Publication
A Locally-Continuous Meshless Local Petrov-Galerkin Method Applied to a Two-point Boundary Value Problem
| Summary: | Abstract In recent years, the Meshless Local Petrov-Galerkin (MLPG) Method has attracted the attention of many researchers in solving several types of boundary value problems. This method is based on a local weak form, evaluated in local subdomains and does not require any mesh, either in the construction of the test and shape functions or in the integration process. However, the shape functions used in MLPG have complicated forms, which makes their computation and their derivative's computation costly. In this work, using the Moving Least Square (MLS) Method, we dissociate the point where the approximating polynomial's coefficients are optimized, from the points where its derivatives are computed. We argue that this approach not only is consistent with the underlying approximation hypothesis, but also makes computation of derivatives simpler. We apply our approach to a two-point boundary value problem and perform several tests to support our claim. The results show that the proposed model is efficient, achieves good precision, and is attractive to be applied to other higher-dimension problems. |
|---|---|
| Main Authors: | Oliveira,Suzana Matos França de |
| Other Authors: | Sousa,Laise Lima de Carvalho; Vidal,Creto Augusto; Cavalcante-Neto,Joaquim Bento |
| Subject: | meshless method meshless local Petrov-Galerkin (MLPG) method boundary value problem |
| Year: | 2020 |
| Country: | Brazil |
| Document type: | article |
| Access type: | open access |
| Associated institution: | IBICT |
| Language: | English |
| Origin: | Oasisbr |
| _version_ | 1871511047968391168 |
|---|---|
| author | Oliveira,Suzana Matos França de |
| author2 | Sousa,Laise Lima de Carvalho Vidal,Creto Augusto Cavalcante-Neto,Joaquim Bento |
| author2_role | author author author |
| author_facet | Oliveira,Suzana Matos França de Sousa,Laise Lima de Carvalho Vidal,Creto Augusto Cavalcante-Neto,Joaquim Bento |
| author_role | author |
| country_str | BR |
| creators_json_txt | [{\"Person.name\":\"Oliveira,Suzana Matos França de\"},{\"Person.name\":\"Sousa,Laise Lima de Carvalho\"},{\"Person.name\":\"Vidal,Creto Augusto\"},{\"Person.name\":\"Cavalcante-Neto,Joaquim Bento\"}] |
| datacite.creators.creator.creatorName.fl_str_mv | Oliveira,Suzana Matos França de Sousa,Laise Lima de Carvalho Vidal,Creto Augusto Cavalcante-Neto,Joaquim Bento |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | meshless method meshless local Petrov-Galerkin (MLPG) method boundary value problem |
| datacite.titles.title.fl_str_mv | A Locally-Continuous Meshless Local Petrov-Galerkin Method Applied to a Two-point Boundary Value Problem |
| dc.creator.none.fl_str_mv | Oliveira,Suzana Matos França de Sousa,Laise Lima de Carvalho Vidal,Creto Augusto Cavalcante-Neto,Joaquim Bento |
| dc.format.none.fl_str_mv | text/html |
| dc.identifier.none.fl_str_mv | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252020000800504 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Associação Brasileira de Ciências Mecânicas |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.source.none.fl_str_mv | Latin American Journal of Solids and Structures v.17 n.8 2020 reponame:Latin American journal of solids and structures (Online) instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) instacron:ABCM |
| dc.subject.none.fl_str_mv | meshless method meshless local Petrov-Galerkin (MLPG) method boundary value problem |
| dc.title.fl_str_mv | A Locally-Continuous Meshless Local Petrov-Galerkin Method Applied to a Two-point Boundary Value Problem |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | Abstract In recent years, the Meshless Local Petrov-Galerkin (MLPG) Method has attracted the attention of many researchers in solving several types of boundary value problems. This method is based on a local weak form, evaluated in local subdomains and does not require any mesh, either in the construction of the test and shape functions or in the integration process. However, the shape functions used in MLPG have complicated forms, which makes their computation and their derivative's computation costly. In this work, using the Moving Least Square (MLS) Method, we dissociate the point where the approximating polynomial's coefficients are optimized, from the points where its derivatives are computed. We argue that this approach not only is consistent with the underlying approximation hypothesis, but also makes computation of derivatives simpler. We apply our approach to a two-point boundary value problem and perform several tests to support our claim. The results show that the proposed model is efficient, achieves good precision, and is attractive to be applied to other higher-dimension problems. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| id | oasisbr_64e878a178a9929e9f7cdcbcc720bb6d |
