Effects of stochastic ordering on preconditioned GMRES algorithm

Abstract

In this paper we investigate the possible application of stochastic renumbering procedure for the improvement of preconditioner effectiveness for incomplete ILU factorization associated to GMRES method or system resolution. Simulated annealing procedure for searching a permutation of the matrix is proposed. Several numerical experiments and test cases are shown which achieve a reduction in the dimension of the Krylov subspace. This procedure is proposed in the context of the resolution of nonlinear evolutive integral operators solved by Finite element Method discretization.