Diffusive Back and Forth Nudging algorithm for data assimilation

Didier Auroux; Jacques Blum; Maëlle Nodet

doi:10.1016/j.crma.2011.07.004

Partial Differential Equations

Diffusive Back and Forth Nudging algorithm for data assimilation
[Une version Diffusive du Nudging Direct et Rétrograde pour lʼassimilation de données]

Présenté par : Alain Bensoussan

Didier Auroux ¹ ; Jacques Blum ¹ ; Maëlle Nodet ²

¹ Laboratoire J.-A. Dieudonné, université de Nice Sophia Antipolis, parc Valrose, 06108 Nice cedex 2, France
² Université Grenoble I / INRIA, laboratoire Jean Kuntzmann, tour IRMA, 51, rue des mathématiques, domaine universitaire, BP 53X, 38041 Grenoble cedex, France

Comptes Rendus. Mathématique, Volume 349 (2011) no. 15-16, pp. 849-854.

Abstract (VO)
Résumé

In this Note, we propose an improvement to the Back and Forth Nudging algorithm for handling diffusion in the context of geophysical data assimilation. We introduce the Diffusive Back and Forth Nudging, in which the sign of the diffusion term is changed in the backward integrations. We study the convergence of this algorithm, in particular for linear transport equations.

Dans cette Note, nous proposons une amélioration de lʼalgorithme du Nudging Direct et Rétrograde pour gérer la diffusion dans le contexte de lʼassimilation de données en géophysique. Nous introduisons la version Diffusive du Nudging Direct et Rétrograde, dans laquelle le signe du terme de diffusion est inversé dans les équations rétrogrades. Nous étudions la convergence de cet algorithme, en particulier pour lʼéquation de transport linéaire.

Reçu le : 2011-06-22
Accepté le : 2011-07-06
Publié le : 2011-07-27

DOI : 10.1016/j.crma.2011.07.004

Affiliations des auteurs :

Didier Auroux ¹ ; Jacques Blum ¹ ; Maëlle Nodet ²

¹ Laboratoire J.-A. Dieudonné, université de Nice Sophia Antipolis, parc Valrose, 06108 Nice cedex 2, France
² Université Grenoble I / INRIA, laboratoire Jean Kuntzmann, tour IRMA, 51, rue des mathématiques, domaine universitaire, BP 53X, 38041 Grenoble cedex, France

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     author = {Didier Auroux and Jacques Blum and Ma\"elle Nodet},
     title = {Diffusive {Back} and {Forth} {Nudging} algorithm for data assimilation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {849--854},
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Didier Auroux; Jacques Blum; Maëlle Nodet. Diffusive Back and Forth Nudging algorithm for data assimilation. Comptes Rendus. Mathématique, Volume 349 (2011) no. 15-16, pp. 849-854. doi : 10.1016/j.crma.2011.07.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.07.004/

Bibliographie
Cité par

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Didier Auroux; Patrick Bansart; Jacques Blum An evolution of the back and forth nudging for geophysical data assimilation: application to Burgers equation and comparisons, Inverse Problems in Science and Engineering, Volume 21 (2013) no. 3, pp. 399-419 | DOI:10.1080/17415977.2012.712528 | Zbl:1281.35093

Cité par 13 documents. Sources : Crossref, zbMATH

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