Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines

This paper derives theoretical estimates of the computational cost for isogeometric multi-frontal direct solver executed on parallel distributed memory machines. We show theoretically that for the Cp-1 global continuity of the isogeometric solution, both the computational cost and the communication...

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Autores: Wozniak, Maciej, Paszynski, Maciej, Pardo, David, Dalcin, Lisandro Daniel, Calo, Victor Manuel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/78612
Acceso en línea:http://hdl.handle.net/11336/78612
Access Level:acceso abierto
Palabra clave:Communication Cost
Computational Cost
Isogeometric Analysis
Multi-Frontal Direct Solver
Parallel Distributed Memory Machine
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spelling Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machinesWozniak, MaciejPaszynski, MaciejPardo, DavidDalcin, Lisandro DanielCalo, Victor ManuelCommunication CostComputational CostIsogeometric AnalysisMulti-Frontal Direct SolverParallel Distributed Memory MachineThis paper derives theoretical estimates of the computational cost for isogeometric multi-frontal direct solver executed on parallel distributed memory machines. We show theoretically that for the Cp-1 global continuity of the isogeometric solution, both the computational cost and the communication cost of a direct solver are of order O(log(N)p2) for the one dimensional (1D) case, O(Np2) for the two dimensional (2D) case, and O(N4/3p2) for the three dimensional (3D) case, where N is the number of degrees of freedom and p is the polynomial order of the B-spline basis functions. The theoretical estimates are verified by numerical experiments performed with three parallel multi-frontal direct solvers: MUMPS, PaStiX and SuperLU, available through PETIGA toolkit built on top of PETSc. Numerical results confirm these theoretical estimates both in terms of p and N. For a given problem size, the strong efficiency rapidly decreases as the number of processors increases, becoming about 20% for 256 processors for a 3D example with 1283 unknowns and linear B-splines with C0 global continuity, and 15% for a 3D example with 643 unknowns and quartic B-splines with C3 global continuity. At the same time, one cannot arbitrarily increase the problem size, since the memory required by higher order continuity spaces is large, quickly consuming all the available memory resources even in the parallel distributed memory version. Numerical results also suggest that the use of distributed parallel machines is highly beneficial when solving higher order continuity spaces, although the number of processors that one can efficiently employ is somehow limited.Fil: Wozniak, Maciej. Agh University Of Science And Technology; PoloniaFil: Paszynski, Maciej. Agh University Of Science And Technology; PoloniaFil: Pardo, David. Universidad del Pais Vasco - Euskal Herriko Unibertsitatea, Campus Bizkaia; EspañaFil: Dalcin, Lisandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaFil: Calo, Victor Manuel. King Abdullah University Of Science And Technology; Arabia SauditaElsevier Science Sa2015-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/78612Wozniak, Maciej; Paszynski, Maciej ; Pardo, David; Dalcin, Lisandro Daniel; Calo, Victor Manuel; Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines; Elsevier Science Sa; Computer Methods in Applied Mechanics and Engineering; 284; 2-2015; 971-9870045-7825CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2014.11.020info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:34:56Zoai:ri.conicet.gov.ar:11336/78612instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982024-05-08 13:34:56.552CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
title Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
spellingShingle Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
Wozniak, Maciej
Communication Cost
Computational Cost
Isogeometric Analysis
Multi-Frontal Direct Solver
Parallel Distributed Memory Machine
title_short Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
title_full Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
title_fullStr Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
title_full_unstemmed Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
title_sort Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
dc.creator.none.fl_str_mv Wozniak, Maciej
Paszynski, Maciej
Pardo, David
Dalcin, Lisandro Daniel
Calo, Victor Manuel
author Wozniak, Maciej
author_facet Wozniak, Maciej
Paszynski, Maciej
Pardo, David
Dalcin, Lisandro Daniel
Calo, Victor Manuel
author_role author
author2 Paszynski, Maciej
Pardo, David
Dalcin, Lisandro Daniel
Calo, Victor Manuel
author2_role author
author
author
author
dc.subject.none.fl_str_mv Communication Cost
Computational Cost
Isogeometric Analysis
Multi-Frontal Direct Solver
Parallel Distributed Memory Machine
topic Communication Cost
Computational Cost
Isogeometric Analysis
Multi-Frontal Direct Solver
Parallel Distributed Memory Machine
description This paper derives theoretical estimates of the computational cost for isogeometric multi-frontal direct solver executed on parallel distributed memory machines. We show theoretically that for the Cp-1 global continuity of the isogeometric solution, both the computational cost and the communication cost of a direct solver are of order O(log(N)p2) for the one dimensional (1D) case, O(Np2) for the two dimensional (2D) case, and O(N4/3p2) for the three dimensional (3D) case, where N is the number of degrees of freedom and p is the polynomial order of the B-spline basis functions. The theoretical estimates are verified by numerical experiments performed with three parallel multi-frontal direct solvers: MUMPS, PaStiX and SuperLU, available through PETIGA toolkit built on top of PETSc. Numerical results confirm these theoretical estimates both in terms of p and N. For a given problem size, the strong efficiency rapidly decreases as the number of processors increases, becoming about 20% for 256 processors for a 3D example with 1283 unknowns and linear B-splines with C0 global continuity, and 15% for a 3D example with 643 unknowns and quartic B-splines with C3 global continuity. At the same time, one cannot arbitrarily increase the problem size, since the memory required by higher order continuity spaces is large, quickly consuming all the available memory resources even in the parallel distributed memory version. Numerical results also suggest that the use of distributed parallel machines is highly beneficial when solving higher order continuity spaces, although the number of processors that one can efficiently employ is somehow limited.
publishDate 2015
dc.date.none.fl_str_mv 2015-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/78612
Wozniak, Maciej; Paszynski, Maciej ; Pardo, David; Dalcin, Lisandro Daniel; Calo, Victor Manuel; Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines; Elsevier Science Sa; Computer Methods in Applied Mechanics and Engineering; 284; 2-2015; 971-987
0045-7825
CONICET Digital
CONICET
url http://hdl.handle.net/11336/78612
identifier_str_mv Wozniak, Maciej; Paszynski, Maciej ; Pardo, David; Dalcin, Lisandro Daniel; Calo, Victor Manuel; Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines; Elsevier Science Sa; Computer Methods in Applied Mechanics and Engineering; 284; 2-2015; 971-987
0045-7825
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2014.11.020
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science Sa
publisher.none.fl_str_mv Elsevier Science Sa
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 15,81155

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