Document Type : Article
Authors
Dept. of Structural Engineering Shahid Chamran University, Ahvaz
Abstract
In recent years, use of meshless methods has been extensively increased. This is probably due to the generality of their applications for the solution of continuous, as well as discontinuous, problems. Nevertheless, discretizetion of
problems in many meshless methods, like many other numerical approaches, leads to integral equations, whose solution requires, in turn, numerical integration, definition of Gauss points, and their weight and mesh generation. Among these methods, however, the Discrete Least Squares Meshless (DLMS) method has been developed, gradually, by researchers in recent years, which possesses the ability to delete integral operations from calculations of the coefficient matrix procedure. Moreover, because of its simplicity, high precision and low computational cost, this approach has been known as a real meshless method. The purpose of this paper is to estimate the error of numerical solutions performed with the discrete least squares meshless method for heat conduction problems.To achieve that point, at first, the governing equations of the heat conduction problem in two dimensional space were extended, and specific boundary conditions of each problem were inserted into the formulations. Then, the Discrete Least Squares Meshless shape of the equations was derived for use in the proposed method. Moving the least squares method for computing the interpolation functions was undertaken. Moreover, the error estimate function was determined using the squares of residuals concept. Finally, the two mentioned examples were solved. The obtained results, between the approximated proposed method and the valid exact solution, which was derived from closed form analytical solutions, were compared, and the accuracy of the discrete least squares meshless method formulation was demonstrated. Furthermore, by using the least squares of residuals concept, error estimation was performed and error distribution or the positions of errors were obtained. By solving these examples, the power of this method to solve other engineering branches, like heat conduction problems, and its high internal error diagnostic property,
was illustrated.
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