Local integral equations and two meshless polynomial interpolations with application to potential problems in non-homogeneous media

CMES - Computer Modeling in Engineering and Sciences

Volumn 7, Issue 1, 2005, Pages 69-83

  Sladek, V ^a   Sladek, J ^a   Tanaka, M ^b  

^a INSTITUTE OF CONSTRUCTION AND ARCHITECTURE   (Slovakia)

^b SHINSHU UNIVERSITY   (Japan)

Author keywords

Anisotropy; Continuous non homogeneity; Fundamental solution; Integral equations; Subdomain

Indexed keywords

ANISOTROPY; APPROXIMATION THEORY; CONTINUUM MECHANICS; FINITE ELEMENT METHOD; INTERPOLATION; NUMERICAL ANALYSIS; POLYNOMIALS; PROBLEM SOLVING;

CONTINUOUS NON-HOMOGENEITY; FUNCTIONAL GRADED MATERIALS (FGM); FUNDAMENTAL SOLUTIONS; SUBDOMAIN;

INTEGRAL EQUATIONS;

EID: 13244264884     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. Abramowitz, M.; Stegun, I. A. (1964): Handbook of Mathematical Functions, Applied Mathematics Series. Dover Publications, New York, 1046 pages.
2. Atluri, S. N.; Zhu, T. (1998a): A new meshless local Petrov-Galerkin (MLPG) approach to nonlinear problems in computational modeling and simulation. Comput. Modeling Simulation in Engrg., vol. 3, pp. 187-196.
3. Atluri, S. N.; Zhu, T. (1998b): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech., vol. 22, pp. 117-127.
4. Atluri, S. N.; Zhu, T. (1999): The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Comput. Mech., vol. 25, pp. 169-179.
5. Atluri, S. N.; Shen, S. (2002a): The Meshless Local Petrov-Galerkin (MLPG) Method. Tech Science Press, Encino, 429 pages.
6. Atluri, S. N.; Shen, S. (2002b): The meshless local Petrov-Galerkin (MLPG) method: A simple & lesscostly alternative to the finite element and boundary element method. CMES: Computer Modeling in Engineering& Sciences, vol. 3, pp. 11-52.
7. Atluri, S. N. (2004): The Meshless Method (MLPG) for Domain & BIE Discretizations, Tech Science Press, Forsyth, GA, 688 pages.
8. Chang, Y. P.; Kang, C. S.; Chen, D. J. (1973): The use of fundamental Green's functions for the solution of problems of heat conduction in anisotropic media. Jour. Heat Mass Transf., vol. 16, pp. 1905-1918.
9. Golberg, M. A.; Chen, C. S.; Bowman, H. (1999): Some recent results and proposals for the use of radial basis functions in the BEM. Engn. Anal. Bound. Elem., vol. 23, pp. 285-296.
10. 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.
11. Li, Q.; Shen, S.; Han, Z. D.; Atluri, S. N. (2003): Application of meshless local Petrov-Galerkin (MLPG) to problems with singularities, and material discontinuities, in 3-D elasticity. CMES: Computer Modeling in Engineering & Sciences, vol. 4, pp. 571-585.
12. Liu, G. R. (2003): Mesh Free Methods, Moving beyond the Finite Element Method. CRC Press, Boca Raton, 691 pages.
13. Mikhailov, S. E. (2002): Localized boundary-domain integral formulations for problems with variable coefficients. Eng. Anal. Bound. Elem., vol. 26, pp. 681-690.
14. Mikhailov, S. E.; Nakhova, I. S. (2003): Numerical solution of a Neumann problem with variable coefficients by the localized boundary-domain integral equation method. In: Sia Amini (ed) Fourth UK Conf. on Boundary Integral Methods, Salford University, UK, ISBN 0-902896-40-7, pp. 175-184.
15. Miyamoto, Y.; Kaysser, W. A.; Rabin, B. H., Kawasaki, A.; Ford, R. G. (1999): Functionally Graded Materials, Design, Processing and Applications. Kluwer Academic Publishers, Dordrecht, 330 pages.
16. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. (1988-1992): Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, 1032 pages.
17. Sladek, J.; Sladek, V.; Atluri, S. N. (2002): Application of local boundary integral equation method to solve boundary value problems. Int. J. Appl. Mech., vol. 38, pp. 3-27.
18. Sladek, J.; Sladek, V.; Atluri, S. N. (2004a): Meshless local Petrov-Galerkin method for heat conduction problem in an anisotropic medium. CMES: Computer Modeling in Engineering & Sciences, vol. 6, pp. 309-318.
19. Sladek, J.; Sladek, V.; Atluri, S. N. (2004b): Meshless local Petrov-Galerkin method in anisotropic elasticity. CMES: Computer Modeling in Engineering & Sciences, vol. 5, pp. 477-489.
20. Sladek, V.; Sladek, J. (2000): Global & local integral equations for potential problems in non-homogeneous media. CTU Report, vol. 4, pp. 133-138.
21. Sladek, V.; Sladek, J.; Van Keer, R. (2002): New integral equation approach to solution of diffusion equation. Comp. Assist. Mech. Engn. Sci., vol. 9, pp. 555-572.
22. Sladek, V.; Sladek, J. (2003): A new formulation for solution of boundary value problems using domain-type approximations and local integral equations. Electronic Jour. Bound. Elem.,vol. 1, pp. 132-153.
23. Sladek, V.; Sladek, J.; Zhang, Ch. (2004): Local integro-differential equations with domain elements for numerical solution of PDE with variable coefficients. Jour. Eng. Mathematics, in print.
24. Wrobel, L.C. (2002): The Boundary Element Method, Vol. 1: Applications in Thermo-Fluids and Acoustics. John Wiley & Sons Ltd., Chichester, England, 451 pages.
25. Zhu, T.; Zhang, J. D.; Atluri, S. N. (1998): A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach. Comput. Mech., vol. 21, pp. 223-235.