The MLPG with improved weight function for two-dimensional heat equation with non-local boundary condition
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Publication Details
Author list: Techapirom T., Luadsong A.
Publisher: Elsevier
Publication year: 2013
Journal: Journal of King Saud University. Science (1018-3647)
Volume number: 25
Issue number: 4
Start page: 341
End page: 348
Number of pages: 8
ISSN: 1018-3647
eISSN: 2213-686X
Languages: English-Great Britain (EN-GB)
Abstract
In this paper, a meshless local Petrov-Galerkin (MLPG) method is presented to treat the heat equation with the Dirichlet, Neumann, and non-local boundary conditions on a square domain. The Moving Least Square (MLS) approximation is a classical MLS method, in which the Gaussian weight function is the most common shape function. However, shape functions for the classical MLS approximation lack the Kronecker delta function property. Thus in this method, the boundary conditions cannot have a penalty parameter imposed easily and directly. In the method we choose a weight function that leads to the MLS approximation shape functions approximating the Kronecker delta function property, and nodes on the Dirichlet boundary conditions, which enables a direct application of essential boundary conditions without the additional numerical method. The improved weight function in MLS approximation has been successfully implemented in solving the diffusion equation problem. Two test problems are presented to verify the efficiency, easiness and accuracy of the method. Also Ne and root mean square errors are obtained to show the convergence of the method. ฉ 2013 King Saud University.
Keywords
Heat equation, Kronecker delta function, MLS approximation
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