A one-dimensional least-square-consistent displacement-based meshless local Petrov-Galerkin method
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...
| Autores: | , , , |
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| Tipo de recurso: | informe técnico |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Brasil |
| Institución: | Universidade Federal do Ceará (UFC) |
| Repositorio: | Repositório Institucional da Universidade Federal do Ceará (UFC) |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.ufc.br:riufc/48390 |
| Acceso en línea: | http://www.repositorio.ufc.br/handle/riufc/48390 |
| Access Level: | acceso abierto |
| Palabra clave: | Meshless method Meshless local Petrov-Galerkin (MLPG) method Boundary value problem |
| Sumario: | 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. |
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