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Efficient iterative solvers: FETI methods with multiple search directions
Multi angle
Authors : Roux, François-Xavier (Author of the conference)
CIRM (Publisher )
65F10 - Iterative methods for linear systems
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)
65Y05 - Parallel computation (numerical methods)
CIRM (Publisher )
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Abstract :
In domain decomposition methods, most of the computational cost lies in the successive solutions of the local problems in subdomains via forward-backward substitutions and in the orthogonalization of interface search directions. All these operations are performed, in the best case, via BLAS-1 or BLAS-2 routines which are inefficient on multicore systems with hierarchical memory. A way to improve the parallel efficiency of the method consists in working with several search directions, since multiple forward-backward substitutions and reorthogonalizations involve BLAS-3 routines. In the case of a problem with several right-hand-sides, using a block Krylov method is a straightforward way to work with multiple search directions. This will be illustrated with an application in electromagnetism using FETI-2LM method. For problems with a single right-hand-side, deriving several search directions that make sense from the optimal one constructed by the Krylov method is not so easy. The recently developed S-FETI method gives a very good approach that does not only improve parallel efficiency but can also reduce the global computational cost in the case of very heterogeneous problems.
MSC Codes : 65F10 - Iterative methods for linear systems
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)
65Y05 - Parallel computation (numerical methods)
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 03/08/2016 Conference Date : 27/07/2016 Subseries : Research talks arXiv category : Numerical Analysis Mathematical Area(s) : Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Video Time : 01:10:22 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-07-27_Roux.mp4 
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Information on the Event
Event Title : CEMRACS: Numerical challenges in parallel scientific computing / CEMRACS : Défis numériques en calcul scientifique parallèleEvent Organizers : Grigori, Laura ; Japhet, Caroline ; Moireau, Philippe ; Parnaudeau, Philippe Dates : 18/07/16 - 26/08/16 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1430.html
Citation Data
DOI : 10.24350/CIRM.V.19026103Cite this video as: Roux, François-Xavier (2016). Efficient iterative solvers: FETI methods with multiple search directions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19026103 URI : http://dx.doi.org/10.24350/CIRM.V.19026103 |
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