Please wait a minute...
Chin. Phys. B, 2009, Vol. 18(10): 4065-4073    DOI: 10.1088/1674-1056/18/10/002
GENERAL Prev   Next  

An improved boundary element-free method (IBEFM) for two-dimensional potential problems

Ren Hong-Ping(任红萍)a), Cheng Yu-Min(程玉民)b)† , and Zhang Wu(张武)a)
aSchool of Computer Engineering and Science, Shanghai University, Shanghai 200072, China;  Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
Abstract  The interpolating moving least-squares (IMLS) method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method (BEFM), combining the boundary integral equation (BIE) method with the IMLS method, the improved boundary element-free method (IBEFM) for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker $\delta$ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker $\delta$  function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.
Keywords:  moving least-squares approximation      interpolating moving least-squares method      meshless method      improved boundary element-free method      potential problem  
Received:  07 October 2008      Revised:  01 February 2009      Accepted manuscript online: 
PACS:  02.70.Rr (General statistical methods)  
  02.30.Em (Potential theory)  
  02.30.Mv (Approximations and expansions)  
  02.30.Rz (Integral equations)  
  02.30.Sa (Functional analysis)  
  02.60.Nm (Integral and integrodifferential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10871124), Innovation Program of Shanghai Municipal Education Commission (Grant No 09ZZ99) and Shanghai Leading Academic Discipline Project (Grant No J50103).

Cite this article: 

Ren Hong-Ping(任红萍), Cheng Yu-Min(程玉民), and Zhang Wu(张武) An improved boundary element-free method (IBEFM) for two-dimensional potential problems 2009 Chin. Phys. B 18 4065

[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 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.
[13] 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.
[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!