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H 1 Parallel preconditioning for time-dependent PDEs and PDE control

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

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    Résumé : We present a novel approach to the solution of time-dependent PDEs via the so-called monolithic or all-at-once formulation. This approach will be explained for simple parabolic problems and its utility in the context of PDE constrained optimization problems will be elucidated.
    The underlying linear algebra includes circulant matrix approximations of Toeplitz-structured matrices and allows for effective parallel implementation. Simple computational results will be shown for the heat equation and the wave equation which indicate the potential as a parallel-in-time method.
    This is joint work with Elle McDonald (CSIRO, Australia), Jennifer Pestana (Strathclyde University, UK) and Anthony Goddard (Durham University, UK)

    Keywords : evolutionary equations; all-at-once methods; parallel preconditioning

    Codes MSC :
    15B05 - Toeplitz, Cauchy, and related matrices
    65F08 - Preconditioners for iterative methods

    Ressources complémentaires :
    https://www.cirm-math.fr/RepOrga/2064/Slides/Wathen.pdf

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 08/10/2019
      Date de captation : 16/09/2019
      Collection : Research talks ; Numerical Analysis and Scientific Computing
      Format : MP4
      Durée : 01:14:30
      Domaine : Numerical Analysis & Scientific Computing
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-09-16_Wathen.mp4

    Informations sur la rencontre

    Nom de la rencontre : Parallel Solution Methods for Systems Arising from PDEs / Méthodes parallèles pour la résolution de systèmes issus d'équations aux dérivées partielles
    Organisateurs de la rencontre : Dolean, Victorita ; Spillane, Nicole ; Szyld, Daniel
    Dates : 16/09/2019 - 20/09/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/2064.html

    Citation Data

    DOI : 10.24350/CIRM.V.19561603
    Cite this video as: Wathen, Andy (2019). Parallel preconditioning for time-dependent PDEs and PDE control. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19561603
    URI : http://dx.doi.org/10.24350/CIRM.V.19561603


    Voir aussi

    Bibliographie

    1. MCDONALD, Eleanor, PESTANA, Jennifer, et WATHEN, Andy. Preconditioning and iterative solution of all-at-once systems for evolutionary partial differential equations. SIAM Journal on Scientific Computing, 2018, vol. 40, no 2, p. A1012-A1033. - https://doi.org/10.1137/16M1062016

    2. PESTANA, Jennifer et WATHEN, Andrew J. A preconditioned MINRES method for nonsymmetric Toeplitz matrices. SIAM Journal on Matrix Analysis and Applications, 2015, vol. 36, no 1, p. 273-288. - https://doi.org/10.1137/140974213

    3. GODDARD, Anthony et WATHEN, Andrew. A note on parallel preconditioning for all-at-once evolutionary PDEs. arXiv preprint arXiv:1810.00615, 2018. - https://arxiv.org/abs/1810.00615

    4. WATHEN, Andy J. Preconditioning. Acta Numerica, 2015, vol. 24, p. 329-376. - https://doi.org/10.1017/S0962492915000021

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