A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation

Detalhes bibliográficos
Autor(a) principal: Costa, Ricardo Daniel Pereira
Data de Publicação: 2015
Outros Autores: Machado, Gaspar J., Clain, Stéphane
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/39020
Resumo: A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.
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spelling A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulationFinite volume methodPolynomial reconstruction operatorHarmonic operatorBiharmonic operatorHigh-order methodCiências Naturais::MatemáticasEngenharia e Tecnologia::Engenharia MecânicaScience & TechnologyA new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.This research was financed by FEDER funds through Programa Operacional Factores de Competitividade-COMPETE and by Portuguese Funds through FCT-Fundacao para a Ciencia e a Tecnologia, within the projects PEst-C/MAT/UI0013/2014 and PTDC/MAT/121185/2010 via a grant for research initiation (BII) awarded by the Centre of Mathematics of the School of Science at the University of Minho, Portugal. G.J. Machado and S. Clain were financed by Programa Pessoa Cooperacao Transnacional Portugal/Franca Fundacao para a Ciencia e a Tecnologia with the reference 130631467126259.Walter de Gruyter GmbHUniversidade do MinhoCosta, Ricardo Daniel PereiraMachado, Gaspar J.Clain, Stéphane20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/39020eng1641-876X10.1515/amcs-2015-0039https://www.amcs.uz.zgora.pl/?action=paper&paper=841info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:04:28Zoai:repositorium.sdum.uminho.pt:1822/39020Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:54:46.756352Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation
title A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation
spellingShingle A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation
Costa, Ricardo Daniel Pereira
Finite volume method
Polynomial reconstruction operator
Harmonic operator
Biharmonic operator
High-order method
Ciências Naturais::Matemáticas
Engenharia e Tecnologia::Engenharia Mecânica
Science & Technology
title_short A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation
title_full A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation
title_fullStr A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation
title_full_unstemmed A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation
title_sort A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation
author Costa, Ricardo Daniel Pereira
author_facet Costa, Ricardo Daniel Pereira
Machado, Gaspar J.
Clain, Stéphane
author_role author
author2 Machado, Gaspar J.
Clain, Stéphane
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Costa, Ricardo Daniel Pereira
Machado, Gaspar J.
Clain, Stéphane
dc.subject.por.fl_str_mv Finite volume method
Polynomial reconstruction operator
Harmonic operator
Biharmonic operator
High-order method
Ciências Naturais::Matemáticas
Engenharia e Tecnologia::Engenharia Mecânica
Science & Technology
topic Finite volume method
Polynomial reconstruction operator
Harmonic operator
Biharmonic operator
High-order method
Ciências Naturais::Matemáticas
Engenharia e Tecnologia::Engenharia Mecânica
Science & Technology
description A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/39020
url http://hdl.handle.net/1822/39020
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1641-876X
10.1515/amcs-2015-0039
https://www.amcs.uz.zgora.pl/?action=paper&paper=841
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Walter de Gruyter GmbH
publisher.none.fl_str_mv Walter de Gruyter GmbH
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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