High-performance model reduction techniques in computational multiscale homogenization

Autores
Hernandez, J. A.; Oliver, J.; Huespe, Alfredo Edmundo; Caicedo, M. A.; Cante, J. C.
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A novel model-order reduction technique for the solution of the fine-scale equilibrium problem appearing in computational homogenization is presented. The reduced set of empirical shape functions is obtained using a partitioned version — that accounts for the elastic/inelastic character of the solution — of the Proper Orthogonal Decomposition (POD). On the other hand, it is shown that the standard approach of replacing the nonaffine term by an interpolant constructed using only POD modes leads to ill-posed formulations. We demonstrate that this ill-posedness can be avoided by enriching the approximation space with the span of the gradient of the empirical shape functions. Furthermore, interpolation points are chosen guided, not only by accuracy requirements, but also by stability considerations. The approach is assessed in the homogenization of a highly complex porous metal material. Computed results show that computational complexity is independent of the size and geometrical complexity of the Representative Volume Element. The speedup factor is over three orders of magnitude — as compared with finite element analysis — whereas the maximum error in stresses is less than 10%.
Fil: Hernandez, J. A.. Technical University of Catalonia; España
Fil: Oliver, J.. Technical University of Catalonia; España
Fil: Huespe, Alfredo Edmundo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; Argentina. Universidad Politecnica de Catalunya; España
Fil: Caicedo, M. A.. Technical University of Catalonia; España
Fil: Cante, J. C.. Technical University of Catalonia; España
Materia
Multiscale
Homogenization
Model Reduction
High-Performance Reduced-Order Model
Hyperreduction
Pod
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19675
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/19675
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling High-performance model reduction techniques in computational multiscale homogenizationHernandez, J. A.Oliver, J.Huespe, Alfredo EdmundoCaicedo, M. A.Cante, J. C.MultiscaleHomogenizationModel ReductionHigh-Performance Reduced-Order ModelHyperreductionPodhttps://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2A novel model-order reduction technique for the solution of the fine-scale equilibrium problem appearing in computational homogenization is presented. The reduced set of empirical shape functions is obtained using a partitioned version — that accounts for the elastic/inelastic character of the solution — of the Proper Orthogonal Decomposition (POD). On the other hand, it is shown that the standard approach of replacing the nonaffine term by an interpolant constructed using only POD modes leads to ill-posed formulations. We demonstrate that this ill-posedness can be avoided by enriching the approximation space with the span of the gradient of the empirical shape functions. Furthermore, interpolation points are chosen guided, not only by accuracy requirements, but also by stability considerations. The approach is assessed in the homogenization of a highly complex porous metal material. Computed results show that computational complexity is independent of the size and geometrical complexity of the Representative Volume Element. The speedup factor is over three orders of magnitude — as compared with finite element analysis — whereas the maximum error in stresses is less than 10%.Fil: Hernandez, J. A.. Technical University of Catalonia; EspañaFil: Oliver, J.. Technical University of Catalonia; EspañaFil: Huespe, Alfredo Edmundo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; Argentina. Universidad Politecnica de Catalunya; EspañaFil: Caicedo, M. A.. Technical University of Catalonia; EspañaFil: Cante, J. C.. Technical University of Catalonia; EspañaElsevier2014-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19675Hernandez, J. A.; Oliver, J.; Huespe, Alfredo Edmundo; Caicedo, M. A.; Cante, J. C.; High-performance model reduction techniques in computational multiscale homogenization; Elsevier; Computer Methods In Applied Mechanics And Engineering; 276; 3-2014; 149-1890045-7825CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2014.03.011info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0045782514000978?via%3Dihubinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:37:40Zoai:ri.conicet.gov.ar:11336/19675instacron: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 10:37:41.024CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv High-performance model reduction techniques in computational multiscale homogenization
title High-performance model reduction techniques in computational multiscale homogenization
spellingShingle High-performance model reduction techniques in computational multiscale homogenization
Hernandez, J. A.
