ARAS: Fully algebraic Two-level domain decomposition precondition technique with approximation on course interfaces Fully
This work provides a fully algebraic preconditioning technique for domain decomposition methods, relevant for solving large-scale PDEs in computational science and engineering.
The paper develops a fully algebraic two-level domain decomposition preconditioner (Aitken-RAS) that accelerates the convergence of the Restricted Additive Schwarz method using Aitken acceleration in a reduced space, enabling application without knowledge of underlying equations. Results include a convergence study and application to an industrial problem.
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.