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A new complex variable element-free Galerkin method for two-dimensional potential problems |
Cheng Yu-Min (程玉民), Wang Jian-Fei (王健菲), Bai Fu-Nong (白福浓) |
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; b Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China |
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Abstract In this paper, based on the element-free Galerkin (EFG) method and the improved complex variable moving least-square (ICVMLS) approximation, a new meshless method, which is the improved complex variable element-free Galerkin (ICVEFG) method, for two-dimensional potential problems is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square (CVMLS) approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method.
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Received: 23 December 2011
Revised: 23 February 2012
Accepted manuscript online:
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PACS:
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02.60.Cb
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(Numerical simulation; solution of equations)
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02.60.Lj
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(Ordinary and partial differential equations; boundary value problems)
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02.30.Em
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(Potential theory)
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Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11171208), the Shanghai Leading Academic Discipline Project, China (Grant No. S30106), and the Innovation Fund Project for Graduate Student of Shanghai University, China (Grant No. SHUCX112359). |
Corresponding Authors:
Cheng Yu-Min
E-mail: ymcheng@shu.edu.cn
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Cite this article:
Cheng Yu-Min (程玉民), Wang Jian-Fei (王健菲), Bai Fu-Nong (白福浓) A new complex variable element-free Galerkin method for two-dimensional potential problems 2012 Chin. Phys. B 21 090203
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