A multiscale formulation for FEM and IgA

A numerical method is formulated based on Finite Elements, Isogeometric Analysis and a Multiscale technique. Isogeometric Analysis, which uses B-Splines and NURBS as basis functions, is applied to evaluate its performance. The analyzed PDE is Poisson's Equation. The method starts with a coarse...

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Autores:
Mora Paz, Jaime David
Mantilla González, Juan Miguel
Calo, Victor
Tipo de recurso:
Article of journal
Fecha de publicación:
2017
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/61873
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/61873
http://bdigital.unal.edu.co/60685/
Palabra clave:
51 Matemáticas / Mathematics
multiescala
análisis isogeométrico
elementos finitos
Poisson
B-splines
NURBS
análisis numérico
multiscale
isogeometric analysis
finite elements
Poisson
B- splines
NURBS
numerical analysis
FLOP
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Mora Paz, Jaime David6cd146fa-339c-448c-a04f-3e33bff09103300Mantilla González, Juan Miguelda6ddb8f-efb4-4db4-aa2b-6591d3993e79300Calo, Victor3456bc45-1df0-4c8c-9823-c13606787c733002019-07-02T20:46:45Z2019-07-02T20:46:45Z2017-01-01ISSN: 2357-6529https://repositorio.unal.edu.co/handle/unal/61873http://bdigital.unal.edu.co/60685/A numerical method is formulated based on Finite Elements, Isogeometric Analysis and a Multiscale technique. Isogeometric Analysis, which uses B-Splines and NURBS as basis functions, is applied to evaluate its performance. The analyzed PDE is Poisson's Equation. The method starts with a coarse mesh which is refined to obtain each scale, considering every current scale mesh's element as a subdomain to the following scale. Local problems of each subdomain are solved independently, and the system is executed iteratively. Isogeometric analysis shows to have a better performance regarding approximation error and convergence in the iterative method that was derived here, which favorably influences computational cost.En este artículo se formula un método numérico basado en elementos finitos, análisis isogeométrico y técnica multiescala. El análisis isogeométrico utilizando B-splines y NURBS como funciones base se aplica para evaluar su funcionamiento. La ecuación diferencial parcial analizada es la de Poisson. El método inicia con una malla burda la cual es refinada para obtener cada escala, considerando cada elemento de la malla como un subdominio de la escala posterior. Los problemas locales de cada subdominio se resuelven independientemente y el sistema de forma iterativa. El análisis isogeométrico muestra un buen comportamiento en lo que respecta a errores de aproximación y convergencia del método iterativo que fue derivado, lo cual favorece el costo computacional.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticashttps://revistas.unal.edu.co/index.php/bolma/article/view/66933Universidad Nacional de Colombia Revistas electrónicas UN Boletín de MatemáticasBoletín de MatemáticasMora Paz, Jaime David and Mantilla González, Juan Miguel and Calo, Victor (2017) A multiscale formulation for FEM and IgA. Boletín de Matemáticas, 24 (1). pp. 101-115. ISSN 2357-652951 Matemáticas / Mathematicsmultiescalaanálisis isogeométricoelementos finitosPoissonB-splinesNURBSanálisis numéricomultiscaleisogeometric analysisfinite elementsPoissonB- splinesNURBSnumerical analysisFLOPA multiscale formulation for FEM and IgAArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL66933-343475-1-SM.pdfapplication/pdf665748https://repositorio.unal.edu.co/bitstream/unal/61873/1/66933-343475-1-SM.pdf12901517b43cd0c011794be0b25a8914MD51THUMBNAIL66933-343475-1-SM.pdf.jpg66933-343475-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg5801https://repositorio.unal.edu.co/bitstream/unal/61873/2/66933-343475-1-SM.pdf.jpgd653cf4e340daa02a8b3b28b525495e0MD52unal/61873oai:repositorio.unal.edu.co:unal/618732024-04-20 23:26:13.933Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv A multiscale formulation for FEM and IgA
title A multiscale formulation for FEM and IgA
spellingShingle A multiscale formulation for FEM and IgA
51 Matemáticas / Mathematics
multiescala
análisis isogeométrico
elementos finitos
Poisson
B-splines
NURBS
análisis numérico
multiscale
isogeometric analysis
finite elements
Poisson
B- splines
NURBS
numerical analysis
FLOP
title_short A multiscale formulation for FEM and IgA
title_full A multiscale formulation for FEM and IgA
title_fullStr A multiscale formulation for FEM and IgA
title_full_unstemmed A multiscale formulation for FEM and IgA
title_sort A multiscale formulation for FEM and IgA
dc.creator.fl_str_mv Mora Paz, Jaime David
Mantilla González, Juan Miguel
Calo, Victor
dc.contributor.author.spa.fl_str_mv Mora Paz, Jaime David
Mantilla González, Juan Miguel
Calo, Victor
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
multiescala
análisis isogeométrico
elementos finitos
Poisson
B-splines
NURBS
análisis numérico
multiscale
isogeometric analysis
finite elements
Poisson
B- splines
NURBS
numerical analysis
FLOP
dc.subject.proposal.spa.fl_str_mv multiescala
análisis isogeométrico
elementos finitos
Poisson
B-splines
NURBS
análisis numérico
multiscale
isogeometric analysis
finite elements
Poisson
B- splines
NURBS
numerical analysis
FLOP
description A numerical method is formulated based on Finite Elements, Isogeometric Analysis and a Multiscale technique. Isogeometric Analysis, which uses B-Splines and NURBS as basis functions, is applied to evaluate its performance. The analyzed PDE is Poisson's Equation. The method starts with a coarse mesh which is refined to obtain each scale, considering every current scale mesh's element as a subdomain to the following scale. Local problems of each subdomain are solved independently, and the system is executed iteratively. Isogeometric analysis shows to have a better performance regarding approximation error and convergence in the iterative method that was derived here, which favorably influences computational cost.
publishDate 2017
dc.date.issued.spa.fl_str_mv 2017-01-01
dc.date.accessioned.spa.fl_str_mv 2019-07-02T20:46:45Z
dc.date.available.spa.fl_str_mv 2019-07-02T20:46:45Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.type.content.spa.fl_str_mv Text
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format http://purl.org/coar/resource_type/c_6501
status_str publishedVersion
dc.identifier.issn.spa.fl_str_mv ISSN: 2357-6529
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/61873
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/60685/
identifier_str_mv ISSN: 2357-6529
url https://repositorio.unal.edu.co/handle/unal/61873
http://bdigital.unal.edu.co/60685/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv https://revistas.unal.edu.co/index.php/bolma/article/view/66933
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Boletín de Matemáticas
Boletín de Matemáticas
dc.relation.references.spa.fl_str_mv Mora Paz, Jaime David and Mantilla González, Juan Miguel and Calo, Victor (2017) A multiscale formulation for FEM and IgA. Boletín de Matemáticas, 24 (1). pp. 101-115. ISSN 2357-6529
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/61873/1/66933-343475-1-SM.pdf
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
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