Blending isogeometric analysis and local maximum entropy meshfree approximants

We present a method to blend local maximum entropy (LME) meshfree approximants and isogeometric analysis. The coupling strategy exploits the optimization program behind LME approximation, treats isogeometric and LME basis functions on an equal footing in the reproducibility constraints, but views th...

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Autores: Rosolen, Adrián, Arroyo Balaguer, Marino|||0000-0003-1647-940X
Tipo de documento: artigo
Data de publicação:2013
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositório:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglês
OAI Identifier:oai:upcommons.upc.edu:2117/116658
Acesso em linha:https://hdl.handle.net/2117/116658
https://dx.doi.org/10.1016/j.cma.2013.05.015
Access Level:Acceso aberto
Palavra-chave:Geometry, Algebraic
Geometry
High-fidelity geometry
Isogeometric analysis
Local refinement
Max-ent approximants
Volume discretization
Geometria algebraica
Geometria
Classificació AMS::51 Geometry::51P05 Geometry and physics
Classificació AMS::51 Geometry::51K Distance geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional
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oai_identifier_str oai:upcommons.upc.edu:2117/116658
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repository_id_str
spelling Blending isogeometric analysis and local maximum entropy meshfree approximantsRosolen, AdriánArroyo Balaguer, Marino|||0000-0003-1647-940XGeometry, AlgebraicGeometryHigh-fidelity geometryIsogeometric analysisLocal refinementMax-ent approximantsVolume discretizationGeometria algebraicaGeometriaClassificació AMS::51 Geometry::51P05 Geometry and physicsClassificació AMS::51 Geometry::51K Distance geometryÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraicaÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacionalWe present a method to blend local maximum entropy (LME) meshfree approximants and isogeometric analysis. The coupling strategy exploits the optimization program behind LME approximation, treats isogeometric and LME basis functions on an equal footing in the reproducibility constraints, but views the former as data in the constrained minimization. The resulting scheme exploits the best features and overcomes the main drawbacks of each of these approximants. Indeed, it preserves the high fidelity boundary representation (exact CAD geometry) of isogeometric analysis, out of reach for bare meshfree methods, and easily handles volume discretization and unstructured grids with possibly local refinement, while maintaining the smoothness and non-negativity of the basis functions. We implement the method with B-Splines in two dimensions, but the procedure carries over to higher spatial dimensions or to other non-negative approximants such as NURBS or subdivision schemes. The performance of the method is illustrated with the heat equation, and linear and nonlinear elasticity. The ability of the proposed method to impose directly essential boundary conditions in non-convex domains, and to deal with unstructured grids and local refinement in domains of complex geometry and topology is highlighted by the numerical examples.Peer Reviewed20132013-09-0120182018-04-25journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/116658https://dx.doi.org/10.1016/j.cma.2013.05.015reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://dx.doi.org/10.13039/100011102 Seventh Framework Programme 240487 Predictive models and simulations in nano- and biomolecular mechanics: a multiscale approachopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1166582026-05-27T15:37:01Z
dc.title.none.fl_str_mv Blending isogeometric analysis and local maximum entropy meshfree approximants
title Blending isogeometric analysis and local maximum entropy meshfree approximants
spellingShingle Blending isogeometric analysis and local maximum entropy meshfree approximants
Rosolen, Adrián
Geometry, Algebraic
Geometry
High-fidelity geometry
Isogeometric analysis
Local refinement
Max-ent approximants
Volume discretization
Geometria algebraica
Geometria
Classificació AMS::51 Geometry::51P05 Geometry and physics
Classificació AMS::51 Geometry::51K Distance geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional
title_short Blending isogeometric analysis and local maximum entropy meshfree approximants
title_full Blending isogeometric analysis and local maximum entropy meshfree approximants
title_fullStr Blending isogeometric analysis and local maximum entropy meshfree approximants
title_full_unstemmed Blending isogeometric analysis and local maximum entropy meshfree approximants
title_sort Blending isogeometric analysis and local maximum entropy meshfree approximants
dc.creator.none.fl_str_mv Rosolen, Adrián
Arroyo Balaguer, Marino|||0000-0003-1647-940X
author Rosolen, Adrián
author_facet Rosolen, Adrián
Arroyo Balaguer, Marino|||0000-0003-1647-940X
author_role author
author2 Arroyo Balaguer, Marino|||0000-0003-1647-940X
author2_role author
dc.subject.none.fl_str_mv Geometry, Algebraic
Geometry
High-fidelity geometry
Isogeometric analysis
Local refinement
Max-ent approximants
Volume discretization
Geometria algebraica
Geometria
Classificació AMS::51 Geometry::51P05 Geometry and physics
Classificació AMS::51 Geometry::51K Distance geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional
topic Geometry, Algebraic
Geometry
High-fidelity geometry
Isogeometric analysis
Local refinement
Max-ent approximants
Volume discretization
Geometria algebraica
Geometria
Classificació AMS::51 Geometry::51P05 Geometry and physics
Classificació AMS::51 Geometry::51K Distance geometry
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional
description We present a method to blend local maximum entropy (LME) meshfree approximants and isogeometric analysis. The coupling strategy exploits the optimization program behind LME approximation, treats isogeometric and LME basis functions on an equal footing in the reproducibility constraints, but views the former as data in the constrained minimization. The resulting scheme exploits the best features and overcomes the main drawbacks of each of these approximants. Indeed, it preserves the high fidelity boundary representation (exact CAD geometry) of isogeometric analysis, out of reach for bare meshfree methods, and easily handles volume discretization and unstructured grids with possibly local refinement, while maintaining the smoothness and non-negativity of the basis functions. We implement the method with B-Splines in two dimensions, but the procedure carries over to higher spatial dimensions or to other non-negative approximants such as NURBS or subdivision schemes. The performance of the method is illustrated with the heat equation, and linear and nonlinear elasticity. The ability of the proposed method to impose directly essential boundary conditions in non-convex domains, and to deal with unstructured grids and local refinement in domains of complex geometry and topology is highlighted by the numerical examples.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-09-01
2018
2018-04-25
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/116658
https://dx.doi.org/10.1016/j.cma.2013.05.015
url https://hdl.handle.net/2117/116658
https://dx.doi.org/10.1016/j.cma.2013.05.015
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://dx.doi.org/10.13039/100011102 Seventh Framework Programme 240487 Predictive models and simulations in nano- and biomolecular mechanics: a multiscale approach
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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 15,300724

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