A comparative study of meshless approximations in local integral equation method

Computers, Materials and Continua

Volumn 4, Issue 3, 2006, Pages 177-188

  Sladek, Vladimir ^a   Sladek, Jan ^a   Zhang, Chuanzeng ^b  

^a INSTITUTE OF CONSTRUCTION AND ARCHITECTURE   (Slovakia)

^b UNIVERSITY OF SIEGEN   (Germany)

Author keywords

Collocation method; Elasticity; Functionally Graded Materials (FGMs); Integral equation method; Integral force equilibrium; Point interpolation method; Radial basis functions

Indexed keywords

APPROXIMATION THEORY; BENCHMARKING; BOUNDARY VALUE PROBLEMS; ELASTIC MODULI; ELASTICITY; INTEGRAL EQUATIONS; INTERPOLATION; NUMERICAL METHODS;

BASIS FUNCTIONS; COLLOCATION METHODS; INTEGRAL FORCE EQUILIBRIUM; POINT INTERPOLATION METHODS; RADIAL BASIS FUNCTIONS;

FUNCTIONALLY GRADED MATERIALS;

EID: 33846882001     PISSN: 15462218     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. Atluri, S.N.; Shen, S. (2002): The meshless local Petrov-Galerkin (MLPG) method. Tech Science Press, Encino, 429.
2. Atluri, S.N. (2004): The meshless method (MLPG) for domain & BIE discretizations, Tech Science Press, Forsyth, 677.
3. Hardy, R.L. (1990): Theory and applications of the multiquadrics-biharmonic method (20 years of discovery 1968-1988). Comput Math Appl., vol. 19, pp. 163-208.
4. Hughes, T.J.R. (1987): The finite element method. Linear static and dynamic finite element analysis. Prentice-Hall, Inc.,Englewood Cliffs.
5. Liu, GR. (2003): Mesh free methods, Moving beyond the finite element method. CRC Press, Boca Raton, 691.
6. Liu, GR.; Gu, Y.T. (2001): A local point interpolation method for stress analysis of two-dimensional solids. Struct. Engrg. Mech., vol. 11, pp. 221-236.
7. Liu, GR.; Gu, Y.T. (2003): A meshfree method: mesh-free weak-strong (MWS) form method for 2-D solids. Comput. Mechanics, vol. 33, pp. 2-14.
8. Rippa, S. (1999): An algorithm for selscting a good value for the parameter c in radial basis functions inter-polation. Adv. Comput. Math., vol. 11, pp. 193-210.
9. Sladek, V.; Sladek, J.; Tanaka, M. (2005a): Local integral equations and two meshless polynomial interpolations with application to potential problems in nonhomogeneous media. CMES: Computer Modeling in Engineering & Sciences, vol. 7, pp. 69-83.
10. Sladek, V.; Sladek, J.; Zhang, Ch. (2005b): Local integro-differential equations with domain elements for numerical solution of PDE with variable coefficients. Jour Engn Mathematics, vol. 51, pp. 261-282.
11. Sladek, V.; Sladek, J.; Zhang, Ch. (2006): A meshless Point Interpolation Method for Local Integral Equations in elasticity of non-homogeneous media. In: Advances in the Meshless Method (J. Sladek, V. Sladek, S.N. Atluri, eds.), Tech Science Press, Forsyth, 2006.
12. Wang, J.G.; Liu, G.R. (2002): On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Comput. Meth. Appl. Mech. Engrg., vol 191, pp. 2611-2630.
13. Xiao, J.R.; McCarthy, M.A. (2003): A local Heaviside weighted meshless method for two-dimensional solids using radial basis functions. Comput. Mechanics, vol. 31, pp. 301-315.
14. Xiao, J.R. (2004): Local Heaviside weighted MLPG meshless method for two-dimensional solids using compactly supported radial basis functions. Comput. Meth. Appl. Mech. Engrg., vol. 193, pp. 117-138.
15. Zhou, X.; Hon, Y.C.; Li, J. (2003): Overlapping domain decomposition method by radial basis functions. Appl. Numer. Math., vol. 44, pp. 241-255.