Multiscale
Homogenization
Model Reduction
High-Performance Reduced-Order Model
Hyperreduction
Pod
title_short High-performance model reduction techniques in computational multiscale homogenization
title_full High-performance model reduction techniques in computational multiscale homogenization
title_fullStr High-performance model reduction techniques in computational multiscale homogenization
title_full_unstemmed High-performance model reduction techniques in computational multiscale homogenization
title_sort High-performance model reduction techniques in computational multiscale homogenization
dc.creator.none.fl_str_mv Hernandez, J. A.
Oliver, J.
Huespe, Alfredo Edmundo
Caicedo, M. A.
Cante, J. C.
author Hernandez, J. A.
author_facet Hernandez, J. A.
Oliver, J.
Huespe, Alfredo Edmundo
Caicedo, M. A.
Cante, J. C.
author_role author
author2 Oliver, J.
Huespe, Alfredo Edmundo
Caicedo, M. A.
Cante, J. C.
author2_role author
author
author
author
dc.subject.none.fl_str_mv Multiscale
Homogenization
Model Reduction
High-Performance Reduced-Order Model
Hyperreduction
Pod
topic Multiscale
Homogenization
Model Reduction
High-Performance Reduced-Order Model
Hyperreduction
Pod
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv A novel model-order reduction technique for the solution of the fine-scale equilibrium problem appearing in computational homogenization is presented. The reduced set of empirical shape functions is obtained using a partitioned version — that accounts for the elastic/inelastic character of the solution — of the Proper Orthogonal Decomposition (POD). On the other hand, it is shown that the standard approach of replacing the nonaffine term by an interpolant constructed using only POD modes leads to ill-posed formulations. We demonstrate that this ill-posedness can be avoided by enriching the approximation space with the span of the gradient of the empirical shape functions. Furthermore, interpolation points are chosen guided, not only by accuracy requirements, but also by stability considerations. The approach is assessed in the homogenization of a highly complex porous metal material. Computed results show that computational complexity is independent of the size and geometrical complexity of the Representative Volume Element. The speedup factor is over three orders of magnitude — as compared with finite element analysis — whereas the maximum error in stresses is less than 10%.
Fil: Hernandez, J. A.. Technical University of Catalonia; España
Fil: Oliver, J.. Technical University of Catalonia; España
Fil: Huespe, Alfredo Edmundo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; Argentina. Universidad Politecnica de Catalunya; España
Fil: Caicedo, M. A.. Technical University of Catalonia; España
Fil: Cante, J. C.. Technical University of Catalonia; España
description A novel model-order reduction technique for the solution of the fine-scale equilibrium problem appearing in computational homogenization is presented. The reduced set of empirical shape functions is obtained using a partitioned version — that accounts for the elastic/inelastic character of the solution — of the Proper Orthogonal Decomposition (POD). On the other hand, it is shown that the standard approach of replacing the nonaffine term by an interpolant constructed using only POD modes leads to ill-posed formulations. We demonstrate that this ill-posedness can be avoided by enriching the approximation space with the span of the gradient of the empirical shape functions. Furthermore, interpolation points are chosen guided, not only by accuracy requirements, but also by stability considerations. The approach is assessed in the homogenization of a highly complex porous metal material. Computed results show that computational complexity is independent of the size and geometrical complexity of the Representative Volume Element. The speedup factor is over three orders of magnitude — as compared with finite element analysis — whereas the maximum error in stresses is less than 10%.
publishDate 2014
dc.date.none.fl_str_mv 2014-03
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/11336/19675
Hernandez, J. A.; Oliver, J.; Huespe, Alfredo Edmundo; Caicedo, M. A.; Cante, J. C.; High-performance model reduction techniques in computational multiscale homogenization; Elsevier; Computer Methods In Applied Mechanics And Engineering; 276; 3-2014; 149-189
0045-7825
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19675
identifier_str_mv Hernandez, J. A.; Oliver, J.; Huespe, Alfredo Edmundo; Caicedo, M. A.; Cante, J. C.; High-performance model reduction techniques in computational multiscale homogenization; Elsevier; Computer Methods In Applied Mechanics And Engineering; 276; 3-2014; 149-189
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.2014.03.011
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0045782514000978?via%3Dihub
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
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str 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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score 13.070432

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