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This paper focuses on the development of a two-level preconditioner based ona fully algebraical enhancement of a Schwarz domain decomposition method. Weconsider the purely divergence of a Restricted Additive Scwharz iterativeprocess leading to the preconditioner developped by X.-C. Cai and M. Sarkis inSIAM Journal of Scientific Computing, Vol. 21 no. 2, 1999. The convergence ofvectorial sequence of traces of this process on the artificial interface can beaccelerated by an Aitken acceleration technique as proposed in the work of M.Garbey and D. Tromeur-Dervout, in International Journal for Numerical Methodsin Fluids, Vol. 40, no. 12,2002. We propose a formulation of the Aitken-Schwarztechnique as a preconditioning technique called Aitken-RAS 1 . The Aitkenacceleration is performed in a reduced space to save computing or permit fullyalgebraic computation of the accelerated solution without knowledge of theunderlying equations. A convergence study of the Aitken-RAS preconditioner isproposed also application on industrial problem.

ARAS: Fully algebraic Two-level domain decomposition precondition technique with approximation on course interfaces Fully