Saturday , June 23 2018

Correction of Meshless FPM Interpolation Sub-domains Using Genetic Algorithms

Luis Perez P.
Universidad Técnica Federico Santa María, Valparaíso, CHILE

Fernando Perez
Pontificia Universidad Católica de Valparaíso
CHILE

Orlando Durán
Pontificia Universidad Católica de Valparaíso
CHILE

Abstract:

This work describes a technique that allows the correction of interpolation sub-domains, using metaheuristics for the implementation of Meshless Methods in the resolution of Partial Differential Equations. A combined strategy has been used based on a specifically developed Genetic Algorithm (GA), and searching and optimization technique. Three sample problems were solved in this work. Results show a decrease in the global error as well as in the quantity of points needed to form the domain.

Keywords:

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CITE THIS PAPER AS:
Luis P. PEREZ, Fernando PEREZ, Orlando DURÁN, Correction of Meshless FPM Interpolation Sub-domains Using Genetic Algorithms, Studies in Informatics and Control, ISSN 1220-1766, vol. 21 (2), pp. 191-200, 2012.

1. Introduction

The meshless or meshfree methods are a family of new numerical techniques that do not require a mesh. In these methods, the body or domain is discretized by a collection of points or nodes. It is divided into local interpolation sub-domains, also called clouds, consisting of one central point, or star node, and several neighbouring points. Generally, these methods are computationally efficient and easy to implement and they have been successfully used in several problems of solid and fluid mechanics.

A detailed review of the most relevant meshless methods and their connections is presented in [1]. An analysis and classification of the most important meshless methods is presented in [2]. Advantages and disadvantages of this techniques are also discussed. A review and important aspects of computer implementation are presented in [3].

The Finite Point Method (FPM) was proposed in [4] with the initial purpose of solving convective transport and fluid flow problems. Later, its application was extended to advection-diffusion transport [5] and incompressible flow problems [6]. In the context of solid mechanics, FPM has been applied successfully in elasticity [7] and non-linear material behaviour problems [8]. The lack of dependence on a mesh or integration procedure is an important feature, which makes the FPM a truly meshless method. A crucial phase of the FPM is the definition of subdomains to perform the local approximations. This paper describes a technique that allows the formation and eventual corrections of the interpolation sub-domains, using Genetic Algorithms. The next section discusses the FPM. Then, in section 3, the Genetic Algorithms are briefly presented. Three sample problems were solved in section 4. Finally, in section 5, conclusions are depicted.

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https://doi.org/10.24846/v21i2y201209