Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis

Handle URI:
http://hdl.handle.net/10754/552428
Title:
Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis
Authors:
Kuźnik, Krzysztof; Paszyński, Maciej; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
This paper introduces the graph grammar based model for developing multi-thread multi-frontal parallel direct solver for two dimensional isogeometric finite element method. Execution of the solver algorithm has been expressed as the sequence of graph grammar productions. At the beginning productions construct the elimination tree with leaves corresponding to finite elements. Following sequence of graph grammar productions generates element frontal matri-ces at leaf nodes, merges matrices at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar productions allows us to explore the concurrency of the algorithm. The graph grammar productions are grouped into sets of independent tasks that can be executed concurrently. The resulting concurrent multi-frontal solver algorithm is implemented and tested on NVIDIA GPU, providing O(NlogN) execution time complexity where N is the number of degrees of freedom. We have confirmed this complexity by solving up to 1 million of degrees of freedom with 448 cores GPU.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis 2012, 9:1454 Procedia Computer Science
Publisher:
Elsevier BV
Journal:
Procedia Computer Science
Conference/Event name:
12th Annual International Conference on Computational Science, ICCS 2012
Issue Date:
2-Jun-2012
DOI:
10.1016/j.procs.2012.04.160
Type:
Conference Paper
ISSN:
18770509
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S1877050912002815
Appears in Collections:
Conference Papers; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKuźnik, Krzysztofen
dc.contributor.authorPaszyński, Maciejen
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-05-07T13:46:55Zen
dc.date.available2015-05-07T13:46:55Zen
dc.date.issued2012-06-02en
dc.identifier.citationGraph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis 2012, 9:1454 Procedia Computer Scienceen
dc.identifier.issn18770509en
dc.identifier.doi10.1016/j.procs.2012.04.160en
dc.identifier.urihttp://hdl.handle.net/10754/552428en
dc.description.abstractThis paper introduces the graph grammar based model for developing multi-thread multi-frontal parallel direct solver for two dimensional isogeometric finite element method. Execution of the solver algorithm has been expressed as the sequence of graph grammar productions. At the beginning productions construct the elimination tree with leaves corresponding to finite elements. Following sequence of graph grammar productions generates element frontal matri-ces at leaf nodes, merges matrices at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar productions allows us to explore the concurrency of the algorithm. The graph grammar productions are grouped into sets of independent tasks that can be executed concurrently. The resulting concurrent multi-frontal solver algorithm is implemented and tested on NVIDIA GPU, providing O(NlogN) execution time complexity where N is the number of degrees of freedom. We have confirmed this complexity by solving up to 1 million of degrees of freedom with 448 cores GPU.en
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S1877050912002815en
dc.rightsArchived with thanks to Procedia Computer Science. http://creativecommons.org/licenses/by-nc-nd/3.0/en
dc.subjectparallel computingen
dc.subjectisogeometric analysisen
dc.subjectmodels of concurrencyen
dc.subjectgraph grammaren
dc.titleGraph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysisen
dc.typeConference Paperen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalProcedia Computer Scienceen
dc.conference.date2012-06-04 to 2012-06-06en
dc.conference.name12th Annual International Conference on Computational Science, ICCS 2012en
dc.conference.locationOmaha, NB, USAen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionAGH University of Science and Technology, Krakow, Polanden
kaust.authorCalo, Victor M.en
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