|
|
|
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 |
|
|
|
|
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.
|
Received: 23 December 2011
Revised: 23 February 2012
Accepted manuscript online:
|
|
PACS:
|
02.60.Cb
|
(Numerical simulation; solution of equations)
|
| |
02.60.Lj
|
(Ordinary and partial differential equations; boundary value problems)
|
| |
02.30.Em
|
(Potential theory)
|
|
| 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
|
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
|
| [1] |
Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P 1996 Comput. Methods Appl. Mech. Engrg. 139 3
|
| [2] |
Qin Y X and Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese)
|
| [3] |
Cheng R J and Cheng Y M 2011 Acta Phys. Sin. 60 070206 (in Chinese)
|
| [4] |
Li S C, Cheng Y M and Li S C 2006 Acta Phys. Sin. 55 4760 (in Chinese)
|
| [5] |
Cheng Y and Li J 2006 Sci. Chin. Ser. G: Phys. Mech. Astron. 49 46
|
| [6] |
Li D M, Peng M J and Cheng Y M 2011 Sci. Sin. Phys. Mech. Astron. 41 1003 (in Chinese)
|
| [7] |
Dai B D and Cheng Y M 2007 Acta Phys. Sin. 56 597 (in Chinese)
|
| [8] |
Cheng R J and Cheng Y M 2008 Acta Phys. Sin. 57 6037 (in Chinese)
|
| [9] |
Cheng R J and Cheng Y M 2011 Chin. Phys. B 20 070206
|
| [10] |
Chen L and Cheng Y M 2010 Chin. Phys. B 19 090204
|
| [11] |
Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese)
|
| [12] |
Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese)
|
| [13] |
Cheng Y M and Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese)
|
| [14] |
Lancaster P and Salkauskas K 1981 Math. Comput. 37 141
|
| [15] |
Afshar M H, Naisipour M and Amani J 2011 Finite Elem. Anal. Des. 47 1315
|
| [16] |
Wang J F, Bai F N and Cheng Y M 2011 Chin. Phys. B 20 030206
|
| [17] |
Zhang Z, Zhao P and Liew K M 2009 Eng. Anal. Bound. Elem. 33 547
|
| [18] |
Li X L and Zhu J L 2011 Adv. Eng. Softw. 42 927
|
| [19] |
Ren H P, Cheng Y M and Zhang W 2009 Chin. Phys. B 18 4065
|
| [20] |
Cheng Y M, Peng M J and Li J H 2005 Chin. J. Theor. Appl. Mech. 37 719 (in Chinese)
|
| [21] |
Bai F N, Li D M, Wang J F and Cheng Y M 2012 Chin. Phys. B 21 020204
|
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
