A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Computational Mechanics Année : 2017

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

Résumé

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method.We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.
Fichier principal
Vignette du fichier
Mercier_18305.pdf (1.13 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03612688 , version 1 (18-03-2022)

Identifiants

Citer

Sylvain Mercier, Serge Gratton, Nicolas Tardieu, Xavier Vasseur. A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity. Computational Mechanics, 2017, 60 (6), pp.969-982. ⟨10.1007/s00466-017-1450-z⟩. ⟨hal-03612688⟩
23 Consultations
81 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More