@inproceedings{33f09609a5844059beb6913741a77368,
title = "A domain decomposition preconditioner of neumann-neumann type for the stokes equations",
abstract = "In this paper we recall a new domain decomposition method for the Stokes problem obtained via the Smith factorization. From the theoretical point of view, this domain decomposition method is optimal in the sense that it converges in two iterations for a decomposition into two equal domains. Previous results illustrated the fast convergence of the proposed algorithm in some cases. Our algorithm has shown a more robust behavior than Neumann-Neumann or FETI type methods for particular decompositions; as far as general decompositions are concerned, the performances of the three algorithms are similar. Nevertheless, the computations of the singular values of the interface preconditioned problem have shown that one needs a coarse space whose dimension is less than the one needed for the Neumann-Neumann algorithm. In this work we present a new strategy in order to improve the convergence of the new algorithm in the presence of cross points.",
keywords = "domain decomposition methods, algorithms, convergence of numerical methods, decomposition, operations research, cross point, fast convergence, preconditioners, Stokes equations",
author = "Vitorita Dolean and Fr{\'e}d{\'e}ric Nataf and Gerd Rapin",
year = "2009",
month = oct,
day = "12",
doi = "10.1007/978-3-642-02677-5_16",
language = "English",
isbn = "9783642026768",
volume = "70",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer",
pages = "161--168",
booktitle = "Domain Decomposition Methods in Science and Engineering XVIII",
note = "18th International Conference of Domain Decomposition Methods ; Conference date: 12-01-2008 Through 17-01-2008",
}