A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers&apos

[EN] The variability of the data and the incomplete knowledge of the true physics require the incorporation of randomness into the formulation of mathematical models. In this setting, the deterministic numerical methods cannot capture the propagation of the uncertainty from the inputs to the model o...

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Autores: Calatayud, Julia, Jornet, Marc, Cortés, J.-C.|||0000-0002-6528-2155
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/181317
Acceso en línea:https://riunet.upv.es/handle/10251/181317
Access Level:acceso abierto
Palabra clave:Burgers&apos
equation
GPC expansion
Navier-Stokes equation
Perturbation method
Randomness analysis
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spelling A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers&apospartial differential equationCalatayud, JuliaJornet, MarcCortés, J.-C.|||0000-0002-6528-2155Burgers&aposequationGPC expansionNavier-Stokes equationPerturbation methodRandomness analysis[EN] The variability of the data and the incomplete knowledge of the true physics require the incorporation of randomness into the formulation of mathematical models. In this setting, the deterministic numerical methods cannot capture the propagation of the uncertainty from the inputs to the model output. For some problems, such as the Burgers' equation (simplification to understand properties of the Navier¿Stokes equations), a small variation in the parameters causes nonnegligible changes in the output. Thus, suitable techniques for uncertainty quantification must be used. The generalized polynomial chaos (gPC) method has been successfully applied to compute the location of the transition layer of the steady-state solution, when a small uncertainty is incorporated into the boundary. On the contrary, the classical perturbation method does not give reliable results, due to the uncertainty magnitude of the output. We propose a modification of the perturbation method that converges and is comparable with the gPC approach in terms of efficiency and rate of convergence. The method is even applicable when the input random parameters are dependent random variables.This work has been supported by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI), and Fondo Europeo de Desarrollo Regional (FEDER UE) Grant MTM2017-89664-P. The author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.John Wiley & SonsFacultad de Administración y Dirección de EmpresasDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarAGENCIA ESTATAL DE INVESTIGACIONEuropean Regional Development FundUniversitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20212021-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/181317reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-89664-P PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION Y APLICACIONESUniversitat Politècnica de València https://doi.org/10.13039/501100004233 PAID Programa de Ayudas de Investigación y Desarrolloopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1813172026-06-13T07:49:27Z
dc.title.none.fl_str_mv A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers&apos
partial differential equation
title A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers&apos
spellingShingle A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers&apos
Calatayud, Julia
Burgers&apos
equation
GPC expansion
Navier-Stokes equation
Perturbation method
Randomness analysis
title_short A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers&apos
title_full A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers&apos
title_fullStr A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers&apos
title_full_unstemmed A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers&apos
title_sort A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers&apos
dc.creator.none.fl_str_mv Calatayud, Julia
Jornet, Marc
Cortés, J.-C.|||0000-0002-6528-2155
author Calatayud, Julia
author_facet Calatayud, Julia
Jornet, Marc
Cortés, J.-C.|||0000-0002-6528-2155
author_role author
author2 Jornet, Marc
Cortés, J.-C.|||0000-0002-6528-2155
author2_role author
author
dc.contributor.none.fl_str_mv Facultad de Administración y Dirección de Empresas
Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
AGENCIA ESTATAL DE INVESTIGACION
European Regional Development Fund
Universitat Politècnica de València
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Burgers&apos
equation
GPC expansion
Navier-Stokes equation
Perturbation method
Randomness analysis
topic Burgers&apos
equation
GPC expansion
Navier-Stokes equation
Perturbation method
Randomness analysis
description [EN] The variability of the data and the incomplete knowledge of the true physics require the incorporation of randomness into the formulation of mathematical models. In this setting, the deterministic numerical methods cannot capture the propagation of the uncertainty from the inputs to the model output. For some problems, such as the Burgers' equation (simplification to understand properties of the Navier¿Stokes equations), a small variation in the parameters causes nonnegligible changes in the output. Thus, suitable techniques for uncertainty quantification must be used. The generalized polynomial chaos (gPC) method has been successfully applied to compute the location of the transition layer of the steady-state solution, when a small uncertainty is incorporated into the boundary. On the contrary, the classical perturbation method does not give reliable results, due to the uncertainty magnitude of the output. We propose a modification of the perturbation method that converges and is comparable with the gPC approach in terms of efficiency and rate of convergence. The method is even applicable when the input random parameters are dependent random variables.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-10-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/181317
url https://riunet.upv.es/handle/10251/181317
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-89664-P PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION Y APLICACIONES
Universitat Politècnica de València https://doi.org/10.13039/501100004233 PAID Programa de Ayudas de Investigación y Desarrollo
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv John Wiley & Sons
publisher.none.fl_str_mv John Wiley & Sons
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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