|
|
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.
|
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
|
[1] |
Minkowycz W J, Sparrow E M, Schneider G E and Pletcher R H 1988 Handbook of Numerical Heat Transfer (New York: John Wiley and Sons, Inc.)
|
[2] |
Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P 1996 Comput. Methods Appl. Mech. Eng. 139 3
|
[3] |
Zhang X, Liu Y and Ma S 2009 Adv. Mech. 39 1 (in Chinese)
|
[4] |
Belytschko T, Lu Y Y and Gu L 1994 Int. J. Numer. Methods Eng. 37 229
|
[5] |
Cheng R J and Cheng Y M 2008 Acta. Phys. Sin. 57 6037 (in Chinese)
|
[6] |
Atluri S N and Zhu T L 1998 Comput. Mech. 22 117
|
[7] |
Zheng B J and Dai B D 2010 Acta Phys. Sin. 59 5182 (in Chinese)
|
[8] |
Zheng B J and Dai B D 2011 Appl. Math. Comput. 218 563
|
[9] |
Liu W K, Jun S and Zhang Y 1995 Int. J. Numer. Methods Fluids 20 1081
|
[10] |
Chen L and Cheng Y M 2010 Chin. Phys. B 19 090204
|
[11] |
Cheng Y M and Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese)
|
[12] |
Liew K M and Cheng Y M 2009 Comput. Methods Appl. Mech. Eng. 198 3925
|
[13] |
Lancaster P and Salkauskas K 1981 Math. Comput. 37 141
|
[14] |
Lu Y Y, Belytschko T and Gu L 1994 Comput. Methods Appl. Mech. Eng. 113 397
|
[15] |
Cheng Y M and Chen M J 2003 Acta Mech. Sin. 35 181 (in Chinese)
|
[16] |
Liew K M, Feng C, Cheng Y and Kitipornchai S 2007 Int. J. Numer. Methods Eng. 70 46
|
[17] |
Cheng Y M, Peng M J and Li J H 2005 Chin. J. Theor. Appl. Mech. 37 1 (in Chinese)
|
[18] |
Peng M J, Liu P and Cheng Y M 2009 Int. J. Appl. Mech. 1 367
|
[19] |
Bai F N, Li D M, Wang J F and Cheng Y M 2012 Chin. Phys. B 21 020204
|
[20] |
Cheng Y M and Li J H 2006 Sci. Chin. G: Phys. Mech. Astron. 49 46
|
[21] |
Li D M, Peng M J and Cheng Y M 2011 Sci. Chin. Phys. Mech. Astron. 41 1003 (in Chinese)
|
[22] |
Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese)
|
[23] |
Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese)
|
[24] |
Gao H F and Cheng Y M 2009 Chin. J. Theor. Appl. Mech. 41 480 (in Chinese)
|
[25] |
Gao H F and Cheng Y M 2010 Int. J. Comput. Methods 7 55
|
[26] |
Yang X L, Dai B D and Li Z F 2012 Acta Phys. Sin. 61 050204 (in Chinese)
|
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
|
|
|