The complex variable meshless local Petrov–Galerkin method of solving two-dimensional potential problems

doi:10.1088/1674-1056/21/10/100208

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

[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)

[1]	Improved reproducing kernel particle method for piezoelectric materials Ji-Chao Ma(马吉超), Gao-Feng Wei(魏高峰), Dan-Dan Liu(刘丹丹). Chin. Phys. B, 2018, 27(1): 010201.
[2]	Topology optimization using the improved element-free Galerkin method for elasticity Yi Wu(吴意), Yong-Qi Ma(马永其), Wei Feng(冯伟), Yu-Min Cheng(程玉民). Chin. Phys. B, 2017, 26(8): 080203.
[3]	Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems Yao-Zong Tang(唐耀宗), Xiao-Lin Li(李小林). Chin. Phys. B, 2017, 26(3): 030203.
[4]	Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method Shen-Shen Chen(陈莘莘), Juan Wang(王娟), Qing-Hua Li(李庆华). Chin. Phys. B, 2016, 25(4): 040203.
[5]	Solving unsteady Schrödinger equation using the improved element-free Galerkin method Rong-Jun Cheng(程荣军) and Yu-Min Cheng(程玉民). Chin. Phys. B, 2016, 25(2): 020203.
[6]	Hybrid natural element method for large deformation elastoplasticity problems Ma Yong-Qi (马永其), Zhou Yan-Kai (周延凯). Chin. Phys. B, 2015, 24(3): 030204.
[7]	Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method Cheng Yu-Min (程玉民), Liu Chao (刘超), Bai Fu-Nong (白福浓), Peng Miao-Juan (彭妙娟). Chin. Phys. B, 2015, 24(10): 100202.
[8]	Hybrid natural element method for viscoelasticity problems Zhou Yan-Kai (周延凯), Ma Yong-Qi (马永其), Dong Yi (董轶), Feng Wei (冯伟). Chin. Phys. B, 2015, 24(1): 010204.
[9]	A meshless algorithm with moving least square approximations for elliptic Signorini problems Wang Yan-Chong (王延冲), Li Xiao-Lin (李小林). Chin. Phys. B, 2014, 23(9): 090202.
[10]	A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation Ge Hong-Xia (葛红霞), Cheng Rong-Jun (程荣军). Chin. Phys. B, 2014, 23(4): 040203.
[11]	Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method Weng Yun-Jie (翁云杰), Cheng Yu-Min (程玉民). Chin. Phys. B, 2013, 22(9): 090204.
[12]	A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems Wang Qi-Fang (王启防), Dai Bao-Dong (戴保东), Li Zhen-Feng (栗振锋). Chin. Phys. B, 2013, 22(8): 080203.
[13]	A meshless Galerkin method with moving least square approximations for infinite elastic solids Li Xiao-Lin (李小林), Li Shu-Ling (李淑玲). Chin. Phys. B, 2013, 22(8): 080204.
[14]	Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method Cheng Rong-Jun, Wei Qi. Chin. Phys. B, 2013, 22(6): 060209.
[15]	An element-free Galerkin (EFG) method for generalized Fisher equations (GFE) Shi Ting-Yu (时婷玉), Cheng Rong-Jun (程荣军), Ge Hong-Xia (葛红霞). Chin. Phys. B, 2013, 22(6): 060210.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

The complex variable meshless local Petrov–Galerkin method of solving two-dimensional potential problems

Cite this article:

Online attention