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Preconditioning for parallel-in-time

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Multi angle
Authors : Wathen, Andy (Author of the conference)
CIRM (Publisher )

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Abstract : 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

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

Additional resources :
https://www.cirm-math.fr/RepOrga/2642/Slides/Wathen.pdf

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 29/07/2022
    Conference Date : 11/07/2022
    Subseries : Research talks
    arXiv category : Numerical Analysis
    Mathematical Area(s) : Numerical Analysis & Scientific Computing
    Format : MP4 (.mp4) - HD
    Video Time : 01:13:23
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-07-11_Wathen.mp4

Information on the Event

Event Title : Jean-Morlet Chair - PinT 2022: 11th Conference on Parallel-in-Time Integration / Chaire Jean-Morlet 2022 - 11ème conférence PinT - Parallel-in-Time Integration
Event Organizers : Gander, Martin ; Hubert, Florence
Dates : 11/07/2022 - 15/07/2022
Event Year : 2022
Event URL : https://www.chairejeanmorlet.com/2642.html

Citation Data

DOI : 10.24350/CIRM.V.19938803
Cite this video as: 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

See Also

Bibliography

  • 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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