Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems

SUMMARY This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature, we present a procedure on the basis of a selection of relevant approximations of the eigenspaces for extracting, selecting and reusing information from the Krylov subspaces generated by previous solutions in order to accelerate the current iteration. Assessments of the method are proposed in the cases of both linear and nonlinear structural problems. Copyright © 2012 John Wiley & Sons, Ltd.