Numerical methods for the dynamics of unbounded domains

Detalhes bibliográficos
Autor(a) principal: Mesquita,Euclides
Data de Publicação: 2005
Outros Autores: Pavanello,Renato
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022005000100001
Resumo: The present article discusses the relation between boundary conditions and the Sommerfeld radiation condition underlying the dynamics of unbounded domains. It is shown that the classical Dirichlet, Neumann and mixed boundary conditions do not fulfill the radiation condition. In the sequence, three strategies to incorporate the radiation condition in numerical methods are outlined. The inclusion of Infinite Elements in the realm of the Finite Element Method (FEM), the Dirichlet-to-Neumann (DtN) mapping and the Boundary Element Method (BEM) are described. Examples of solved dynamic problems in unbounded domains are given for the Helmholtz and the Navier operators. The advantages and limitations of the methodologies are discussed and pertinent literature is provided.
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spelling Numerical methods for the dynamics of unbounded domainsSommerfeld radiation conditionFinite Element MethodInfinite ElementsDirichlet-to-Neumann MappingBoundary Element MethodThe present article discusses the relation between boundary conditions and the Sommerfeld radiation condition underlying the dynamics of unbounded domains. It is shown that the classical Dirichlet, Neumann and mixed boundary conditions do not fulfill the radiation condition. In the sequence, three strategies to incorporate the radiation condition in numerical methods are outlined. The inclusion of Infinite Elements in the realm of the Finite Element Method (FEM), the Dirichlet-to-Neumann (DtN) mapping and the Boundary Element Method (BEM) are described. Examples of solved dynamic problems in unbounded domains are given for the Helmholtz and the Navier operators. The advantages and limitations of the methodologies are discussed and pertinent literature is provided.Sociedade Brasileira de Matemática Aplicada e Computacional2005-04-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022005000100001Computational & Applied Mathematics v.24 n.1 2005reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S0101-82052005000100001info:eu-repo/semantics/openAccessMesquita,EuclidesPavanello,Renatoeng2009-05-07T00:00:00Zoai:scielo:S1807-03022005000100001Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2009-05-07T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv Numerical methods for the dynamics of unbounded domains
title Numerical methods for the dynamics of unbounded domains
spellingShingle Numerical methods for the dynamics of unbounded domains
Mesquita,Euclides
Sommerfeld radiation condition
Finite Element Method
Infinite Elements
Dirichlet-to-Neumann Mapping
Boundary Element Method
title_short Numerical methods for the dynamics of unbounded domains
title_full Numerical methods for the dynamics of unbounded domains
title_fullStr Numerical methods for the dynamics of unbounded domains
title_full_unstemmed Numerical methods for the dynamics of unbounded domains
title_sort Numerical methods for the dynamics of unbounded domains
author Mesquita,Euclides
author_facet Mesquita,Euclides
Pavanello,Renato
author_role author
author2 Pavanello,Renato
author2_role author
dc.contributor.author.fl_str_mv Mesquita,Euclides
Pavanello,Renato
dc.subject.por.fl_str_mv Sommerfeld radiation condition
Finite Element Method
Infinite Elements
Dirichlet-to-Neumann Mapping
Boundary Element Method
topic Sommerfeld radiation condition
Finite Element Method
Infinite Elements
Dirichlet-to-Neumann Mapping
Boundary Element Method
description The present article discusses the relation between boundary conditions and the Sommerfeld radiation condition underlying the dynamics of unbounded domains. It is shown that the classical Dirichlet, Neumann and mixed boundary conditions do not fulfill the radiation condition. In the sequence, three strategies to incorporate the radiation condition in numerical methods are outlined. The inclusion of Infinite Elements in the realm of the Finite Element Method (FEM), the Dirichlet-to-Neumann (DtN) mapping and the Boundary Element Method (BEM) are described. Examples of solved dynamic problems in unbounded domains are given for the Helmholtz and the Navier operators. The advantages and limitations of the methodologies are discussed and pertinent literature is provided.
publishDate 2005
dc.date.none.fl_str_mv 2005-04-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022005000100001
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022005000100001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0101-82052005000100001
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational & Applied Mathematics v.24 n.1 2005
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
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reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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