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.
Accepted:
Published online:
Yvon Maday 1; Gabriel Turinici 2, 3
@article{CRMATH_2002__335_4_387_0, author = {Yvon Maday and Gabriel Turinici}, title = {A parareal in time procedure for the control of partial differential equations}, journal = {Comptes Rendus. Math\'ematique}, pages = {387--392}, publisher = {Elsevier}, volume = {335}, number = {4}, year = {2002}, doi = {10.1016/S1631-073X(02)02467-6}, language = {en}, }
TY - JOUR AU - Yvon Maday AU - Gabriel Turinici TI - A parareal in time procedure for the control of partial differential equations JO - Comptes Rendus. Mathématique PY - 2002 SP - 387 EP - 392 VL - 335 IS - 4 PB - Elsevier DO - 10.1016/S1631-073X(02)02467-6 LA - en ID - CRMATH_2002__335_4_387_0 ER -
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/
[1] L. Baffico, S. Bernard, Y. Maday, G. Turinici, G. Zerah, Parallel in time molecular dynamics simulations, CEMRACS'01 Proceedings, submitted
[2] Virtual and effective control for distributed systems and decomposition of everything, J. Anal. Math., Volume 80 (2000), pp. 257-297
[3] 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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