The Shifted Boundary Method in Isogeometric Analysis

This work presents a novel application of the Shifted Boundary Method (SBM) within the Isogeometric Analysis (IGA) framework, applying it to two-dimensional and three-dimensional Poisson problems with Dirichlet and Neumann boundary conditions. The SBM boundary condition imposition is achieved by mea...

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Autores: Antonelli, Nicolò, Aristio, Ricky, Gorgi, Andrea, Zorrilla Martínez, Rubén|||0000-0001-8270-7170, Rossi, Riccardo|||0000-0003-0528-7074, Scovazzi, Guglielmo, Wüchner, Roland
Formato: artículo
Fecha de publicación:2024
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/413651
Acesso em linha:https://hdl.handle.net/2117/413651
https://dx.doi.org/10.1016/j.cma.2024.117228
Access Level:acceso abierto
Palavra-chave:Mathematical models
Shifted Boundary Method (SBM)
Isogeometric Analysis (IGA)
Isogeometric Boundary Representation Analysis (IBRA)
Unfitted boundary methods
Small cut-cell problem
Geometria computacional
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica
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spelling The Shifted Boundary Method in Isogeometric AnalysisAntonelli, NicolòAristio, RickyGorgi, AndreaZorrilla Martínez, Rubén|||0000-0001-8270-7170Rossi, Riccardo|||0000-0003-0528-7074Scovazzi, GuglielmoWüchner, RolandMathematical modelsShifted Boundary Method (SBM)Isogeometric Analysis (IGA)Isogeometric Boundary Representation Analysis (IBRA)Unfitted boundary methodsSmall cut-cell problemGeometria computacionalÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàticaThis work presents a novel application of the Shifted Boundary Method (SBM) within the Isogeometric Analysis (IGA) framework, applying it to two-dimensional and three-dimensional Poisson problems with Dirichlet and Neumann boundary conditions. The SBM boundary condition imposition is achieved by means of a fully penalty-free formulation, eliminating the need for penalty calibration. The numerical experiments demonstrate how order elevation, coupled with SBM through higher-order Taylor expansions, consistently achieves optimal convergence rates. Additionally, analyzing the condition number of the problem matrix reveals that SBM, when integrated with IGA, effectively circumvents the small cut-cell problem, a common issue in numerical methods with unfitted boundaries.Peer ReviewedElsevier20242024-10-0120242024-09-02journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/413651https://dx.doi.org/10.1016/j.cma.2024.117228reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://doi.org/10.13039/501100000780 HE 101073106 Design for IGA-type discretization workflowsopen 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:2117/4136512026-05-27T15:37:01Z
dc.title.none.fl_str_mv The Shifted Boundary Method in Isogeometric Analysis
title The Shifted Boundary Method in Isogeometric Analysis
spellingShingle The Shifted Boundary Method in Isogeometric Analysis
Antonelli, Nicolò
Mathematical models
Shifted Boundary Method (SBM)
Isogeometric Analysis (IGA)
Isogeometric Boundary Representation Analysis (IBRA)
Unfitted boundary methods
Small cut-cell problem
Geometria computacional
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica
title_short The Shifted Boundary Method in Isogeometric Analysis
title_full The Shifted Boundary Method in Isogeometric Analysis
title_fullStr The Shifted Boundary Method in Isogeometric Analysis
title_full_unstemmed The Shifted Boundary Method in Isogeometric Analysis
title_sort The Shifted Boundary Method in Isogeometric Analysis
dc.creator.none.fl_str_mv Antonelli, Nicolò
Aristio, Ricky
Gorgi, Andrea
Zorrilla Martínez, Rubén|||0000-0001-8270-7170
Rossi, Riccardo|||0000-0003-0528-7074
Scovazzi, Guglielmo
Wüchner, Roland
author Antonelli, Nicolò
author_facet Antonelli, Nicolò
Aristio, Ricky
Gorgi, Andrea
Zorrilla Martínez, Rubén|||0000-0001-8270-7170
Rossi, Riccardo|||0000-0003-0528-7074
Scovazzi, Guglielmo
Wüchner, Roland
author_role author
author2 Aristio, Ricky
Gorgi, Andrea
Zorrilla Martínez, Rubén|||0000-0001-8270-7170
Rossi, Riccardo|||0000-0003-0528-7074
Scovazzi, Guglielmo
Wüchner, Roland
author2_role author
author
author
author
author
author
dc.subject.none.fl_str_mv Mathematical models
Shifted Boundary Method (SBM)
Isogeometric Analysis (IGA)
Isogeometric Boundary Representation Analysis (IBRA)
Unfitted boundary methods
Small cut-cell problem
Geometria computacional
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica
topic Mathematical models
Shifted Boundary Method (SBM)
Isogeometric Analysis (IGA)
Isogeometric Boundary Representation Analysis (IBRA)
Unfitted boundary methods
Small cut-cell problem
Geometria computacional
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica
description This work presents a novel application of the Shifted Boundary Method (SBM) within the Isogeometric Analysis (IGA) framework, applying it to two-dimensional and three-dimensional Poisson problems with Dirichlet and Neumann boundary conditions. The SBM boundary condition imposition is achieved by means of a fully penalty-free formulation, eliminating the need for penalty calibration. The numerical experiments demonstrate how order elevation, coupled with SBM through higher-order Taylor expansions, consistently achieves optimal convergence rates. Additionally, analyzing the condition number of the problem matrix reveals that SBM, when integrated with IGA, effectively circumvents the small cut-cell problem, a common issue in numerical methods with unfitted boundaries.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-10-01
2024
2024-09-02
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/2117/413651
https://dx.doi.org/10.1016/j.cma.2024.117228
url https://hdl.handle.net/2117/413651
https://dx.doi.org/10.1016/j.cma.2024.117228
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://doi.org/10.13039/501100000780 HE 101073106 Design for IGA-type discretization workflows
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.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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 15,811543

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