Fast explicit time integration schemes for parabolic problems in mechanics

We present a family of fast explicit time integration schemes of first, second and third order accuracy for parabolic problems in mechanics solved via standard numerical methods that have considerable higher computational efficiency versus existing explicit methods of the same order. The derivation...

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Autores: Oñate Ibáñez de Navarra, Eugenio|||0000-0002-0804-7095, Zárate Araiza, José Francisco|||0000-0002-7344-4425, Gimenez, Juan Marcelo, Löhner, Rainald, Idelsohn Barg, Sergio Rodolfo
Tipo de recurso: artículo
Fecha de publicación:2024
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:2117/407193
Acceso en línea:https://hdl.handle.net/2117/407193
https://dx.doi.org/10.1002/nme.7477
Access Level:acceso abierto
Palabra clave:Differential equations, Parabolic
Explicit time integration schemes
Fast explicit time integration
FIC
Finite element method
Finite increment calculus
Parabolic equation
Equacions diferencials parabòliques
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
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spelling Fast explicit time integration schemes for parabolic problems in mechanicsOñate Ibáñez de Navarra, Eugenio|||0000-0002-0804-7095Zárate Araiza, José Francisco|||0000-0002-7344-4425Gimenez, Juan MarceloLöhner, RainaldIdelsohn Barg, Sergio RodolfoDifferential equations, ParabolicExplicit time integration schemesFast explicit time integrationFICFinite element methodFinite increment calculusParabolic equationEquacions diferencials parabòliquesÀrees temàtiques de la UPC::Enginyeria civil::Materials i estructuresWe present a family of fast explicit time integration schemes of first, second and third order accuracy for parabolic problems in mechanics solved via standard numerical methods that have considerable higher computational efficiency versus existing explicit methods of the same order. The derivation of the new explicit schemes is inspired on the finite increment calculus (FIC) procedure used for obtaining stabilized numerical schemes in fluid and solid mechanics. The new (so-called) explicit FIC-Time (EFT) schemes allow considerable larger time steps than the standard first order forward Euler (FE) scheme and the second and third order Adams–Bashforth schemes. The comparison with Runge–Kutta schemes also favors the FIC-Time schemes in terms of the limit time step size (for second order schemes) and the total number of matrix-vector multiplications per time step (for second and third order schemes). The new first order explicit schemes have a faster convergence to steady-state than the FE scheme. The accuracy and efficiency of the new EFT schemes are verified in examples of application to the transient heat conduction equation using the finite element method.Peer Reviewed20242024-07-0120242024-04-26journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/407193https://dx.doi.org/10.1002/nme.7477reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4071932026-05-27T15:37:01Z
dc.title.none.fl_str_mv Fast explicit time integration schemes for parabolic problems in mechanics
title Fast explicit time integration schemes for parabolic problems in mechanics
spellingShingle Fast explicit time integration schemes for parabolic problems in mechanics
Oñate Ibáñez de Navarra, Eugenio|||0000-0002-0804-7095
Differential equations, Parabolic
Explicit time integration schemes
Fast explicit time integration
FIC
Finite element method
Finite increment calculus
Parabolic equation
Equacions diferencials parabòliques
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
title_short Fast explicit time integration schemes for parabolic problems in mechanics
title_full Fast explicit time integration schemes for parabolic problems in mechanics
title_fullStr Fast explicit time integration schemes for parabolic problems in mechanics
title_full_unstemmed Fast explicit time integration schemes for parabolic problems in mechanics
title_sort Fast explicit time integration schemes for parabolic problems in mechanics
dc.creator.none.fl_str_mv Oñate Ibáñez de Navarra, Eugenio|||0000-0002-0804-7095
Zárate Araiza, José Francisco|||0000-0002-7344-4425
Gimenez, Juan Marcelo
Löhner, Rainald
Idelsohn Barg, Sergio Rodolfo
author Oñate Ibáñez de Navarra, Eugenio|||0000-0002-0804-7095
author_facet Oñate Ibáñez de Navarra, Eugenio|||0000-0002-0804-7095
Zárate Araiza, José Francisco|||0000-0002-7344-4425
Gimenez, Juan Marcelo
Löhner, Rainald
Idelsohn Barg, Sergio Rodolfo
author_role author
author2 Zárate Araiza, José Francisco|||0000-0002-7344-4425
Gimenez, Juan Marcelo
Löhner, Rainald
Idelsohn Barg, Sergio Rodolfo
author2_role author
author
author
author
dc.subject.none.fl_str_mv Differential equations, Parabolic
Explicit time integration schemes
Fast explicit time integration
FIC
Finite element method
Finite increment calculus
Parabolic equation
Equacions diferencials parabòliques
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
topic Differential equations, Parabolic
Explicit time integration schemes
Fast explicit time integration
FIC
Finite element method
Finite increment calculus
Parabolic equation
Equacions diferencials parabòliques
Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures
description We present a family of fast explicit time integration schemes of first, second and third order accuracy for parabolic problems in mechanics solved via standard numerical methods that have considerable higher computational efficiency versus existing explicit methods of the same order. The derivation of the new explicit schemes is inspired on the finite increment calculus (FIC) procedure used for obtaining stabilized numerical schemes in fluid and solid mechanics. The new (so-called) explicit FIC-Time (EFT) schemes allow considerable larger time steps than the standard first order forward Euler (FE) scheme and the second and third order Adams–Bashforth schemes. The comparison with Runge–Kutta schemes also favors the FIC-Time schemes in terms of the limit time step size (for second order schemes) and the total number of matrix-vector multiplications per time step (for second and third order schemes). The new first order explicit schemes have a faster convergence to steady-state than the FE scheme. The accuracy and efficiency of the new EFT schemes are verified in examples of application to the transient heat conduction equation using the finite element method.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-07-01
2024
2024-04-26
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://hdl.handle.net/2117/407193
https://dx.doi.org/10.1002/nme.7477
url https://hdl.handle.net/2117/407193
https://dx.doi.org/10.1002/nme.7477
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
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
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
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
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
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score 15,301603

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