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A boundary meshless method using Chebyshev interpolation and trigonometric basis function for solving heat conduction problems
Author(s) -
Reutskiy S. Yu.,
Chen C. S.,
Tian H. Y.
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2230
Subject(s) - regularized meshless method , mathematics , interpolation (computer graphics) , singular boundary method , trigonometric functions , trigonometric series , boundary value problem , boundary (topology) , scheme (mathematics) , chebyshev polynomials , mathematical analysis , method of fundamental solutions , series (stratigraphy) , meshfree methods , thermal conduction , radial basis function , trigonometry , computer science , finite element method , geometry , boundary element method , physics , animation , paleontology , computer graphics (images) , machine learning , biology , artificial neural network , thermodynamics
A boundary meshless method has been developed to solve the heat conduction equations through the use of a newly established two‐stage approximation scheme and a trigonometric series expansion scheme to approximate the particular solution and fundamental solution, respectively. As a result, no fundamental solution is required and the closed form of approximate particular solution is easy to obtain. The effectiveness of the proposed computational scheme is demonstrated by several examples in 2D and 3D. We also compare our proposed method with the finite‐difference method and the other meshless method showed in Šarler and Vertnik ( Comput. Math. Appl. 2006; 51 :1269–1282). Excellent numerical results have been observed. Copyright © 2007 John Wiley & Sons, Ltd.