ARAS: FULLY ALGEBRAIC TWO-LEVEL DOMAIN DECOMPOSITION PRECONDITIONING TECHNIQUE WITH APPROXIMATION ON COARSE INTERFACES

Thomas Dufaud (1) , Tromeur-Dervout Damien (2)

1 SAGE - Simulations and Algorithms on Grids for Environment
2 ICJ - Institut Camille Jordan

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.

Keywords: Domain decomposition; Restricted Additive Schwarz preconditioner; Aitken-Schwarz method; Algebraic Multilevel preconditioner

Domains: Numerical Analysis [math.NA]

Thomas Dufaud, Tromeur-Dervout Damien. ARAS: FULLY ALGEBRAIC TWO-LEVEL DOMAIN DECOMPOSITION PRECONDITIONING TECHNIQUE WITH APPROXIMATION ON COARSE INTERFACES. 2012. ⟨hal-00805313⟩