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Chin. Phys. B, 2012, Vol. 21(10): 100208    DOI: 10.1088/1674-1056/21/10/100208
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The complex variable meshless local Petrov–Galerkin method of solving two-dimensional potential problems

Yang Xiu-Li (杨秀丽), Dai Bao-Dong (戴保东), Zhang Wei-Wei (张伟伟)
Department of Engineering Mechanics, Taiyuan University of Science & Technology, Taiyuan 030024, China
Abstract  Based on the complex variable moving least-square (CVMLS) approximation and a local symmetric weak form, the complex variable meshless local Petrov-Galerkin (CVMLPG) method of solving two-dimensional potential problems is presented in this paper. In the present formulation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square (MLS) approximation. The essential boundary conditions are imposed by the penalty method. The main advantage of this approach over the conventional meshless local Petrov-Galerkin (MLPG) method is its computational efficiency. Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.
Keywords:  meshless method      complex variable moving least-square method      complex variable meshless local Petrov-Galerkin method      potential problems  
Received:  28 February 2012      Revised:  22 March 2012      Accepted manuscript online: 
PACS:  02.60.-x (Numerical approximation and analysis)  
  02.70.Pt (Boundary-integral methods)  
  02.70.-c (Computational techniques; simulations)  
  46.25.-y (Static elasticity)  
Fund: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11102125).
Corresponding Authors:  Dai Bao-Dong     E-mail:  Dai_baodong@126.com

Cite this article: 

Yang Xiu-Li (杨秀丽), Dai Bao-Dong (戴保东), Zhang Wei-Wei (张伟伟) The complex variable meshless local Petrov–Galerkin method of solving two-dimensional potential problems 2012 Chin. Phys. B 21 100208

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