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

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.

arXiv commentInternational Journal for Numerical Methods in Engineering (2013) 24 pages

References in corpus (3)

• Non-overlapping domain decomposition methods in structural mechanics
• On the initial estimate of interface forces in FETI methods
• A domain decomposition strategy to efficiently solve structures containing repeated patterns

Cited by in corpus (3)

• A new impedance accounting for short and long range effects in mixed substructured formulations of nonlinear problems
• Substructured formulations of nonlinear structure problems - influence of the interface condition
• Strict lower bounds with separation of sources of error in non-overlapping domain decomposition methods