A one-dimensional least-square-consistent displacement-based meshless local Petrov-Galerkin method

• Autor(a) principal: Sousa, Laise Lima de Carvalho
• Data de Publicação: 2019
• Outros Autores: Oliveira, Suzana Matos França de, Vidal, Creto Augusto, Cavalcante Neto, Joaquim Bento
• Tipo de documento: Relatório
• Idioma: eng
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/48390
• topic: Meshless method; Meshless local Petrov-Galerkin (MLPG) method; Boundary value problem

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.