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

TL;DR

This paper introduces the Aitken-RAS preconditioner, a fully algebraic two-level domain decomposition method that accelerates convergence using Aitken's technique in a reduced space, applicable to industrial problems.

Contribution

It develops a novel algebraic Aitken-RAS preconditioner that accelerates domain decomposition methods without requiring explicit equation knowledge.

Findings

Accelerates convergence of domain decomposition methods.

Provides a fully algebraic implementation of Aitken acceleration.

Demonstrates effectiveness on industrial problems.

Abstract

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.