A boundary element-free method (BEFM) for two-dimensional potential problems

Engineering Analysis with Boundary Elements

Volumn 33, Issue 1, 2009, Pages 77-82

  Peng, Miaojuan ^a   Cheng, Yumin ^a  

^a SHANGHAI UNIVERSITY   (China)

Author keywords

Boundary element free method (BEFM); Boundary integral equation; Improved moving least squares (IMLS) approximation; Meshless method; Moving least squares (MLS) approximation; Potential problems; Weighted orthogonal function

Indexed keywords

ALGEBRA; BOUNDARY INTEGRAL EQUATIONS; BOUNDARY VALUE PROBLEMS; COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL MECHANICS; FOURIER ANALYSIS; INTEGRAL EQUATIONS; INVERSE PROBLEMS; LEAST SQUARES APPROXIMATIONS; MATRIX ALGEBRA; POLYNOMIAL APPROXIMATION; PROBABILITY DENSITY FUNCTION; TWO DIMENSIONAL;

BOUNDARY ELEMENT-FREE METHOD (BEFM); IMPROVED MOVING LEAST-SQUARES (IMLS) APPROXIMATION; MESHLESS METHOD; MOVING LEAST-SQUARES (MLS) APPROXIMATION; POTENTIAL PROBLEMS; WEIGHTED ORTHOGONAL FUNCTION;

BOUNDARY ELEMENT METHOD;

EID: 56249135922     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2008.03.005     Document Type: Article

References (22)

1. Belytschko T., Krongauz Y., Organ D., Fleming M., and Krysl P. Meshless method: an overview and recent developments. Comput Methods Appl Mech Eng 139 (1996) 3-47
2. Shaofan L., and Liu W.K. Meshfree and particle methods and their applications. Appl Mech Rev 55 (2002) 1-34
3. Lancaster P., and Salkauskas K. Surface generated by moving least squares methods. Math Comput 37 (1981) 141-158
4. Liew K.M., Huang Y.Q., and Reddy J.N. Moving least squares differential quadrature method and its application to the analysis of shear deformable plates. Int J Numer Methods Eng 56 (2003) 2331-2351
5. Liew K.M., Zou G.P., and Rajendran S. A spline strip kernel particle method and its application to two-dimensional elasticity problems. Int J Numer Methods Eng 57 (2003) 599-616
6. Mukherjee Y.X., and Mukherjee S. The boundary node method for potential problems. Int J Numer Methods Eng 40 (1997) 797-815
7. Kothnur V.S., Mukherjee S., and Mukherjee Y.X. Two-dimensional linear elasticity by the boundary node method. Int J Solids Struct 36 (1999) 1129-1147
8. Chati M.K., Mukherjee S., and Mukherjee Y.X. The boundary node method for three-dimensional linear elasticity. Int J Numer Methods Eng 46 (1999) 1163-1184
9. Chati M.K., and Mukherjee S. The boundary node method for three-dimensional problems in potential theory. Int J Numer Methods Eng 47 (2000) 1523-1547
10. Zhu T., Zhang J., and Atluri S.N. A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and non-linear boundary value problems. Eng Anal Boundary Elem 23 (1999) 375-389
11. Atluri S.N., Sladek J., Sladek V., and Zhu T. The local boundary integral equation (LBIE) and it's meshless implementation for linear elasticity. Comput Mech 25 (2000) 180-198
12. Sladek V., Sladek J., Atluri S.N., and Van Keer R. Numerical integration of singularities in meshless implementation of local boundary integral equations. Comput Mech 25 (2000) 394-403
13. Liew K.M., Yumin C., and Kitipornchai S. Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems. Int J Numer Methods Eng 65 (2006) 1310-1332
14. Kitipornchai S., Liew K.M., and Yumin C. A boundary element-free method (BEFM) for three-dimensional elasticity problems. Comput Mech 36 (2005) 13-20
15. Cheng Y., and Peng M. Boundary element-free method for elastodynamics. Sci China Ser G Phys Mech Astron 48 (2005) 641-657
16. Liew K.M., Yumin C., and Kitipornchai S. Boundary element-free method (BEFM) for two-dimensional elastodynamic analysis using Laplace transform. Int J Numer Methods Eng 64 (2005) 1610-1627
17. Yuzhou S., Zan Z., Kitipornchai S., and Liew K.M. Analyzing the interaction between collinear interfacial cracks by an efficient boundary element-free method. Int J Eng Sci 44 (2006) 37-48
18. Liew K.M., Yumin C., and Kitipornchai S. Analyzing the 2D fracture problems via the enriched boundary element-free method. Int J Solids Struct 44 (2007) 4220-4233
19. Liew K.M., Yuzhou S., and Kitipornchai S. Boundary element-free method for fracture analysis of 2D anisotropic piezoelectric solids. Int J Numer Methods Eng 69 (2007) 729-749
20. Yuzhou S., Hu Y.G., and Liew K.M. A mesh-free simulation of cracking and failure using the cohesive segments method. Int J Eng Sci 45 (2007) 541-553
21. Zan Z., Liew K.M., and Yumin C. Coupling of improved element-free Galerkin and boundary element methods for the 2D elasticity problems. Eng Anal Boundary Elem 32 (2008) 100-107
22. Zan Z., Liew K.M., Yumin C., and Lee Y.Y. Analyzing 2D fracture problems with the improved element-free Galerkin method. Eng Anal Boundary Elem 32 (2008) 241-250