Multigrid solvers and multigrid preconditioners for the solution of variational data assimilation problems

Laurent Debreu 1, * Emilie Neveu 2 Ehouarn Simon 3 François-Xavier Le Dimet 1 Arthur Vidard 1, *
* Auteur correspondant
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In order to lower the computational cost of the variational data assimilation process, we investigate the use of multigrid methods to solve the associated optimal control system. On a linear advection equation, we study the impact of the regularization term of the optimal control and the impact of discretization errors on the efficiency of the coarse grid correction step. We show that even if the optimal control problem leads to the solution of an elliptic system, numerical errors introduced by the discretization can alter the success of the multigrid methods. The view of the multigrid iteration as a preconditioner for a Krylov optimization method leads to a more robust algorithm. A scale dependent weighting of the multigrid preconditioner and the usual background error covariance matrix based preconditioner is proposed and brings significant improvements.
Type de document :
Pré-publication, Document de travail
2013
Liste complète des métadonnées

Littérature citée [6 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00874643
Contributeur : Laurent Debreu <>
Soumis le : vendredi 18 octobre 2013 - 12:39:44
Dernière modification le : jeudi 3 mai 2018 - 22:26:01
Document(s) archivé(s) le : dimanche 19 janvier 2014 - 04:26:29

Fichier

multigrid_debreu_qjrms.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00874643, version 1

Collections

Citation

Laurent Debreu, Emilie Neveu, Ehouarn Simon, François-Xavier Le Dimet, Arthur Vidard. Multigrid solvers and multigrid preconditioners for the solution of variational data assimilation problems. 2013. 〈hal-00874643〉

Partager

Métriques

Consultations de la notice

710

Téléchargements de fichiers

365