Structural schemes for one dimension stationary equations
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/1822/86694 |
Resumo: | In this paper, we propose a new paradigm for finite differences numerical methods, based on compact schemes to provide high order accurate approximations of a smooth solution. The method involves its derivatives approximations at the grid points and the construction of structural equations deriving from the kernels of a matrix that gathers the variables belonging to a small stencil. Numerical schemes involve combinations of physical equations and the structural relations. We have analysed the spectral resolution of the most common structural equations and performed numerical tests to address both the stability and accuracy issues for popular linear and non-linear problems. Several benchmarks are presented that ensure that the developed technology can cope with several problems that may involve non-linearity. |
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Structural schemes for one dimension stationary equationsStructural equationCompact schemeVery high-orderFinite differenceCiências Naturais::MatemáticasIn this paper, we propose a new paradigm for finite differences numerical methods, based on compact schemes to provide high order accurate approximations of a smooth solution. The method involves its derivatives approximations at the grid points and the construction of structural equations deriving from the kernels of a matrix that gathers the variables belonging to a small stencil. Numerical schemes involve combinations of physical equations and the structural relations. We have analysed the spectral resolution of the most common structural equations and performed numerical tests to address both the stability and accuracy issues for popular linear and non-linear problems. Several benchmarks are presented that ensure that the developed technology can cope with several problems that may involve non-linearity.S. Clain acknowledges the financial support by Portuguese Funds through Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/00324/2020. R. M. S. Pereira acknowledges the financial support by Portuguese Funds through Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020. P. A. Pereira acknowledges the financial support by Portuguese Funds through Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/00013/2020. Diogo Lopes acknowledges the financial support by national funds (PIDDAC), through the FCT – Fundação para a Ciência e a Tecnologia and FCT/MCTES under the scope of the projects UIDB/05549/2020 and UIDP/05549/2020. S. Clain and R. M.Pereira acknowledge the financial support by FEDER – Fundo Europeu de Desenvolvimento Regional, through COMPETE 2020 – Programa Operacional Fatores de Competitividade, and the National Funds through FCT, project N◦. POCI-01-0145-FEDER-028118.ElsevierUniversidade do MinhoClain, StéphanePereira, Rui M. S.Pereira, Paulo A.Lopes, Diogo20232023-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/86694engClain, S., Pereira, R. M. S., Pereira, P. A., & Lopes, D. (2023, November). Structural schemes for one dimension stationary equations. Applied Mathematics and Computation. Elsevier BV. http://doi.org/10.1016/j.amc.2023.1282070096-300310.1016/j.amc.2023.128207128207https://www.sciencedirect.com/science/article/pii/S0096300323003764info: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:RCAAP2023-12-30T01:29:16Zoai:repositorium.sdum.uminho.pt:1822/86694Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:33:32.146070Repositório 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 |
Structural schemes for one dimension stationary equations |
title |
Structural schemes for one dimension stationary equations |
spellingShingle |
Structural schemes for one dimension stationary equations Clain, Stéphane Structural equation Compact scheme Very high-order Finite difference Ciências Naturais::Matemáticas |
title_short |
Structural schemes for one dimension stationary equations |
title_full |
Structural schemes for one dimension stationary equations |
title_fullStr |
Structural schemes for one dimension stationary equations |
title_full_unstemmed |
Structural schemes for one dimension stationary equations |
title_sort |
Structural schemes for one dimension stationary equations |
author |
Clain, Stéphane |
author_facet |
Clain, Stéphane Pereira, Rui M. S. Pereira, Paulo A. Lopes, Diogo |
author_role |
author |
author2 |
Pereira, Rui M. S. Pereira, Paulo A. Lopes, Diogo |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Clain, Stéphane Pereira, Rui M. S. Pereira, Paulo A. Lopes, Diogo |
dc.subject.por.fl_str_mv |
Structural equation Compact scheme Very high-order Finite difference Ciências Naturais::Matemáticas |
topic |
Structural equation Compact scheme Very high-order Finite difference Ciências Naturais::Matemáticas |
description |
In this paper, we propose a new paradigm for finite differences numerical methods, based on compact schemes to provide high order accurate approximations of a smooth solution. The method involves its derivatives approximations at the grid points and the construction of structural equations deriving from the kernels of a matrix that gathers the variables belonging to a small stencil. Numerical schemes involve combinations of physical equations and the structural relations. We have analysed the spectral resolution of the most common structural equations and performed numerical tests to address both the stability and accuracy issues for popular linear and non-linear problems. Several benchmarks are presented that ensure that the developed technology can cope with several problems that may involve non-linearity. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023 2023-01-01T00:00:00Z |
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 |
https://hdl.handle.net/1822/86694 |
url |
https://hdl.handle.net/1822/86694 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Clain, S., Pereira, R. M. S., Pereira, P. A., & Lopes, D. (2023, November). Structural schemes for one dimension stationary equations. Applied Mathematics and Computation. Elsevier BV. http://doi.org/10.1016/j.amc.2023.128207 0096-3003 10.1016/j.amc.2023.128207 128207 https://www.sciencedirect.com/science/article/pii/S0096300323003764 |
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 |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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 |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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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1799133600990363648 |