English
Parallel preconditioning for time-dependent PDEs and PDE control
Multi angle
Auteurs : Wathen, Andy (Auteur de la Conférence)
CIRM (Editeur )
15B05 - Toeplitz, Cauchy, and related matrices
65F08 - Preconditioners for iterative methods
65M22 - Solution of discretized equations [See also 65Fxx, 65Hxx]
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2064/Slides/Wathen.pdf
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 : 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
15B05 - Toeplitz, Cauchy, and related matrices
65F08 - Preconditioners for iterative methods
65M22 - Solution of discretized equations [See also 65Fxx, 65Hxx]
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2064/Slides/Wathen.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 08/10/2019 Date de captation : 16/09/2019 Sous collection : Research talks arXiv category : Numerical Analysis ; Optimization and Control Domaine : Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Durée : 01:14:30 Audience : Researchers Download : https://videos.cirm-math.fr/2019-09-16_Wathen.mp4 
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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 partiellesOrganisateurs 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
Données de citation
DOI : 10.24350/CIRM.V.19561603Citer cette vidéo: 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
- [Multi angle] Multigrid and domain decomposition: similarities and differences / Auteur de la Conférence Gander, Martin.
- [Multi angle] Generalised finite elements: domain decomposition, optimal local approximation, reduced order modelling / Auteur de la Conférence Scheichl, Robert.
- [Multi angle] Computational methods for large-scale matrix equations and application to PDEs / Auteur de la Conférence Simoncini, Valeria.
- [ Post-edited] Challenges in achieving scalable and robust linear solvers / Auteur de la Conférence Grigori, Laura.
Bibliographie
- 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
- 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
- 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
- WATHEN, Andy J. Preconditioning. Acta Numerica, 2015, vol. 24, p. 329-376. - https://doi.org/10.1017/S0962492915000021
