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

This paper focuses on the development of a two-level preconditioner based on a fully algebraical enhancement of a Schwarz domain decomposition method. We consider the purely divergence of a Restricted Additive Scwharz iterative process leading to the preconditioner developped by X.-C. Cai and M. Sar...

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Bibliographic Details
Published inarXiv.org
Main Authors Dufaud, Thomas, Tromeur-Dervout Damien
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.03.2013
Subjects
Acceleration
Algebra
Computational fluid dynamics
Convergence
Divergence
Domain decomposition methods
Iterative methods
Numerical methods
Preconditioning
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Summary:This paper focuses on the development of a two-level preconditioner based on a fully algebraical enhancement of a Schwarz domain decomposition method. We consider the purely divergence of a Restricted Additive Scwharz iterative process leading to the preconditioner developped by X.-C. Cai and M. Sarkis in SIAM Journal of Scientific Computing, Vol. 21 no. 2, 1999. The convergence of vectorial sequence of traces of this process on the artificial interface can be accelerated by an Aitken acceleration technique as proposed in the work of M. Garbey and D. Tromeur-Dervout, in International Journal for Numerical Methods in Fluids, Vol. 40, no. 12,2002. We propose a formulation of the Aitken-Schwarz technique as a preconditioning technique called Aitken-RAS 1 . The Aitken acceleration is performed in a reduced space to save computing or permit fully algebraic computation of the accelerated solution without knowledge of the underlying equations. A convergence study of the Aitken-RAS preconditioner is proposed also application on industrial problem.
ISSN:2331-8422