Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers

Handle URI:
http://hdl.handle.net/10754/563571
Title:
Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers
Authors:
Woźniak, Maciej; Kuźnik, Krzysztof M.; Paszyński, Maciej R.; Calo, Victor M. ( 0000-0002-1805-4045 ) ; Pardo, D.
Abstract:
In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O( p2log(N/p)) for one dimensional problems, O(Np2) for two dimensional problems, and O(N4/3p2) for three dimensional problems, where N is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to O(N p2) for the one dimensional case, O(N1.5p3) for the two dimensional case, and O(N2p3) for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of N and p. Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions. © 2014 Elsevier Ltd. All rights reserved.
KAUST Department:
Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Numerical Porous Media SRI Center (NumPor)
Publisher:
Elsevier BV
Journal:
Computers & Mathematics with Applications
Issue Date:
Jun-2014
DOI:
10.1016/j.camwa.2014.03.017
Type:
Article
ISSN:
08981221
Sponsors:
The work of KK was supported by the Polish National Science Center Grant No. NN 519 447739. The work of MP was supported by the Polish National Science Center Grant Nos. NN 519 447739 and DEC-2011/01/B/ST6/00674. The work of MW was supported by Polish National Science Grant Nos. DEC-2011/01/B/ST6/00674 and 2012/07/B/ST6/01229. The work of DP was partially funded by the Project of the Spanish Ministry of Sciences and Innovation MTM2010-16511, the Laboratory of Mathematics (UFI 11/52), and the Ibero American Project CYTED 2011 (P711RT0278).
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorWoźniak, Maciejen
dc.contributor.authorKuźnik, Krzysztof M.en
dc.contributor.authorPaszyński, Maciej R.en
dc.contributor.authorCalo, Victor M.en
dc.contributor.authorPardo, D.en
dc.date.accessioned2015-08-03T11:54:44Zen
dc.date.available2015-08-03T11:54:44Zen
dc.date.issued2014-06en
dc.identifier.issn08981221en
dc.identifier.doi10.1016/j.camwa.2014.03.017en
dc.identifier.urihttp://hdl.handle.net/10754/563571en
dc.description.abstractIn this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O( p2log(N/p)) for one dimensional problems, O(Np2) for two dimensional problems, and O(N4/3p2) for three dimensional problems, where N is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to O(N p2) for the one dimensional case, O(N1.5p3) for the two dimensional case, and O(N2p3) for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of N and p. Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions. © 2014 Elsevier Ltd. All rights reserved.en
dc.description.sponsorshipThe work of KK was supported by the Polish National Science Center Grant No. NN 519 447739. The work of MP was supported by the Polish National Science Center Grant Nos. NN 519 447739 and DEC-2011/01/B/ST6/00674. The work of MW was supported by Polish National Science Grant Nos. DEC-2011/01/B/ST6/00674 and 2012/07/B/ST6/01229. The work of DP was partially funded by the Project of the Spanish Ministry of Sciences and Innovation MTM2010-16511, the Laboratory of Mathematics (UFI 11/52), and the Ibero American Project CYTED 2011 (P711RT0278).en
dc.publisherElsevier BVen
dc.subjectComputational costen
dc.subjectIsogeometric finite element methoden
dc.subjectMulti-frontal direct solveren
dc.subjectNVIDIA CUDA GPUen
dc.titleComputational cost estimates for parallel shared memory isogeometric multi-frontal solversen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalComputers & Mathematics with Applicationsen
dc.contributor.institutionAGH University of Science and Technology, Krakow, Polanden
dc.contributor.institutionUniversity of the Basque Country (UPV/EHU), BCAM, Ikerbasque, Bilbao, Spainen
kaust.authorCalo, Victor M.en
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