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

Maciej Woźniak; Krzysztof M. Kuźnik; Maciej R. Paszyński; Victor M. Calo; D. Pardo

doi:10.1016/j.camwa.2014.03.017

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

Maciej Woźniak, Krzysztof M. Kuźnik, Maciej R. Paszyński, Victor M. Calo, D. Pardo

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1864-1883
Number of pages	20
Journal	Computers & Mathematics with Applications
Volume	67
Issue number	10
DOIs	https://doi.org/10.1016/j.camwa.2014.03.017
State	Published - Jun 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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).

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2014.03.017

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title = "Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers",

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. {\textcopyright} 2014 Elsevier Ltd. All rights reserved.",

author = "Maciej Wo{\'z}niak and Ku{\'z}nik, {Krzysztof M.} and Paszy{\'n}ski, {Maciej R.} and Calo, {Victor M.} and D. Pardo",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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).",

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AU - Woźniak, Maciej

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AU - Calo, Victor M.

AU - Pardo, D.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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).

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N2 - 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.

AB - 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.

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

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