A local mesh free numerical method with automatic parameter optimization
| Autor: | E. Santana, Wilber Vélez, A. Portela, F. Martins, Tiago Oliveira, A. Araújo |
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| Rok vydání: | 2020 |
| Předmět: |
Basis (linear algebra)
Discretization Computer science Applied Mathematics Numerical analysis Linear elasticity General Engineering 02 engineering and technology 01 natural sciences Numerical integration 010101 applied mathematics Computational Mathematics 020303 mechanical engineering & transports 0203 mechanical engineering Search algorithm Benchmark (computing) Node (circuits) 0101 mathematics Algorithm Analysis |
| Zdroj: | Engineering Analysis with Boundary Elements. 113:55-71 |
| ISSN: | 0955-7997 |
| DOI: | 10.1016/j.enganabound.2019.12.013 |
| Popis: | The concern of the paper is a local mesh free numerical method, implemented with automatic optimization of the discretization parameters, to solve problems of two-dimensional linear elasticity. For a nodal discretization, the mesh free local method uses a node-by-node process to generate the global system of equilibrium equations; in the local domain of each node, the respective equilibrium equations are generated with a reduced numerical integration and used as the formulation basis of the numerical method. Application of the local numerical method, to each node of a mesh free discretization, requires the use of two arbitrary parameters which specify the size of, respectively the compact support and the local domain of integration. In this paper, these parameters are automatically defined by means of a multi-objective optimization process, based on genetic algorithms, which is the novelty of the present numerical method. For the sake of efficiency a comparison between genetic algorithms and another robust evolutionary optimization method, the symbiotic organism search algorithm, is carried out. A benchmark problem was analyzed to assess the accuracy and efficiency of these techniques. The results presented in the paper are in perfect agreement with those of analytical solutions and therefore, make reliable and robust this mesh free numerical method, implemented with automatic parameter optimization. |
| Databáze: | OpenAIRE |
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