Multilevel balancing domain decomposition at extreme scales

© 2016 Society for Industrial and Applied Mathematics. In this paper we present a fully distributed, communicator-aware, recursive, and interlevel-overlapped message-passing implementation of the multilevel balancing domain decomposition by constraints (MLBDDC) preconditioner. The implementation hig...

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Autores: Badia, Santiago|||0000-0003-2391-4086, Martín Huertas, Alberto Francisco|||0000-0001-5751-4561, Principe, Ricardo Javier|||0000-0002-1478-2651
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/86557
Acceso en línea:https://hdl.handle.net/2117/86557
https://dx.doi.org/10.1137/15M1013511
Access Level:acceso abierto
Palabra clave:High performance computing
Domain decomposition
Finite elements
High-performance computing
Parallel computing
Perdominant preconditioning
Scientific software
Càlcul intensiu (Informàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica
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network_acronym_str ES
network_name_str España
repository_id_str
spelling Multilevel balancing domain decomposition at extreme scalesBadia, Santiago|||0000-0003-2391-4086Martín Huertas, Alberto Francisco|||0000-0001-5751-4561Principe, Ricardo Javier|||0000-0002-1478-2651High performance computingDomain decompositionFinite elementsHigh-performance computingParallel computingPerdominant preconditioningScientific softwareCàlcul intensiu (Informàtica)Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàticaÀrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica© 2016 Society for Industrial and Applied Mathematics. In this paper we present a fully distributed, communicator-aware, recursive, and interlevel-overlapped message-passing implementation of the multilevel balancing domain decomposition by constraints (MLBDDC) preconditioner. The implementation highly relies on subcommunicators in order to achieve the desired effect of coarse-grain overlapping of computation and communication, and communication and communication among levels in the hierarchy (namely, interlevel overlapping). Essentially, the main communicator is split into as many nonoverlapping subsets of message-passing interface (MPI) tasks (i.e., MPI subcommunicators) as levels in the hierarchy. Provided that specialized resources (cores and memory) are devoted to each level, a careful rescheduling and mapping of all the computations and communications in the algorithm lets a high degree of overlapping be exploited among levels. All subroutines and associated data structures are expressed recursively, and therefore MLBDDC preconditioners with an arbitrary number of levels can be built while re-using significant and recurrent parts of the codes. This approach leads to excellent weak scalability results as soon as level-1 tasks can fully overlap coarser-levels duties. We provide a model to indicate how to choose the number of levels and coarsening ratios between consecutive levels and determine qualitatively the scalability limits for a given choice. We have carried out a comprehensive weak scalability analysis of the proposed implementation for the three-dimensional Laplacian and linear elasticity problems on structured and unstructured meshes. Excellent weak scalability results have been obtained up to 458,752 IBM BG/Q cores and 1.8 million MPI being, being the first time that exact domain decomposition preconditioners (only based on sparse direct solvers) reach these scales.20162016-01-0120162016-05-04journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/86557https://dx.doi.org/10.1137/15M1013511reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/865572026-05-27T15:37:01Z
dc.title.none.fl_str_mv Multilevel balancing domain decomposition at extreme scales
title Multilevel balancing domain decomposition at extreme scales
spellingShingle Multilevel balancing domain decomposition at extreme scales
Badia, Santiago|||0000-0003-2391-4086
High performance computing
Domain decomposition
Finite elements
High-performance computing
Parallel computing
Perdominant preconditioning
Scientific software
Càlcul intensiu (Informàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica
title_short Multilevel balancing domain decomposition at extreme scales
title_full Multilevel balancing domain decomposition at extreme scales
title_fullStr Multilevel balancing domain decomposition at extreme scales
title_full_unstemmed Multilevel balancing domain decomposition at extreme scales
title_sort Multilevel balancing domain decomposition at extreme scales
dc.creator.none.fl_str_mv Badia, Santiago|||0000-0003-2391-4086
Martín Huertas, Alberto Francisco|||0000-0001-5751-4561
Principe, Ricardo Javier|||0000-0002-1478-2651
author Badia, Santiago|||0000-0003-2391-4086
author_facet Badia, Santiago|||0000-0003-2391-4086
Martín Huertas, Alberto Francisco|||0000-0001-5751-4561
Principe, Ricardo Javier|||0000-0002-1478-2651
author_role author
author2 Martín Huertas, Alberto Francisco|||0000-0001-5751-4561
Principe, Ricardo Javier|||0000-0002-1478-2651
author2_role author
author
dc.subject.none.fl_str_mv High performance computing
Domain decomposition
Finite elements
High-performance computing
Parallel computing
Perdominant preconditioning
Scientific software
Càlcul intensiu (Informàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica
topic High performance computing
Domain decomposition
Finite elements
High-performance computing
Parallel computing
Perdominant preconditioning
Scientific software
Càlcul intensiu (Informàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica
description © 2016 Society for Industrial and Applied Mathematics. In this paper we present a fully distributed, communicator-aware, recursive, and interlevel-overlapped message-passing implementation of the multilevel balancing domain decomposition by constraints (MLBDDC) preconditioner. The implementation highly relies on subcommunicators in order to achieve the desired effect of coarse-grain overlapping of computation and communication, and communication and communication among levels in the hierarchy (namely, interlevel overlapping). Essentially, the main communicator is split into as many nonoverlapping subsets of message-passing interface (MPI) tasks (i.e., MPI subcommunicators) as levels in the hierarchy. Provided that specialized resources (cores and memory) are devoted to each level, a careful rescheduling and mapping of all the computations and communications in the algorithm lets a high degree of overlapping be exploited among levels. All subroutines and associated data structures are expressed recursively, and therefore MLBDDC preconditioners with an arbitrary number of levels can be built while re-using significant and recurrent parts of the codes. This approach leads to excellent weak scalability results as soon as level-1 tasks can fully overlap coarser-levels duties. We provide a model to indicate how to choose the number of levels and coarsening ratios between consecutive levels and determine qualitatively the scalability limits for a given choice. We have carried out a comprehensive weak scalability analysis of the proposed implementation for the three-dimensional Laplacian and linear elasticity problems on structured and unstructured meshes. Excellent weak scalability results have been obtained up to 458,752 IBM BG/Q cores and 1.8 million MPI being, being the first time that exact domain decomposition preconditioners (only based on sparse direct solvers) reach these scales.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01
2016
2016-05-04
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/86557
https://dx.doi.org/10.1137/15M1013511
url https://hdl.handle.net/2117/86557
https://dx.doi.org/10.1137/15M1013511
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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