Dolean, Victorita; Nataf, Frédéric; Rapin, Gerd New constructions of domain decomposition methods for systems of PDEs. (English) Zbl 1071.65166 C. R., Math., Acad. Sci. Paris 340, No. 9, 693-696 (2005). Summary: We propose new domain decomposition methods for systems of partial differential equations (PDEs) in two and three dimensions. The algorithms are derived with the help of the Smith factorization. This could also be validated by numerical experiments. Cited in 5 Documents MSC: 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 35Q30 Navier-Stokes equations 76D07 Stokes and related (Oseen, etc.) flows 65F10 Iterative numerical methods for linear systems 65F35 Numerical computation of matrix norms, conditioning, scaling 76M25 Other numerical methods (fluid mechanics) (MSC2010) Keywords:Stokes system; preconditioning; domain decomposition methods; algorithms; Smith factorization; numerical experiments PDFBibTeX XMLCite \textit{V. Dolean} et al., C. R., Math., Acad. Sci. Paris 340, No. 9, 693--696 (2005; Zbl 1071.65166) Full Text: DOI arXiv References: [1] Proceedings of the 15th International Domain Decomposition Conference, 2003; Proceedings of the 15th International Domain Decomposition Conference, 2003 [2] Achdou, Y.; Nataf, F., A robin-robin preconditioner for an advection-diffusion problem, C. R. Acad. Sci. Paris, Ser. I, 325, 1211-1216 (1997) · Zbl 0893.65061 [3] Achdou, Y.; Le Tallec, P.; Nataf, F.; Vidrascu, M., A domain decomposition preconditioner for an advection-diffusion problem, Comput. Methods Appl. Mech. Engrg., 184, 145-170 (2000) · Zbl 0979.76043 [4] Bourgat, J.-F.; Glowinski, R.; Le Tallec, P.; Vidrascu, M., Variational formulation and algorithm for trace operator in domain decomposition calculations, (Chan, T.; Glowinski, R.; Périaux, J.; Widlund, O., Domain Decomposition Methods (1989), SIAM: SIAM Philadelphia, PA), 3-16 · Zbl 0684.65094 [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.pdfhttp://hal.ccsd.cnrs.fr/ccsd-00004319; 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.pdfhttp://hal.ccsd.cnrs.fr/ccsd-00004319 [6] F. Nataf, A new construction of perfectly matched layers for the linearized Euler equations, http://www.cmap.polytechnique.fr/preprint/repository/566.pdfhttp://hal.ccsd.cnrs.fr/ccsd-00004155; F. Nataf, A new construction of perfectly matched layers for the linearized Euler equations, http://www.cmap.polytechnique.fr/preprint/repository/566.pdfhttp://hal.ccsd.cnrs.fr/ccsd-00004155 · Zbl 1159.76365 [7] F. Nataf, G. Rapin, A new domain decomposition method for the Stokes and Oseen systems, submitted for publication; F. Nataf, G. Rapin, A new domain decomposition method for the Stokes and Oseen systems, submitted for publication [8] Pavarino, L. F.; Widlund, O. B., Balancing Neumann-Neumann methods for incompressible stokes equations, Comm. Pure Appl. Math., 55, 302-335 (2002) · Zbl 1024.76025 [9] Le Tallec, P.; Patra, A., Non-overlapping domain decomposition methods for adaptive hp approximations of the Stokes problem with discontinuous pressure fields, Comput. Methods Appl. Mech Engrg., 145, 361-379 (1997) · Zbl 0891.76053 [10] Wloka, J. T.; Rowley, B.; Lawruk, B., Boundary Value Problems for Elliptic Systems (1995), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0836.35042 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.