Jean-Morlet Chair - PinT 2022: 11th Conference on Parallel-in-Time Integration / Chaire Jean-Morlet 2022 - 11ème conférence PinT - Parallel-in-Time Integration

Collection Jean-Morlet Chair - PinT 2022: 11th Conference on Parallel-in-Time Integration / Chaire Jean-Morlet 2022 - 11ème conférence PinT - Parallel-in-Time Integration

Organisateur(s) Gander, Martin ; Hubert, Florence

Date(s) 11/07/2022 - 15/07/2022

URL associée https://www.chairejeanmorlet.com/2642.html

00:00:00 / 00:00:00

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Preconditioning for parallel-in-time

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.

Informations sur la vidéo

Date de captation 11/07/2022
Date de publication 29/07/2022
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19938803
Citer cette vidéo Wathen, Andy (11/07/2022). Preconditioning for parallel-in-time. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19938803
URL https://dx.doi.org/10.24350/CIRM.V.19938803

Domaine(s)

Analyse numérique

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

Codes MSC

Document(s)

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

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