Parallel preconditioning for time-dependent PDEs and PDE control | Vidéo | Carmin.tv

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Parallel preconditioning for time-dependent PDEs and PDE control

Appears in collection : Parallel Solution Methods for Systems Arising from PDEs / Méthodes parallèles pour la résolution de systèmes issus d'équations aux dérivées partielles

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)

Information about the video

Date of recording 16/09/2019
Date of publication 08/10/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19561603
Cite this video Wathen, Andy (16/09/2019). Parallel preconditioning for time-dependent PDEs and PDE control. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19561603
URL https://dx.doi.org/10.24350/CIRM.V.19561603

Domain(s)

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

MSC codes

Document(s)

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

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