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Parallel preconditioning for time-dependent PDEs and PDE control
Multi angle
Authors : Wathen, Andy (Author of the conference)
CIRM (Publisher )
15B05 - Toeplitz, Cauchy, and related matrices
65F08 - Preconditioners for iterative methods
65M22 - Solution of discretized equations [See also 65Fxx, 65Hxx]
Additional resources :
https://www.cirm-math.fr/RepOrga/2064/Slides/Wathen.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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]
Additional resources :
https://www.cirm-math.fr/RepOrga/2064/Slides/Wathen.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 08/10/2019 Conference Date : 16/09/2019 Subseries : Research talks arXiv category : Numerical Analysis ; Optimization and Control Mathematical Area(s) : Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Video Time : 01:14:30 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-09-16_Wathen.mp4 
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Information on the Event
Event Title : Parallel Solution Methods for Systems Arising from PDEs / Méthodes parallèles pour la résolution de systèmes issus d'équations aux dérivées partiellesEvent Organizers : Dolean, Victorita ; Spillane, Nicole ; Szyld, Daniel Dates : 16/09/2019 - 20/09/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2064.html
Citation Data
DOI : 10.24350/CIRM.V.19561603Cite 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 |
See Also
- [Multi angle] Multigrid and domain decomposition: similarities and differences / Author of the conference Gander, Martin.
- [Multi angle] Generalised finite elements: domain decomposition, optimal local approximation, reduced order modelling / Author of the conference Scheichl, Robert.
- [Multi angle] Computational methods for large-scale matrix equations and application to PDEs / Author of the conference Simoncini, Valeria.
- [Post-edited] Challenges in achieving scalable and robust linear solvers / Author of the conference Grigori, Laura.
Bibliography
- 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
