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dc.contributor.authorBadia, Santiago
dc.contributor.authorMartín Huertas, Alberto Francisco
dc.contributor.authorPrincipe, Ricardo Javier
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Mecànica de Fluids
dc.identifier.citationBadia, S., Martín, A. F., Principe, J. Multilevel balancing domain decomposition at extreme scales. "SIAM journal on scientific computing", 01 Gener 2016, vol. 38, núm. 1, p. C22-C52.
dc.description.abstract© 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.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
dc.subjectÀrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica
dc.subject.lcshHigh performance computing
dc.subject.otherDomain decomposition
dc.subject.otherFinite elements
dc.subject.otherHigh-performance computing
dc.subject.otherParallel computing
dc.subject.otherPerdominant preconditioning
dc.subject.otherScientific software
dc.titleMultilevel balancing domain decomposition at extreme scales
dc.subject.lemacCàlcul intensiu (Informàtica)
dc.contributor.groupUniversitat Politècnica de Catalunya. ANiComp - Anàlisi numèrica i computació científica
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
local.citation.authorBadia, S.; Martín, A. F.; Principe, J.
local.citation.publicationNameSIAM journal on scientific computing

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