. Widlund Balancing Neumann–Neumann methods for incompressible stokes equations, Comm. Pure Appl. Math., Volume 55 (2002), pp. 302-335

[9] P. Le Tallec; A. Patra 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] J.T. Wloka; B. Rowley; B. Lawruk Boundary Value Problems for Elliptic Systems, Cambridge University Press, Cambridge, 1995

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