A parareal in time procedure for the control of partial differential equations

Yvon Maday; Gabriel Turinici

doi:10.1016/S1631-073X(02)02467-6

A parareal in time procedure for the control of partial differential equations

Yvon Maday ¹; Gabriel Turinici ^2,³

¹ Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boı̂te courrier 187, 75252 Paris cedex 05, France
² INRIA Rocquencourt, BP 105, 78153 Le Chesnay cedex, France
³ CERMICS, ENPC, Marne la Vallée, France

Comptes Rendus. Mathématique, Volume 335 (2002) no. 4, pp. 387-392.

Abstract (Original language)
Résumé

We have proposed in a previous note a time discretization for partial differential evolution equation that allows for parallel implementations. This scheme is here reinterpreted as a preconditioning procedure on an algebraic setting of the time discretization. This allows for extending the parallel methodology to the problem of optimal control for partial differential equations. We report a first numerical implementation that reveals a large interest.

On a proposé dans une précédente note, un schéma permettant de profiter d'une architecture parallèle pour la discrétisation en temps d'équation d'évolution aux dérivées partielles. Ce schéma est ici interprété sous un angle différent et matriciel, permettant d'étendre le concept pour le contrôle d'EDP. Les premières expériences numériques sont extrèmement encourageantes.

Received: 2002-03-05
Accepted: 2002-06-07
Published online: 2002-01-01

DOI: 10.1016/S1631-073X(02)02467-6

Author's affiliations:

Yvon Maday ¹; Gabriel Turinici ^{2, 3}

¹ Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boı̂te courrier 187, 75252 Paris cedex 05, France
² INRIA Rocquencourt, BP 105, 78153 Le Chesnay cedex, France
³ CERMICS, ENPC, Marne la Vallée, France

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     title = {A parareal in time procedure for the control of partial differential equations},
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Yvon Maday; Gabriel Turinici. A parareal in time procedure for the control of partial differential equations. Comptes Rendus. Mathématique, Volume 335 (2002) no. 4, pp. 387-392. doi : 10.1016/S1631-073X(02)02467-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02467-6/

References
Cited by

[1] L. Baffico, S. Bernard, Y. Maday, G. Turinici, G. Zerah, Parallel in time molecular dynamics simulations, CEMRACS'01 Proceedings, submitted

[2] J.-L. Lions Virtual and effective control for distributed systems and decomposition of everything, J. Anal. Math., Volume 80 (2000), pp. 257-297

[3] J.-L. Lions; Y. Maday; G. Turinici Résolution d'EDP par un schéma en temps « pararéel », C. R. Acad. Sci. Paris, Série I, Volume 332 (2001) no. 7, pp. 661-668

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