Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems

In the framework of stochastic non-intrusive finite element modeling, a common practice is using Monte Carlo simulation. The main drawback of this approach is the computational cost, because it requires computing a large number of deterministic finite element solutions. The different Monte Carlo sam...

Descripción completa

Detalles Bibliográficos
Autores: Florentin, Eric, Díez, Pedro|||0000-0001-6464-6407
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/116664
Acceso en línea:https://hdl.handle.net/2117/116664
https://dx.doi.org/10.1016/j.cma.2012.03.016
Access Level:acceso abierto
Palabra clave:Numerical analysis
Stochastic analysis
Reduced basis
Adaptivity
Stochastic modeling
Goal-oriented error assessment
Anàlisi numèrica
Anàlisi estocàstica
Classificació AMS::65 Numerical analysis::65G Error analysis and interval analysis
Classificació AMS::60 Probability theory and stochastic processes::60H Stochastic analysis
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariant
id ES_55f2e3aab47798555cc8fadc8dfd99e9
oai_identifier_str oai:upcommons.upc.edu:2117/116664
network_acronym_str ES
network_name_str España
repository_id_str
spelling Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problemsFlorentin, EricDíez, Pedro|||0000-0001-6464-6407Numerical analysisStochastic analysisReduced basisAdaptivityStochastic modelingGoal-oriented error assessmentAnàlisi numèricaAnàlisi estocàsticaClassificació AMS::65 Numerical analysis::65G Error analysis and interval analysisClassificació AMS::60 Probability theory and stochastic processes::60H Stochastic analysisÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèricaÀrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariantIn the framework of stochastic non-intrusive finite element modeling, a common practice is using Monte Carlo simulation. The main drawback of this approach is the computational cost, because it requires computing a large number of deterministic finite element solutions. The different Monte Carlo samplings correspond to realizations of the random variables characterizing the stochastic behavior of the model. Thus, this requires solving a set deterministic problems with the same structure, that is with variations concerning the material parameters and the loading data. Consequently, the different problems to be solved are in practice similar to each other. The reduced basis strategy is therefore a sensible option to reduce computational cost, provided that the quality of the numerical solution is guaranteed. The paper introduces a goal-oriented strategy allowing to successively enrich the reduced basis along the Monte Carlo process. The method is based on assessing the error of the reduced basis solution with a residual estimate for the prescribed quantity of interest. The efficiency of the proposed approach, which is particularly important if the number of independent random variables is large, is illustrated in 1D and 2D mechanical examples.Peer Reviewed20122012-06-0120182018-04-25journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/116664https://dx.doi.org/10.1016/j.cma.2012.03.016reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1166642026-05-27T15:37:01Z
dc.title.none.fl_str_mv Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems
title Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems
spellingShingle Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems
Florentin, Eric
Numerical analysis
Stochastic analysis
Reduced basis
Adaptivity
Stochastic modeling
Goal-oriented error assessment
Anàlisi numèrica
Anàlisi estocàstica
Classificació AMS::65 Numerical analysis::65G Error analysis and interval analysis
Classificació AMS::60 Probability theory and stochastic processes::60H Stochastic analysis
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariant
title_short Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems
title_full Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems
title_fullStr Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems
title_full_unstemmed Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems
title_sort Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems
dc.creator.none.fl_str_mv Florentin, Eric
Díez, Pedro|||0000-0001-6464-6407
author Florentin, Eric
author_facet Florentin, Eric
Díez, Pedro|||0000-0001-6464-6407
author_role author
author2 Díez, Pedro|||0000-0001-6464-6407
author2_role author
dc.subject.none.fl_str_mv Numerical analysis
Stochastic analysis
Reduced basis
Adaptivity
Stochastic modeling
Goal-oriented error assessment
Anàlisi numèrica
Anàlisi estocàstica
Classificació AMS::65 Numerical analysis::65G Error analysis and interval analysis
Classificació AMS::60 Probability theory and stochastic processes::60H Stochastic analysis
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariant
topic Numerical analysis
Stochastic analysis
Reduced basis
Adaptivity
Stochastic modeling
Goal-oriented error assessment
Anàlisi numèrica
Anàlisi estocàstica
Classificació AMS::65 Numerical analysis::65G Error analysis and interval analysis
Classificació AMS::60 Probability theory and stochastic processes::60H Stochastic analysis
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariant
description In the framework of stochastic non-intrusive finite element modeling, a common practice is using Monte Carlo simulation. The main drawback of this approach is the computational cost, because it requires computing a large number of deterministic finite element solutions. The different Monte Carlo samplings correspond to realizations of the random variables characterizing the stochastic behavior of the model. Thus, this requires solving a set deterministic problems with the same structure, that is with variations concerning the material parameters and the loading data. Consequently, the different problems to be solved are in practice similar to each other. The reduced basis strategy is therefore a sensible option to reduce computational cost, provided that the quality of the numerical solution is guaranteed. The paper introduces a goal-oriented strategy allowing to successively enrich the reduced basis along the Monte Carlo process. The method is based on assessing the error of the reduced basis solution with a residual estimate for the prescribed quantity of interest. The efficiency of the proposed approach, which is particularly important if the number of independent random variables is large, is illustrated in 1D and 2D mechanical examples.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-06-01
2018
2018-04-25
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/116664
https://dx.doi.org/10.1016/j.cma.2012.03.016
url https://hdl.handle.net/2117/116664
https://dx.doi.org/10.1016/j.cma.2012.03.016
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869408344358256640
score 15.301603

Similares en LA Referencia