A matrix triangularization algorithm for the polynomial point interpolation method

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 19, 2003, Pages 2269-2295

  Liu, G R ^a   Gu, Y T ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Computational mechanics; Interpolation function; Meshfree method; Meshless method; Polynomial interpolation

Indexed keywords

ALGORITHMS; MECHANICS; POLYNOMIALS; PROBLEM SOLVING;

SINGULARITY PROBLEMS;

INTERPOLATION;

MATHEMATICAL METHOD;

EID: 0037981463     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(03)00266-4     Document Type: Article

References (31)

1. Gingold, R. A., & Moraghan, J. J. (1977). Smooth particle hydrodynamics: theory and applications to non-spherical stars. Man. Not. Roy. Astron. Soc., 181 375-389.
2. Zhang, X., Song, K. Z., Lu, M. W., & Liu, X. (2000). Meshless methods based on collocation with radial basis functions. Comput. Mech., 26(4), 333-343.
3. Nayroles, B., Touzot, G., & Villon, P. (1992). Generalizing the finite element method diffuse approximation and diffuse elements. Comput. Mech., 10 307-318.
4. Belytschko, T., Lu, Y. Y., & Gu, L. (1994). Element-free Galerkin methods. Int. J. Numer. Methods Engrg., 37 229-256.
5. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M., & Krysl, P. (1996). Meshless methods: an overview and recent development. Comput. Mech. Engrg., 139 3-47.
6. Liu, G. R., & Gu, Y. T. (2001). A point interpolation method for two-dimensional solids. Int. J. Numer. Methods Engrg., 50 937-951.
7. Atluri, S. N., & Zhu, T. (1998). A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech., 22 117-127.
8. Atluri, S. N., & Zhu, T. (2000). New concepts in meshless methods. Int. J. Numer. Methods Engrg., 47 537-556.
9. Gu, Y. T., & Liu, G. R. (2001). A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids. Comput. Mech., 27 188-198.
10. Kothnur, V. S., Mukherjee, S., & Mukherjee, Y. X. (1999). Two-dimensional linear elasticity by the boundary node method. Int. J. Solids Struct., 36 1129-1147.
11. Gu, Y. T., & Liu, G. R. (2002). A boundary point interpolation method for stress analysis of solids. Comput. Mech., 28(1), 47-54.
12. Belytschko, T., & Organ, D. (1995). Coupled finite element-element-free Galerkin method. Comput. Mech., 17 186-195.
13. Gu, Y. T., & Liu, G. R. (2001). A coupled element free Galerkin/boundary element method for stress analysis of two-dimension solid. Comput. Methods Appl. Mech. Engrg., 190 4405-4419.
14. Liu, G. R., & Gu, Y. T. (2000). Coupling element free Galerkin and hybrid boundary element methods using modified variational formulation. Comput. Mech., 26 166-173.
15. Liu, G. R., & Gu, Y. T. (2000). Meshless local Petrov-Galerkin (MLPG) method in combination with finite element and boundary element approaches. Comput. Mech., 26 536-546.
16. Lancaster, P., & Salkauskas, K. (1981). Surfaces generated by moving least squares methods. Math. Comput., 37 141-158.
17. Oden, J. T., Duarte, C. A., & Zienkiewicz, O. C. (1998). A new cloud-based hp finite element method. Comput. Methods Appl. Mech. Engrg., 153 117-126.
18. Babuska, I., & Melenk, J. M. (1997). The partition of unity method. Int. J. Numer. Methods Engrg., 40 727-758.
19. Liu, G. R., & Gu, Y. T. (2001). A local point interpolation method for stress analysis of two-dimensional solids. Struct. Engrg. Mech.--An Int. J., 11(2), 221-236.
20. Gu, Y. T., & Liu, G. R. (2001). A local point interpolation method for static and dynamic analysis of thin beams. Comput. Methods Appl. Mech. Engrg., 190 5515-5528.
21. Liu, G. R., & Gu, Y. T. (2002). Comparisons of two meshfree local point interpolation methods for structural analyses. Comput. Mech., 29 107-121.
22. Liu, G. R., & Gu, Y. T. (2001). A local radial point interpolation method (LR-PIM) for free vibration analyses of 2-D solids. J. Sound Vibr., 246(1), 29-46.
23. Lancaster, P., & Salkauskas, K. (1986). Curve and surface fitting, An introduction. : Academic Press.
24. Liu, G. R. (2002). Mesh Free Methods: Moving Beyond the Finite Element Method. USA: CRC press.
25. Schaback, R., & Wendland, H. (2000). Characterzation and construction of radial basis functions. In N. Dyn, D. Leviatan, D. Levin, & A. Pinkus (Eds.), Multivariate Approximation and Applications, : Cambridge University Press.
26. M.J.D. Powell, Theory of Radial Basis Function Approximation in 1990, in: F.W. Light (Ed.), The Advanced in Numerical Analysis, 1992, pp. 303-322
27. Wendland, H. (1998). Error estimates for interpolation by compactly supported radial basis functions of minimal degree. J. Approx. Theory, 93 258-396.
28. Atluri, S. N., Kim, H. G., & Cho, J. Y. (1999). A critical assessment of the truly meshless local Petrov-Galerkin (MLPG) and local boundary integral equation (LBIE) methods. Comput. Mech., 24 348-372.
29. Timoshenko, S. P., & Goodier, J. N. (1970). Theory of Elasticity. New York: McGraw-Hill.
30. Lu, Y. Y., Belytschko, T., & Gu, L. (1994). A new implementation of the element-free Galerkin method. Comput. Methods Appl. Mech. Engrg., 113 397-414.
31. Roark, R. J., & Young, W. C. (1975). Formulas for Stress and Strain. : McGraw-Hill.