| identifier.url.fl_str_mv | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252020000800504 |
| inst_facet_str | urn:organizationAcronym:oasisbr{{{_:::_}}}IBICT |
| instacron_str | OASISBR |
| institution | IBICT |
| instname_str | IBICT |
| language | eng |
| network_acronym_str | oasisbr |
| network_name_str | Oasisbr |
| oai_identifier_str | oai:scielo:S1679-78252020000800504 |
| organization_str_mv | urn:organizationAcronym:oasisbr |
| person_str_mv | Oliveira,Suzana Matos França de Sousa,Laise Lima de Carvalho Vidal,Creto Augusto Cavalcante-Neto,Joaquim Bento |
| publishDate | 2020 |
| publisher.none.fl_str_mv | Associação Brasileira de Ciências Mecânicas |
| repo_facet_str | urn:repositoryAcronym:oasisbr{{{_:::_}}}Oasisbr |
| reponame_str | Oasisbr |
| repository_id_str | urn:repositoryAcronym:oasisbr |
| service_str_mv | urn:repositoryAcronym:oasisbr |
| spelling | A Locally-Continuous Meshless Local Petrov-Galerkin Method Applied to a Two-point Boundary Value ProblemOliveira,Suzana Matos França deSousa,Laise Lima de CarvalhoVidal,Creto AugustoCavalcante-Neto,Joaquim Bentomeshless methodmeshless local Petrov-Galerkin (MLPG) methodboundary value problemopen accesshttp://purl.org/coar/access_right/c_abf2http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252020000800504URLhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252020000800504URLHasVersion2020-01-01Abstract In recent years, the Meshless Local Petrov-Galerkin (MLPG) Method has attracted the attention of many researchers in solving several types of boundary value problems. This method is based on a local weak form, evaluated in local subdomains and does not require any mesh, either in the construction of the test and shape functions or in the integration process. However, the shape functions used in MLPG have complicated forms, which makes their computation and their derivative's computation costly. In this work, using the Moving Least Square (MLS) Method, we dissociate the point where the approximating polynomial's coefficients are optimized, from the points where its derivatives are computed. We argue that this approach not only is consistent with the underlying approximation hypothesis, but also makes computation of derivatives simpler. We apply our approach to a two-point boundary value problem and perform several tests to support our claim. The results show that the proposed model is efficient, achieves good precision, and is attractive to be applied to other higher-dimension problems.engtext/htmlAssociação Brasileira de Ciências MecânicasLatin American Journal of Solids and Structures v.17 n.8 2020reponame:Latin American journal of solids and structures (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCMjournal articlehttp://purl.org/coar/resource_type/c_6501literatureVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85 |
| spellingShingle | A Locally-Continuous Meshless Local Petrov-Galerkin Method Applied to a Two-point Boundary Value Problem Oliveira,Suzana Matos França de meshless method meshless local Petrov-Galerkin (MLPG) method boundary value problem |
| status | SINGLETON |
| status_str | VoR |
| subject.fl_str_mv | meshless method meshless local Petrov-Galerkin (MLPG) method boundary value problem |
| title | A Locally-Continuous Meshless Local Petrov-Galerkin Method Applied to a Two-point Boundary Value Problem |
| title_full | A Locally-Continuous Meshless Local Petrov-Galerkin Method Applied to a Two-point Boundary Value Problem |
| title_fullStr | A Locally-Continuous Meshless Local Petrov-Galerkin Method Applied to a Two-point Boundary Value Problem |
| title_full_unstemmed | A Locally-Continuous Meshless Local Petrov-Galerkin Method Applied to a Two-point Boundary Value Problem |
| title_short | A Locally-Continuous Meshless Local Petrov-Galerkin Method Applied to a Two-point Boundary Value Problem |
| title_sort | A Locally-Continuous Meshless Local Petrov-Galerkin Method Applied to a Two-point Boundary Value Problem |
| topic | meshless method meshless local Petrov-Galerkin (MLPG) method boundary value problem |
| topic_facet | meshless method meshless local Petrov-Galerkin (MLPG) method boundary value problem |
| url | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252020000800504 |
| visible | 1 |
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