Boundary meshfree methods based on the boundary point interpolation methods

Engineering Analysis with Boundary Elements

Volumn 28, Issue 5, 2004, Pages 475-487

  Liu, G R ^a,b   Gu, Y T ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b SINGAPORE MIT ALLIANCE   (Singapore)

Author keywords

Boundary Element Method; Boundary Integral Equation; Mesh free method; Meshless methods; Numerical Analysis

Indexed keywords

COMPUTATIONAL METHODS; GALERKIN METHODS; INTEGRAL EQUATIONS; INTERPOLATION; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL OPERATORS; POLYNOMIALS; PROBLEM SOLVING;

BOUNDARY INTEGRAL EQUATIONS; MESH FREE METHODS; MESHLESS METHODS;

BOUNDARY ELEMENT METHOD;

EID: 1842864921     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0955-7997(03)00101-2     Document Type: Conference Paper

References (22)

1. Brebbia C.A. The boundary element method for engineers. 1978;Pentech Press/Halstead Press, London/New York.
2. Brebbia C.A., Telles J.C., Wrobel L.C. Boundary element techniques. 1984;Springer, Berlin.
3. Belytschko T., Lu Y.Y., Gu L. Element-free Galerkin methods. Int J Numer Meth Engng. 37:1994;229-256.
4. Liu W.K., Jun S., Zhang Y.F. Reproducing kernel particle methods. Int J Numer Meth Engng. 20:1995;1081-1106.
5. Liu G.R., Gu Y.T. A Point Interpolation Method for two-dimensional solid. Int J Numer Meth Engng. 50:2001;937-951.
6. Liu G.R., Gu Y.T. A local point interpolation method for stress analysis of two-dimensional solids. Struct Engng Mech. 11:(2):2001;221-236.
7. Atluri S.N., Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech. 22:1998;117-127.
8. Gu Y.T., Liu G.R. A coupled Element Free Galerkin/Boundary Element method for stress analysis of two-dimension solid. Comput Meth Appl Mech Engng. 190:2001;4405-4419.
9. Liu G.R., Gu Y.T. Coupling Element Free Galerkin and Hybrid Boundary Element methods using modified variational formulation. Comput Mech. 26:2000;166-173.
10. Liu G.R., Gu Y.T. Meshless Local Petrov-Galerkin (MLPG) method in combination with finite element and boundary element approaches. Comput Mech. 26:(6):2000;536-546.
11. Liu G.R. Meshfree methods - moving beyond the Finite Element Method. 2002;CRC Press, Boca Raton.
12. Kothnur V.S., Mukherjee S., Mukherjee Y.X. Two-dimensional linear elasticity by the boundary node method. Int J Solids Struct. 36:1999;1129-1147.
13. Chati M.K., Mukherjee S., Mukherjee Y.X. The boundary node method for three-dimensional linear elasticity. Int J Numer Meth Engng. 46:1999;1163-1184.
14. Liu G.R., Gu Y.T. A matrix triangularization algorithm for point interpolation method. Computer Methods in Applied Mechanic and Engineering. 28:(1):2003;2269-2295.
15. Gu Y.T., Liu G.R. A boundary point interpolation method for stress analysis of solids. Comput Mech. 28:(1):2002;47-54.
16. Franke C., Schaback R. Solving partial differential equations by collocation using radial basis functions. Appl Math Comput. 93:1997;73-82.
17. Schaback R., Wendland H. Characterzation and construction of radial basis functions. Dyn N., Leviatan D., Levin D., Pinkus A. Multivariate approximation and applications. 2000;Cambridge University Press, Cambridge.
18. Cheng AHD, Golberg MA, Kansa EJ, Zammito G. Exponential convergence and H-c Multiquadric collocation method for PDE. Numer Meth PDE; 2003. Submitted for publication.
19. Timoshenko S.P., Goodier J.N. Theory of elasticity. 3rd edl:1970;McGraw-Hill, New York.
20. DeFigueiredo T.G.B. A new boundary element formulation in engineering. 1991;Springer, Berlin.
21. Kansa E.J. Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics. Comput Math Appl. 19:(8/9):1990;127-145.
22. Poulos H.G., Davis E.H. Elastic solution for soil and rock mechanics. 1974;Wiley, London.