Development of a new meshless - Point weighted least-squares (PWLS) method for computational mechanics

Computational Mechanics

Volumn 35, Issue 3, 2005, Pages 170-181

  Wang, Q X ^a   Li, Hua ^a   Lam, K Y ^b  

^a INSTITUTE OF HIGH PERFORMANCE COMPUTING   (Singapore)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Collocation method; Least squares technique; Meshless method; Numerical analysis; Radial point interpolation method

Indexed keywords

COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; FUNCTIONS; INTERPOLATION; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

COLLOCATION METHOD; MESHLESS METHOD; POINT WEIGHTED LEAST-SQUARES (PWLS); RADIAL POINT INTERPOLATION METHOD;

LEAST SQUARES APPROXIMATIONS;

EID: 16344373076     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-004-0611-z     Document Type: Article

References (31)

1. Atluri SN, Zhu T (1998) A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech. 22:117-127
2. Atluri SN, Kim HG, Cho JY (1999) A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods. Comput. Mech. 24:348-372
3. Balakrishnan K, Ramachandran PA (2001) Osculatory interpolation in the method of fundamental solution for nonlinear Poisson problems. J. Comput. Phys. 172:1-18
4. Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int. J. Numer. Meth. Eng. 37:229-256
5. Dai KY, Liu GR, Lim KM, Gu YT (2003) Comparison between the radial point interpolation and the Kriging interpolation used in meshfree methods. Comput. Mech. 32:60-70
6. De S, Bathe KJ (2000) The method of finite spheres. Comput. Mech. 25:329-345
7. Gingold RA, Moraghan JJ (1977) Smooth particle hydrodynamics:theory and applications to non spherical stars. Man. Not. Roy. Astron. Soc. 181:375-389
8. Golberg MA, Chen CS, Bowman H (1999) Some recent results and proposals for the use of radial basis function in the BEM. Engineering Analysis with Boundary Elements 23:285-296
9. Gu Lei (2003) Moving kriging interpolation and element-free Galerkin method. Int. J. Numer. Meth. Eng. 56:1-11
10. Gu YT, Liu GR (2001a) A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids. Comput. Mech. 27:188-198
11. Gu YT, Liu GR (2001b) A meshless local Petrov-Galerkin (MLPG) formulation for static and free vibration analyses of thin plates. CMES-Comp. Model. Eng. Sci. 2(4):463-476
12. Gu YT, Liu GR (2001c) A local point interpolation method for static and dynamic analysis of thin beams. Comput. Meth. Appl. Mech. Eng. 190(42):5515-5528
13. Gu YT, Liu GR (2002) A boundary point interpolation method for stress analysis of solids. Comput. Mech. 28:47-54
14. Gu YT, Liu GR (2003) A boundary radial point interpolation method (BRPIM) for 2-D structural analyses. Struct. Eng. Mech. An International Journal, 15(5):535-550
15. Kansa EJ (1990) Multiquadrics-A Scattered Data Approximation Scheme with Applications to Computational Fluid dynamics. Comput. Math. Appl. 19(8/9):127-145
16. Lam KY, Wang QX, Li Hua (2004) A novel meshless approach - Local Kriging (LoKriging) method with two-dimensional structural analysis. Comput. Mech. 33(3):235-244
17. Lancaster P, Salkauskas K (1986) Curve and Surface Fitting, an Introduction. Academic Press.
18. Liszka T, Orkisz J (1980) The finite difference methods at arbitrary irregular grids and its applications in applied mechanics. Comp. Struct. 11:83-95
19. Liu GR (2002) Mesh free methods: moving beyond the finite element method. CRC press, USA
20. Liu GR, Gu YT (2001a) A point interpolation method for two-dimensional solids. Int. J. Numer. Meth. Eng 50:937-951
21. Liu GR, Gu YT (2001b) A local point interpolation method for stress analysis of two-dimensional solids. Struct. Eng. Mech. 11(2):221-236
22. Liu GR, Gu YT (2001c) A local radial point interpolation method (LR-PIM) for free vibration analyses of 2-D solids. J. Sound Vibration 246(1):29-46
23. Liu GR, Gu YT (2003a) A meshfree method: meshfree weak-strong (MWS) form method, for 2-D solids. Comput. Mech. 33(1):2-14
24. Liu GR, Gu YT (2003b) An Introduction to MFree Methods and Their Programming. Kluwer Academic Publishers (in press)
25. Liu WK, Jun S, Zhang Y (1995) Reproducing kernel particle methods. Int. J. Numer. Meth. Eng. 20:1081-1106
26. Liu Xin, Liu GR, Tai Kang, Lam KY (2002) Radial basis point interpolation collocation method for 2-D solid problem. In: Liu GR (ed) Advances in Meshfree and X-FEM Methods, Proceedings of the 1st Asian Workshop on Meshfree Methods, World Scientific, pp 35-40
27. Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech. 10:307-318
28. Oñate E, Idelsohn S, Zienkiewicz OZ, Taylor RL (1996) A finite point method in computational mechanics. Applications to convective transport and fluid flow. Int. J. Numer. Meth. Eng. 39:3839-3867
29. Press WH et al (1992) Numerical Recipes in Fortran, 2nd ed. Cambridge, UK
30. Schaback R, Wendland H (2000) Characterzation and construction of radial basis functions. In: Multivariate Approximation and Applications, Dyn N, Leviatan D, Levin D, Pinkus A (eds), Cambridge University Press
31. Zhang X, Liu XH, Song KZ, Lu MW (2001) Least-squares collocation meshless method. Int. J. Numer. Meth. Eng. 51:1089-1100