CIRM - Videos & books Library - PinT schemes using time as a parameter

Multi angle

Auteurs : Mula Hernandez, Olga (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : When thinking about parallel in time schemes, one often tends to view time as a variable to discretize within a numerical scheme (that usually involves a time marching strategy). In this talk, I propose to review alternative strategies where time can be seen as a parameter so that computing the PDE solution at a given time would consist in evaluating closed formulas or in solving tasks of very low computational cost that do not involve any time marching. This type of approach is by nature entirely parallelizable. It can be achieved by either leveraging analytic formulas (whose existence strongly depends on the nature of the PDE), or by learning techniques such as model order reduction. For the later strategy, convection dominated problems are challenging (just like in classical PinT schemes such as parareal) and I will present recent contributions to address this type of problems.

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Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2642/Slides/mula-pint-2022.pdf

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2022-07-14_Mula_Hernandez.mp4

Informations sur la Rencontre

Nom de la rencontre : Jean-Morlet Chair - PinT 2022: 11th Conference on Parallel-in-Time Integration / Chaire Jean-Morlet 2022 - 11ème conférence PinT - Parallel-in-Time Integration
Organisateurs de la rencontre : Gander, Martin ; Hubert, Florence
Dates : 11/07/2022 - 15/07/2022
Année de la rencontre : 2022
URL Congrès : https://www.chairejeanmorlet.com/2642.html

Données de citation

DOI : 10.24350/CIRM.V.19938703
Citer cette vidéo: Mula Hernandez, Olga (2022). PinT schemes using time as a parameter. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19938703
URI : http://dx.doi.org/10.24350/CIRM.V.19938703

Voir aussi

[Multi angle] A mathematical introduction to deep learning / Auteur de la Conférence Xu, Jinchao.
[Multi angle] Preconditioning for parallel-in-time / Auteur de la Conférence Wathen, Andy.
[Multi angle] Analysis of a three-Level vriant of parareal / Auteur de la Conférence Kwok, Felix.
[Multi angle] On waveform-relaxation type methods for wave-type equation / Auteur de la Conférence Ciaramella, Gabriele.

Bibliographie

S. Aouadi, D. Q. Bui, R. Guetat, and Y. Maday, Convergence analysis of the coupled parareal-schwarz waveform relaxation method, 2017, in preparation. -

S. Bahmani, B. Raj, and P. T. Boufounos, Greedy sparsity-constrained optimization, Journal of Machine Learning Research 14 (2013), no. Mar, 807841. -

A. Cohen and R. DeVore, Kolmogorov widths under holomorphic mappings, IMA Journal of Numerical Analysis 36 (2016), no. 1, 112. - https://doi.org/10.1093/imanum/dru066

Huy Dinh, Harbir Antil, Yanlai Chen, Elena Cherkaev, and Akil Narayan, Model reduction for fractional elliptic problems using kato's formula, arXiv preprint arXiv:1904.09332 (2019) - https://doi.org/10.48550/arXiv.1904.09332

W. Dahmen, R. DeVore, L. Grasedyck, and E. Süli, Tensor-sparsity of solutions to high-dimensional elliptic partial dierential equations, Foundations of Computational Mathematics (2015), 162. - http://dx.doi.org/10.1007/s10208-015-9265-9

I. P. Gavrilyuk, W. Hackbusch, and B. N. Khoromskij, H-matrix approximation for the operator exponential with applications, Numerische Mathematik 92 (2002), no. 1, 83111 - http://dx.doi.org/10.1007/s002110100360

R. Guetat, Méthode de parallélisation en temps: Application aux méthodes de décomposition de domaine, Ph.D. thesis, Paris VI, 2012. -

M. Hochbruck and A. Ostermann, Exponential integrators, Acta Numerica 19 (2010), 209286. - https://doi.org/10.1017/S0962492910000048

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M. Minion, A hybrid parareal spectral deferred corrections method, Comm. App. Math. and Comp. Sci. 5 (2010), no. 2. - http://dx.doi.org/10.2140/camcos.2010.5.265

Y. Maday and O. Mula, An adaptive parareal algorithm, Journal of Computational and Applied Mathematics (2020) - https://doi.org/10.1016/j.cam.2020.112915

M. L. Minion, R. Speck, M. Bolten, M. Emmett, and D. Ruprecht, Interweaving PFASST and parallel multigrid, SIAM Journal on Scientific Computing 37 (2015), no. 5, S244S263. - https://doi.org/10.1137/14097536X

Y. Maday, J. Salomon, and G. Turinici, Monotonic parareal control for quantum systems, SIAM Journal on Numerical Analysis 45 (2007), no. 6, 24682482. - https://doi.org/10.1137/050647086

Y. Maday and G. Turinici, The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation, Domain Decomposition Methods in Science and Engineering, Springer Berlin Heidelberg, 2005, pp. 441448. - http://dx.doi.org/10.1007/3-540-26825-1_45

O. Mula, Some contributions towards the parallel simulation of time dependent neutron transport and the integration of observed data in real time, Ph.D. thesis, Université Pierre et Marie Curie-Paris VI, 2014. - https://tel.archives-ouvertes.fr/tel-01081601

M. L. Minion, A. Williams, T. E. Simos, G. Psihoyios, and C. Tsitouras, Parareal and spectral deferred corrections, AIP Conference Proceedings, vol. 1048, 2008, p. 388. - https://doi.org/10.1063/1.2990941

D. Needell and J. A. Tropp, Cosamp: Iterative signal recovery from incomplete and inaccurate samples, Applied and computational harmonic analysis 26 (2009), no. 3, 301321. - https://doi.org/10.1016/j.acha.2008.07.002

D. Sheen, I. Sloan, and V. Thomée, A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature, Mathematics of Computation 69 (2000), no. 229, 177195. - http://dx.doi.org/10.1090/S0025-5718-99-01098-4

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