A local mesh free numerical method with automatic parameter optimization. (April 2020)

• Record Type: Journal Article
• Authors: Santana, E.; Oliveira, T.; Vélez, W.; Araújo, A.; Martins, F.; Portela, A.
• Is Part Of: Engineering analysis with boundary elements. Volume 113(2020)
• Page Start: 55
• Page End: 71
• Publication Date: 2020-04
• Subjects: Local mesh less method -- Local mesh free method -- Parameter optimization -- Genetic algorithms -- Symbiotic organisms search -- Local formulation; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2019.12.013
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: 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.