Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method

Detalhes bibliográficos
Autor(a) principal: Clain, Stéphane
Data de Publicação: 2024
Outros Autores: Figueiredo, Jorge
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/87322
Resumo: Generalised Finite Difference Methods and similar mesh-free methods (Point set method, Multipoint method) are based on three main ingredients: a stencil around the reference node, a polynomial reconstruction and a weighted functional to provide the relation sbetween the derivatives at the reference node and the nodes of the stencil.Very few studies were dedicated to the optimal choice of the stencil together with the other parameters that could reduce the global conditioning of the system and bring more stability and better accuracy. We propose a detailed construction of the very high-order polynomial representation and define a functional that assesses the quality of the reconstruction. We propose and implement several techniques of optimisation and demonstrate the advantages in terms of accuracy and stability.
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spelling Stencil and kernel optimisation for mesh-free very high-order generalised finite difference methodGeneral finite differenceMesh-freeStencil optimisationVery high-orderCiências Naturais::MatemáticasGeneralised Finite Difference Methods and similar mesh-free methods (Point set method, Multipoint method) are based on three main ingredients: a stencil around the reference node, a polynomial reconstruction and a weighted functional to provide the relation sbetween the derivatives at the reference node and the nodes of the stencil.Very few studies were dedicated to the optimal choice of the stencil together with the other parameters that could reduce the global conditioning of the system and bring more stability and better accuracy. We propose a detailed construction of the very high-order polynomial representation and define a functional that assesses the quality of the reconstruction. We propose and implement several techniques of optimisation and demonstrate the advantages in terms of accuracy and stability.J. Figueiredo acknowledges the financial support by FEDER – Fundo Europeu de Desenvolvimento Regional, through COMPETE 2020 – Programa Operational Fatores de Competitividade through FCT – Fundação para a Ciência e a Tecnologia, project N° UID/FIS/04650/2019. S. Clain the financial support by FEDER – Fundo Europeu de Desenvolvimento Regional , through COMPETE 2020 – Programa Operational Fatores de Competitividade through FCT – Fundação para a Ciência e a Tecnologia, project N° UIDB/00324/2020.ElsevierUniversidade do MinhoClain, StéphaneFigueiredo, Jorge20242024-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/87322engClain, S., & Figueiredo, J. (2024, April). Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method. Mathematics and Computers in Simulation. Elsevier BV. http://doi.org/10.1016/j.matcom.2023.11.0090378-475410.1016/j.matcom.2023.11.009https://www.sciencedirect.com/science/article/pii/S0378475423004706info: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:RCAAP2023-11-25T01:17:12Zoai:repositorium.sdum.uminho.pt:1822/87322Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T23:19:39.848450Repositório 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 Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method
title Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method
spellingShingle Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method
Clain, Stéphane
General finite difference
Mesh-free
Stencil optimisation
Very high-order
Ciências Naturais::Matemáticas
title_short Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method
title_full Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method
title_fullStr Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method
title_full_unstemmed Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method
title_sort Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method
author Clain, Stéphane
author_facet Clain, Stéphane
Figueiredo, Jorge
author_role author
author2 Figueiredo, Jorge
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Clain, Stéphane
Figueiredo, Jorge
dc.subject.por.fl_str_mv General finite difference
Mesh-free
Stencil optimisation
Very high-order
Ciências Naturais::Matemáticas
topic General finite difference
Mesh-free
Stencil optimisation
Very high-order
Ciências Naturais::Matemáticas
description Generalised Finite Difference Methods and similar mesh-free methods (Point set method, Multipoint method) are based on three main ingredients: a stencil around the reference node, a polynomial reconstruction and a weighted functional to provide the relation sbetween the derivatives at the reference node and the nodes of the stencil.Very few studies were dedicated to the optimal choice of the stencil together with the other parameters that could reduce the global conditioning of the system and bring more stability and better accuracy. We propose a detailed construction of the very high-order polynomial representation and define a functional that assesses the quality of the reconstruction. We propose and implement several techniques of optimisation and demonstrate the advantages in terms of accuracy and stability.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-01-01T00:00:00Z
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/1822/87322
url https://hdl.handle.net/1822/87322
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Clain, S., & Figueiredo, J. (2024, April). Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method. Mathematics and Computers in Simulation. Elsevier BV. http://doi.org/10.1016/j.matcom.2023.11.009
0378-4754
10.1016/j.matcom.2023.11.009
https://www.sciencedirect.com/science/article/pii/S0378475423004706
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
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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