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An improved interpolating element-free Galerkin method with nonsingular weight function for two-dimensional potential problems |
| Wang Ju-Feng (王聚丰)a b, Sun Feng-Xin (孙凤欣)a c, Cheng Yu-Min (程玉民)a |
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
c Faculty of Science, Ningbo University of Technology, Ningbo 315016, China |
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Abstract In this paper, an improved interpolating moving least-square (IIMLS) method is presented. The shape function of the IIMLS method satisfies the property of Kronecker δ function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. And the number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square (MLS) approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin (IIEFG) method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin (EFG) method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has a higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.
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Received: 20 February 2012
Revised: 04 March 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) and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106). |
Corresponding Authors:
Cheng Yu-Min
E-mail: ymcheng@shu.edu.cn
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Cite this article:
Wang Ju-Feng (王聚丰), Sun Feng-Xin (孙凤欣), Cheng Yu-Min (程玉民) An improved interpolating element-free Galerkin method with nonsingular weight function for two-dimensional potential problems 2012 Chin. Phys. B 21 090204
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| [1] |
Li S C and Cheng Y 2005 Theoretical and Applied Fracture Mechanics 44 234
|
| [2] |
Liew K M, Ren J and Reddy J N 2005 International Journal for Numerical Methods in Engineering 63 1014
|
| [3] |
Liew K M, Cheng Y and Kitipornchai S 2005 International Journal for Numerical Methods in Engineering 64 1610
|
| [4] |
Chen L and Cheng Y 2010 Chin. Phys. B 19 090204
|
| [5] |
Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P 1996 Computer Methods in Applied Mechanics and Engineering 139 3
|
| [6] |
Shepard D 1968 Proceeding of the 23rd ACM National Conference (New York: ACM) p. 517
|
| [7] |
Lancaster P and Salkauskas K 1981 Mathematics of Computation 37 141
|
| [8] |
Belytschko T, Lu Y Y and Gu L 1994 International Journal for Numerical Methods in Engineering 37 229
|
| [9] |
Wang J, Sun F and Cheng R 2010 Chin. Phys. B 19 060201
|
| [10] |
Cheng R and Cheng Y 2007 Acta Phys. Sin. 56 5569 (in Chinese)
|
| [11] |
Wang J, Bai F and Cheng Y 2011 Chin. Phys. B 20 030206
|
| [12] |
Cheng Y, Peng M and Li J 2005 Chinese Journal of Theoretical and Applied Mechanics 37 719
|
| [13] |
Ge H, Liu Y and Cheng R 2012 Chin. Phys. B 21 010206
|
| [14] |
Liew K M, Cheng Y and Kitipornchai S 2006 International Journal for Numerical Methods in Engineering 65 1310
|
| [15] |
Liew K M, Cheng Y and Kitipornchai S 2007 International Journal of Solids and Structures 44 4220
|
| [16] |
Kaljevic I and Saigal S 1997 International Journal for Numerical Methods in Engineering 40 2953
|
| [17] |
Ren H, Cheng Y and Zhang W 2009 Chin. Phys. B 18 4065
|
| [18] |
Ren H, Cheng Y and Zhang W 2010 Science in China Series G: Physics Mechanics and Astronomy 53 758
|
| [19] |
Netuzhylov H 2008 Engineering Analysis with Boundary Elements 32 512
|
| [20] |
Friedrich J 2002 Computers & Geosciences 28 679
|
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