Numerical methods for the dynamics of unbounded domains
Autor(a) principal: | |
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Data de Publicação: | 2005 |
Outros Autores: | |
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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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) |
instacron_str |
SBMAC |
institution |
SBMAC |
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 |
_version_ |
1754734889720086528 |