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Multigrid algorithms and local mesh refinement methods in the context of variational data assimilation

Laurent Debreu 1 Emilie Neveu 2 François Xavier Le Dimet 1 Ehouarn Simon 3, 4
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
4 IRIT-APO - Algorithmes Parallèles et Optimisation
IRIT - Institut de recherche en informatique de Toulouse
Abstract : This chapter looks at the use of multigrid methods and local mesh refinement algorithms in the context of the variational data assimilation method. Firstly, the chapter looks back at basic properties of the traditional variational data assimilation method and considers on the role of the background error covariance matrix. The next section shows how multigrid algorithms can efficiently solve the resulting system. Then the chapter deals with local mesh refinements and the final part of the chapter gives some ideas on how to couple the two approaches in the view of local multigrid algorithms.
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Laurent Debreu, Emilie Neveu, François Xavier Le Dimet, Ehouarn Simon. Multigrid algorithms and local mesh refinement methods in the context of variational data assimilation. Eric Blayo; Marc Bocquet; Emmanuel Cosme; F. Cugliandolo Leticia. Advanced Data Assimilation for Geosciences: Lecture Notes of the Les Houches School of Physics: Special Issue, June 2012, Oxford University Press, pp.576, 2014, Lecture notes of "Les Houches" summer school 2012, 9780198723844. ⟨10.1093/acprof:oso/9780198723844.003.0017⟩. ⟨hal-01095939⟩



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