Topology optimization for the elasticity problem

In this work, we propose several preconditioners for the elasticity equation. The preconditioners are built based on domain decomposition and multiscale methods for the heat and elasticity equations. The main goal of the application of preconditioners is to decrease the condition number of the matri...

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Autores:
Serrano De La Torre, Sintya Esmeralda
Tipo de recurso:
Fecha de publicación:
2019
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/76649
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/76649
http://bdigital.unal.edu.co/73259/
Palabra clave:
Elasticity problem
Multiscale method
Domain decomposition method
Two levels Schwarz preconditioner
Topology Optimization
Ecuación de elasticidad
Método multiescala
Descomposición de dominios
Precondicionador de dos niveles de Schwarz
Optimización Topológica
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_a18057014d129bbe369f7080d82b4210
oai_identifier_str oai:repositorio.unal.edu.co:unal/76649
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
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_abf2Galvis, JuanLazarov, Boyan (Thesis advisor)d945df9f-60ac-4ac4-aa1d-36b320e465a4-1Serrano De La Torre, Sintya Esmeraldabdbf8273-74c0-40bc-965d-2d8cba76c8683002020-03-30T06:24:05Z2020-03-30T06:24:05Z2019https://repositorio.unal.edu.co/handle/unal/76649http://bdigital.unal.edu.co/73259/In this work, we propose several preconditioners for the elasticity equation. The preconditioners are built based on domain decomposition and multiscale methods for the heat and elasticity equations. The main goal of the application of preconditioners is to decrease the condition number of the matrix associated with the elasticity problem and the number of iterations needed to arrive at the solution of the elasticity equation. We also present an elasticity topology optimization problem, where we apply the preconditioners to the minimum compliance design problems. We present numerical experiments in order to show the advantages of our approach to the solution of these type of problems.Resumen: En este libro vamos a proponer varios precondicionadores para la ecuación de elasticidad. Los precondicionadores están construidos en base los métodos de descomposición de dominios y métodos de multiescala para las ecuaciones de calor y elasticidad. El objetivo de la aplicación de dichos precondicionadores es disminuir la condición de la matriz asociada al problema de elasticidad y el número de iteraciones para llegar a la solución del problema. Además presentaremos el problema de optimización topológica donde aplicaremos los precondicionadores al problema de minimización y haremos varios experimentos para mostrar su utilidad en la solución de este tipo de problemas.Maestríaapplication/pdfspaUniversidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de MatemáticasDepartamento de Matemáticas51 Matemáticas / MathematicsSerrano De La Torre, Sintya Esmeralda (2019) Topology optimization for the elasticity problem. Maestría thesis, Universidad Nacional de Colombia - Sede Bogotá.Topology optimization for the elasticity problemTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMElasticity problemMultiscale methodDomain decomposition methodTwo levels Schwarz preconditionerTopology OptimizationEcuación de elasticidadMétodo multiescalaDescomposición de dominiosPrecondicionador de dos niveles de SchwarzOptimización TopológicaORIGINAL662029.2019.pdfapplication/pdf1259794https://repositorio.unal.edu.co/bitstream/unal/76649/1/662029.2019.pdffc369523f6fec358c9805d29f414b5e1MD51THUMBNAIL662029.2019.pdf.jpg662029.2019.pdf.jpgGenerated Thumbnailimage/jpeg3738https://repositorio.unal.edu.co/bitstream/unal/76649/2/662029.2019.pdf.jpga33a80c6b5f3b899f4572777775fbb1cMD52unal/76649oai:repositorio.unal.edu.co:unal/766492023-07-15 23:03:37.457Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Topology optimization for the elasticity problem
title Topology optimization for the elasticity problem
spellingShingle Topology optimization for the elasticity problem
Elasticity problem
Multiscale method
Domain decomposition method
Two levels Schwarz preconditioner
Topology Optimization
Ecuación de elasticidad
Método multiescala
Descomposición de dominios
Precondicionador de dos niveles de Schwarz
Optimización Topológica
title_short Topology optimization for the elasticity problem
title_full Topology optimization for the elasticity problem
title_fullStr Topology optimization for the elasticity problem
title_full_unstemmed Topology optimization for the elasticity problem
title_sort Topology optimization for the elasticity problem
dc.creator.fl_str_mv Serrano De La Torre, Sintya Esmeralda
dc.contributor.advisor.spa.fl_str_mv Lazarov, Boyan (Thesis advisor)
dc.contributor.author.spa.fl_str_mv Serrano De La Torre, Sintya Esmeralda
dc.contributor.spa.fl_str_mv Galvis, Juan
dc.subject.proposal.spa.fl_str_mv Elasticity problem
Multiscale method
Domain decomposition method
Two levels Schwarz preconditioner
Topology Optimization
Ecuación de elasticidad
Método multiescala
Descomposición de dominios
Precondicionador de dos niveles de Schwarz
Optimización Topológica
topic Elasticity problem
Multiscale method
Domain decomposition method
Two levels Schwarz preconditioner
Topology Optimization
Ecuación de elasticidad
Método multiescala
Descomposición de dominios
Precondicionador de dos niveles de Schwarz
Optimización Topológica
description In this work, we propose several preconditioners for the elasticity equation. The preconditioners are built based on domain decomposition and multiscale methods for the heat and elasticity equations. The main goal of the application of preconditioners is to decrease the condition number of the matrix associated with the elasticity problem and the number of iterations needed to arrive at the solution of the elasticity equation. We also present an elasticity topology optimization problem, where we apply the preconditioners to the minimum compliance design problems. We present numerical experiments in order to show the advantages of our approach to the solution of these type of problems.
publishDate 2019
dc.date.issued.spa.fl_str_mv 2019
dc.date.accessioned.spa.fl_str_mv 2020-03-30T06:24:05Z
dc.date.available.spa.fl_str_mv 2020-03-30T06:24:05Z
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/76649
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/73259/
url https://repositorio.unal.edu.co/handle/unal/76649
http://bdigital.unal.edu.co/73259/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Matemáticas
Departamento de Matemáticas
dc.relation.haspart.spa.fl_str_mv 51 Matemáticas / Mathematics
dc.relation.references.spa.fl_str_mv Serrano De La Torre, Sintya Esmeralda (2019) Topology optimization for the elasticity problem. Maestría thesis, Universidad Nacional de Colombia - Sede Bogotá.
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
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/76649/1/662029.2019.pdf
https://repositorio.unal.edu.co/bitstream/unal/76649/2/662029.2019.pdf.jpg
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bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
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