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H 1 Generalised finite elements: domain decomposition, optimal local approximation, reduced order modelling

Auteurs : Scheichl, Robert (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : I will present an efficient implementation of the highly robust and scalable GenEO preconditioner in the high-performance PDE framework DUNE. The GenEO coarse space is constructed by combining low energy solutions of local generalised eigenproblems using a partition of unity. In this talk, both weak and strong scaling for the GenEO solver on over 15,000 cores will be demonstrated by solving an industrially motivated problem with over 200 million degrees of freedom in aerospace composites modelling. Further, it will be shown that for highly complex parameter distributions in certain real-world applications, established methods can become intractable while GenEO remains fully effective. In the context of multilevel Markov chain Monte Carlo (MLMCMC), the GenEO coarse space also plays an important role as an effective surrogate model in PDE-constrained Bayesian inference. The second part will therefore focus on the approximation properties of the GenEO coarse space and on a high-performance parallel implementation of MLMCMC.
    This is joint work with Tim Dodwell (Exeter), Anne Reinarz (TU Munich) and Linus Seelinger (Heidelberg).

    Keywords : generalised finite elements ; multiscale methods ; domain decomposition ; strong coefficient variation ; anisotropic linear elasticity ; parallel scaling

    Codes MSC :
    65N22 - Solution of discretized equations (BVP of PDE)
    65N30 - Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
    65N55 - Multigrid methods; domain decomposition (BVP of PDE)
    65F08 - Preconditioners for iterative methods

    Ressources complémentaires :

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 08/10/2019
      Date de captation : 16/09/2019
      Collection : Research talks
      Format : MP4
      Durée : 01:03:49
      Domaine : Numerical Analysis & Scientific Computing
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-09-16_Scheichl.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.19561903
    Cite this video as: Scheichl, Robert (2019). Generalised finite elements: domain decomposition, optimal local approximation, reduced order modelling. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19561903
    URI : http://dx.doi.org/10.24350/CIRM.V.19561903

    Voir aussi


    1. Spillane, N., Dolean, V., Hauret, P., Nataf, F., Pechstein, C. and Scheichl, R., Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps. Numerische Mathematik 126(4):741-770, 2014. - http://dx.doi.org/10.1007/s00211-013-0576-y

    2. Bastian, P., Heimann, F. and Marnach, S., Generic implementation of finite element methods in the distributed and unified numerics environment (DUNE). Kybernetika 46(2):294–315, 2010. - https://dml.cz/bitstream/handle/10338.dmlcz/140745/Kybernetika_46-2010-2_6.pdf