English
Challenges in achieving scalable and robust linear solvers
Post-edited
Auteurs : Grigori, Laura (Auteur de la conférence)
CIRM (Editeur )
65F10 - Iterative methods for linear systems
65N55 - Multigrid methods; domain decomposition (BVP of PDE)
65F08 - Preconditioners for iterative methods
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2064/Slides/LGrigori.pdf
CIRM (Editeur )
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| domain decomposition two level preconditioners condition number algebraic setting multilevel methods parallel performance enlarged Krylov methods |
Résumé :
This talk focuses on challenges that we address when designing linear solvers that aim at achieving scalability on large scale computers, while also preserving numerical robustness. We will consider preconditioned Krylov subspace solvers. Getting scalability relies on reducing global synchronizations between processors, while also increasing the arithmetic intensity on one processor. Achieving robustness relies on ensuring that the condition number of the preconditioned matrix is bounded. We will discuss two different approaches for this. The first approach relies on enlarged Krylov subspace methods that aim at computing an enlarged subspace and obtain a faster convergence of the iterative method. The second approach relies on a multilevel Schwarz preconditioner, a multilevel extension of the GenEO preconditioner, that is basedon constructing robustly a hierarchy of coarse spaces. Numerical results on large scale computers, in particular for linear systems arising from solving linear elasticity problems, will discuss the efficiency of the proposed methods.
Mots-Clés : preconditioned Krylov subspace solvers; domain decomposition; multilevel methods; subspace correction; condition number; parallel performance; enlarged Krylov methods
Codes MSC : Mots-Clés : preconditioned Krylov subspace solvers; domain decomposition; multilevel methods; subspace correction; condition number; parallel performance; enlarged Krylov methods
65F10 - Iterative methods for linear systems
65N55 - Multigrid methods; domain decomposition (BVP of PDE)
65F08 - Preconditioners for iterative methods
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2064/Slides/LGrigori.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 08/10/2019 Date de Captation : 18/09/2019 Sous Collection : Research talks Catégorie arXiv : Numerical Analysis Domaine(s) : Analyse Numérique & Calcul Formel ; Informatique Format : MP4 (.mp4) - HD Durée : 00:55:43 Audience : Chercheurs Download : https://videos.cirm-math.fr/2019-09-18_Grigory.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 de la Rencontre : https://conferences.cirm-math.fr/2064.html
Données de citation
DOI : 10.24350/CIRM.V.19561203Citer cette vidéo: Grigori, Laura (2019). Challenges in achieving scalable and robust linear solvers. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19561203 URI : http://dx.doi.org/10.24350/CIRM.V.19561203 |
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] Parallel preconditioning for time-dependent PDEs and PDE control / Auteur de la conférence Wathen, Andy.
- [Multi angle] Computational methods for large-scale matrix equations and application to PDEs / Auteur de la conférence Simoncini, Valeria.
Bibliographie
- H. Al Daas and L. Grigori. A class of efficient locally constructed preconditioners based on coarse spaces. SIAM Journal on Matrix Analysis and Applications, 40, pp. 66–91, 2019. - https://doi.org/10.1137/18M1194365
- H. Al Daas, L. Grigori, P. Jolivet, P. H. Tournier. A multilevel Schwarz preconditioner based on a hierarchy of robust coarse spaces. Tech report hal-02151184, 2019. - https://hal.archives-ouvertes.fr/hal-02151184/
- L. Grigori, S. Moufawad, and F. Nataf. Enlarged Krylov Subspace Conjugate Gradient Methods for Reducing Communication. SIAM Journal on Scientific Computing, 37(2):744–773, 2016. - https://doi.org/10.1137/140989492
- L. Grigori and O. Tissot. Scalable linear solvers based on enlarged Krylov subspaces with dynamic reduction of search directions. SIAM Journal on Scientific Computing, in press, 2019. - https://hal.inria.fr/hal-01828521/
- N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein, and R. Scheichl. Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps, Numerische Mathematik, 126, pp. 741–770, 2014. - http://dx.doi.org/10.1007/s00211-013-0576-y
