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

TL;DR

This paper introduces a method to enhance the convergence of iterative solvers for sequences of linear and nonlinear structural problems by reusing Krylov subspaces through selective augmentation, improving computational efficiency.

Contribution

It proposes a novel approach for total and selective reuse of Krylov subspaces to accelerate convergence in solving sequences of structural problems.

Findings

Improved convergence rates demonstrated in linear structural problems.

Effective reuse of eigenspace approximations enhances nonlinear problem solving.

Method outperforms traditional approaches in computational efficiency.

Abstract

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 based on 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.