Title: Vector extrapolation method for non-overlapping Schwarz iterations

Authors: Nabila Nagid; Hassan Belhadj; Mohamed Ridouan Amattouch

Addresses: Department of Mathematics, Faculty of Sciences and Techniques, University of Abdelmalek Essaadi, BP. 416 Tangier, Morocco ' Department of Mathematics, Faculty of Sciences and Techniques, University of Abdelmalek Essaadi, BP. 416 Tangier, Morocco ' Department of Mathematics, Faculty of Sciences and Techniques, University of Abdelmalek Essaadi, BP. 416 Tangier, Morocco

Abstract: In this paper, we propose a vector extrapolation method for accelerating the non-overlapping Schwarz iterations in the case of the non-linear reaction diffusion equations. The acceleration occurs at two levels: the acceleration of sequences produced by the fixed point algorithm, and the acceleration of sequences generated by Schwarz method. Specifically, the acceleration occurs in the internal Dirichlet boundary conditions. In order to illustrate the interest of the proposed algorithm, we have performed different test-cases of analytical examples, all results show the efficiency of the proposed approach in terms of CPU-Time, number of iterations and the rate of convergence.

Keywords: domain decomposition method; extrapolation method; finite element method; fixed point method; non-linear reaction diffusion problems; non-overlapping Schwarz algorithm; vector ε-algorithm.

DOI: 10.1504/IJDSDE.2018.089098

International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.1/2, pp.95 - 112

Received: 21 Oct 2016
Accepted: 31 May 2017
Published online: 05 Jan 2018 *

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