Title: Optimal Interface Conditions for Domain Decomposition Methods
Authors: F. Nataf*, F. Rogier** and E. de Sturler***

*CMAP, CNRS URA756, Ecole Polytechnique
91128 Palaiseau Cedex, France
E-mail address: nataf@cmapx.polytechnique.fr

**Division Calcul parall\`ele, ONERA,  29 Av. de la Division Leclerc
 92322 Ch\^atillon, France
E-mail address: rogier@onera.fr

***CSCS, ETH,  Via Cantonale
6928 Manno, Switzerland
E-mail address: sturler@cscs.ch




Abstract: We define optimal interface conditions for the additive Schwarz method
(ASM) in the sense that convergence is achieved in a number of steps
equals to the number of subdomains. Since these boundary conditions are
difficult to use, we approximate them by partial differential
operators that are easier to use. We present numerical results using
these
approximate interface conditions for the ASM and Schur type
methods (substructuring). We also give a new result of convergence for
BiCG which is then used for BiCGSTAB.


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        ABSTRACT.nataf_rogier_sturler_301