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Preconditioning for parallel-in-time

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Multi angle
Auteurs : Wathen, Andy (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : This talk consists of two parts, one elementary and one related to the solution of complicated systems of evolutionary partial differential equations. In the first part we show how preconditioning for all-at-once descriptions of linear time-dependent differential equations can defeat the everpresent danger of high-index nilpotency associated with the principle of causality. In particular we will describe some theory for periodic preconditioning of initial value problems that establishes it as a viable Parallelin-time (PinT) approach. The second part builds on much excellent work on PinT methods for scalar parabolic PDEs such as the diffusion equation to propose PinT methods for more complicated evolutionary PDE systems. We will explain the idea with reference to the time-dependent incompressible Stokes and Navier-Stokes equations and indicate it's more broad applicability. This part of the talk is joint with Federico Danieli and Ben Southworth.

Keywords : preconditioning; parallel-in-time

Codes MSC :
65F10 - Iterative methods for linear systems
65L99 - None of the above but in this section
65M99 - None of the above but in this section

Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2642/Slides/Wathen.pdf

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 29/07/2022
    Date de captation : 11/07/2022
    Sous collection : Research talks
    arXiv category : Numerical Analysis
    Domaine : Numerical Analysis & Scientific Computing
    Format : MP4 (.mp4) - HD
    Durée : 01:13:23
    Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-07-11_Wathen.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.19938803
Citer cette vidéo: Wathen, Andy (2022). Preconditioning for parallel-in-time. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19938803
URI : http://dx.doi.org/10.24350/CIRM.V.19938803

Voir aussi

Bibliographie

  • WATHEN, Andy. Some observations on preconditioning for non-self-adjoint and time-dependent problems. Computers & Mathematics with Applications, 2022, vol. 116, p. 176-180. - https://doi.org/10.1016/j.camwa.2021.05.037

  • DANIELI, Federico, SOUTHWORTH, Ben S., et WATHEN, Andrew J. Space-time block preconditioning for incompressible flow. SIAM Journal on Scientific Computing, 2022, vol. 44, no 1, p. A337-A363. - https://doi.org/10.1137/21M1390773



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