Conference Paper

Sistema LExVE -SOLVER: Módulo de processamento CAD/CAE em JAVA voltado ao método element-free Galerkin

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Abstract

This paper presents the development of a solver module for a CAD / CAE system developed in JAVA language called LExVE with the Element-Free Galerkin method (EFGM). The EFGM interpolating approach combined with the consistency one is enriched with additional techniques that support intrinsic needs to apply the method for solving equations of Laplace and Poisson type involving heterogeneous media.

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... O LExVE está organizado em três módulos, sendo: um módulo de desenho, denominado Modeler (Pereira et al., 2012), que oferece ferramentas para a modelagem geométrica de dispositivos variados e ainda permite ajustar parâmetros livres associados ao EFGM; um módulo de cálculo, denominado Solver ( Sperotto et al., 2012), que efetua os cálculos inerentes à resolução das EDP´s fazendo uso da formulação interpolante do EFGM; e um módulo de exploração, denominado Explorer (Almeida et al., 2012), que fornece a representação gráfica das aproximações obtidas, permitindo a observação do comportamento dos fenômenos físicos de interesse por meio de sua visualização científica. As ferramentas desenvolvidas foram incorporadas às interfaces gráficas dos módulos LExVE-Modeler e LExVE-Explorer. ...
... Essas não são as únicas situações em que tais representações visuais são pertinentes. Uma técnica para tratamento de condições de interface recentemente proposta ( Sperotto et al., 2012) e em investigação é denominada de ajuste de domínios de influência, e a ideia básica é reduzir o tamanho dos raios de influência quando esses ultrapassarem interfaces materiais, deixando apenas os nós sobre a linha da interface conectando ambos os lados da interface material. Essa técnica pode ser aplicada livremente como uma atividade de pré-processamento a partir de uma ferramenta que permita ao usuário ajustar os raios de influência nodais dos nós, nesse caso, os nós de interesse seriam os localizados nas vizinhanças de interfaces críticas. ...
... Vale lembrar que convencionalmente utiliza-se domínios de influência centrados nos pontos nodais, e desse modo ressalta-se que a opção de domínios excêntricos é de carater experimental pois flexibiliza do ponto de vista técnico-científico o uso do software para testar diferentes abordagens de configuração dos parâmetros do EFGM, como a técnica de ajustes de domínio para tratamento de interface material ( Sperotto et al., 2012;2013 ...
Conference Paper
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The Element Free Galerkin Method (EFGM) has been successfully applied in various fields providing accurate approximations in wide variety of relatively complex problems, often presenting results of higher accuracy than those obtained by the Finite Element Method (FEM) of first order for the same nodal discretization. Despite the recognized numerical efficiency, the main drawback lies in the greater computational cost compared to the FEM and the adjustment of the free numerical parameters. This paper describes the development of software tools to handle theoretical concepts of EFGM through the free parameters in the process of specifying a simulation design CAD /CAE (Computer Aided Design /Computer Aided Engineering). The main contributions are the description and analysis of novel tools that allow new forms of interaction, inspection and adjustment in the pre-and post-processing stages of a CAD /CAE system based on the EFGM, looking for advances of pre-processing tools for a better support in the EFGM application.
... O sistema de software LExVE, totalmente desenvolvido em linguagem JAVA, dispõe de interfaces gráficas para especificação geométricas e físicas do modelo [9], para especificação numérica dos parâmetros do MEFG/MEFGI e de técnicas auxiliares [10] e para visualização científica dos resultados numéricos [11]. A partir de uma versão estável, novas técnicas numéricas foram testadas e implementadas separadamente devido às condições de desenvolvimento i.e. para o melhoramento de algoritmos de visualização científica em [12] e para ajuste avançado de parâmetros numéricos em [13]. ...
... Quanto ao tratamento de interfaces materiais, o LExVE implementa o truncamento modificado e uma abordagem à técnica em pesquisa inspirada no ajuste de domínios [4,10]. Uma abordagem autoadaptativa para tratamento de interfaces materiais vem sendo investigada pelo grupo obtendo os primeiros parâmetros para aplicação delimitados [13] e será incorporada ao sistema LExVE, inicialmente para facilitar os processos de teste dessa abordagem. ...
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Simulation software for Engineering are important tools to the sector of production because they are related to cost reduction and innovation processes. We propose to continue the development of a simulation software system, named LExVE, for electromagnetic phenomena using the Interpolating Element-Free Galerkin Method. From versions developed in JAVA, we will hold the system's software re-engineering integrating all versions, translate the calculation core for the C++ language, and analyze the robustness of recently proposed auxiliary techniques.
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Este trabalho apresenta um sistema de software em desenvolvimento no Laboratório de Engenharia Virtual do Instituto de Estudos Avançados (IEAv/CTA). O sistema de software permite a análise de dispositivos e componentes de óptica integrada, microondas e fibras ópticas, assim como dispositivos eletromagnéticos, e térmicos utilizando o Método dos Elementos Finitos (MEF) bidimensional.
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Purpose – This paper proposes an interpolating approach of the element-free Galerkin method (EFGM) coupled with a modified truncation scheme for solving Poisson's boundary value problems in domains involving material non-homogeneities. The suitability and efficiency of the proposed implementation are evaluated for a given set of test cases of electrostatic field in domains involving different material interfaces. Design/methodology/approach – The authors combined an interpolating approximation with a modified domain truncation scheme, which avoids additional techniques for enforcing the Dirichlet boundary conditions and for dealing with material interfaces usually employed in meshfree formulations. Findings – The local electric potential and field distributions were correctly described as well as the global quantities like the total potency and resistance. Since, the treatment of the material interfaces becomes practically the same for both the finite element method (FEM) and the proposed EFGM, FEM-oriented programs can, thus, be easily extended to provide EFGM approximations. Research limitations/implications – The robustness of the proposed formulation became evident from the error analyses of the local and global variables, including in the case of high-material discontinuity. Practical implications – The proposed approach has shown to be as robust as linear FEM. Thus, it becomes an attractive alternative, also because it avoids the use of additional techniques to deal with boundary/interface conditions commonly employed in meshfree formulations. Originality/value – This paper reintroduces the domain truncation in the EFGM context, but by using a set of interpolating shape functions the authors avoided the use of Lagrange multipliers as well as of a penalty strategy. The resulting formulation provided accurate results including in the case of high-material discontinuity.
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An element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least-squares interpolants and the choices of the weight function are also discussed in this paper.
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A method is presented for application of the Element-Free Galerkin method (EFG) to solid mechanics problems containing material discontinuities. By using the EFG method, the trial and test functions for the weak form are constructed with moving least-square interpolants in each material domain. Additional constraints are imposed at the variational level to ensure satisfaction of interface conditions. As a result, only nodal data (no elemental connectivity) is needed. Given C1 continuity of the interpolant weighting function, the dependent variable and its gradient are continuous in each material domain. Two linear elastic bi-material examples are presented to illustrate the effectiveness of the method.
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Modelos e Projetos Baseados em Objetos com UML2
  • M Blaha
  • J Rumbaugh
M. Blaha e J. Rumbaugh, Modelos e Projetos Baseados em Objetos com UML2, 2ª Ed., Trad. Daniel Vieira. Rio de Janeiro: Elsevier, 2006.