New approach for accelerating the nonlinear Schwarz iterations

Abstract

The vector Epsilon algorithm is an effective extrapolation method used for accelerating the convergence of vector sequences. In this paper, this method is used to accelerate the convergence of Schwarz iterative methods for stationary linear and nonlinear partial differential equations (PDEs). The vector Epsilon algorithm is applied to the vector sequences produced by additive Schwarz (AS) or restricted additive Schwarz (RAS) methods after discretization. Some convergence analysis is presented, and several test-cases of analytical problems are performed in order to illustrate the interest of such algorithm. The obtained results show that the proposed algorithm yields much faster convergence than the classical Schwarz iterations.