A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , |
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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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 |
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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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1799132330784194561 |