Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
- Autores
- Wozniak, Maciej; Paszynski, Maciej; Pardo, David; Dalcin, Lisandro Daniel; Calo, Victor Manuel
- Año de publicación
- 2015
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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.
Fil: Wozniak, Maciej. Agh University Of Science And Technology; Polonia
Fil: Paszynski, Maciej. Agh University Of Science And Technology; Polonia
Fil: Pardo, David. Universidad del Pais Vasco - Euskal Herriko Unibertsitatea, Campus Bizkaia; España
Fil: 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; Argentina
Fil: Calo, Victor Manuel. King Abdullah University Of Science And Technology; Arabia Saudita - Materia
-
Communication Cost
Computational Cost
Isogeometric Analysis
Multi-Frontal Direct Solver
Parallel Distributed Memory Machine - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/78612
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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 Técnicas2025-09-29T09:35:52Zoai: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:34982025-09-29 09:35:52.898CONICET 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 |
dc.description.none.fl_txt_mv |
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. Fil: Wozniak, Maciej. Agh University Of Science And Technology; Polonia Fil: Paszynski, Maciej. Agh University Of Science And Technology; Polonia Fil: Pardo, David. Universidad del Pais Vasco - Euskal Herriko Unibertsitatea, Campus Bizkaia; España Fil: 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; Argentina Fil: Calo, Victor Manuel. King Abdullah University Of Science And Technology; Arabia Saudita |
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 |
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CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
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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13.070432 |