Vector extrapolation method for non-overlapping Schwarz iterations

Abstract

In this paper, we propose a vector extrapolation method for accelerating the non-overlapping Schwarz iterations in the case of the nonlinear 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.