Meshless local Petrov-Galerkin method for heat conduction problem in an anisotropic medium

CMES - Computer Modeling in Engineering and Sciences

Volumn 6, Issue 3, 2004, Pages 309-318

  Sladek, J ^a   Sladek, V ^a   Atluri, S N ^b  

^a INSTITUTE OF CONSTRUCTION AND ARCHITECTURE   (Slovakia)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Fundamental solution; Heaviside step function; Laplace transform; Local weak form; Meshless method; Moving least squares interpolation

Indexed keywords

ANISOTROPY; APPROXIMATION THEORY; GALERKIN METHODS; HEAT CONDUCTION; INTERPOLATION; LAPLACE TRANSFORMS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

FUNDAMENTAL SOLUTION; HEAVISIDE STEP FUNCTION; LOCAL WEAK FORM; MESHLESS METHOD; MOVING LEAST SQUARES INTERPOLATION;

MATERIALS SCIENCE;

EID: 8344270336     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. Atluri, S. N. (2004): The Meshless Method(MLPG) for Domain & BIE Discretizations, 688 pages, Tech Science Press, Forsyth, GA.
2. Atluri S. N.,; Shen S. (2002a): The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple & Less-costly Alternative to the Finite Element and Boundary Element Methods, CMES: Computer Modeling in Engineering & Sciences, 3: 11-52.
3. Atluri, S. N.; Shen, S. (2002b): The Meshless Local Petrov-Galerkin (MLPG) Method, Tech Science Press, Forsyth, GA.
4. Atluri, S. N.; Sladek, J.; Sladek, V.; Zhu, T. (2000): The local boundary integral equation (LBIE) and its meshless implementation for linear elasticity. Comput. Mech., 25: 180-198.
5. Atluri, S. N.; Han, Z. D.; Shen, S. (2003): Meshless local Petrov-Galerkin (MLPG) approaches for solving the weakly-singular traction & displacement boundary integral equations. CMES: Computer Modeling in Engineering & Sciences, 4: 507-516.
6. Belytschko, T.; Lu, Y.; Gu, L. (1994): Element free Galerkin methods. Int. J. Num. Meth. Engn., 37: 229-256.
7. Belytschko, T.; Krogauz, Y.; Organ, D.; Fleming, M.; Krysl, P. (1996): Meshless methods; an overview and recent developments. Comp. Meth. Appl. Mech. Engn., 139: 3-47.
8. Brebbia, C. A.; Telles, J. C. F.; Wrobel, L. C. (1984): Boundary Element Techniques, Springer.
9. 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. J. Heat and Mass Transfer, 16: 1905-1918.
10. Mikhailov, S. E. (2002): Localized boundary-domain integral formulations for problems with variable coefficients. Engn. Analysis with Boundary Elements, 26: 681-690.
11. Sladek, J.; Sladek, V.; Atluri, S. N. (2001): A pure contour formulation for the meshless local boundary integral equation method in thermoelasticity. CMES: Computer Modeling in Engineering & Sciences, 2: 423-434.
12. Sladek, J.; Sladek, Y.; Mang, H. A. (2002): Meshless formulations for simply supported and clamped plate problems. Int. J. Num. Meth. Engn. 55: 359-375.
13. Sladek, J.; Sladek, V.; Van Keer, R. (2003a): Meshless local boundary integral equation method for 2D elastodynamic problems. Int. J. Num. Meth. Engn., 57: 235-249.
14. Sladek, J.; Sladek, V.; Zhang, Ch. (2003b): Application of meshless local Petrov-Galerkin (MLPG) method to elastodynamic problems in continuously nonhomogeneous solids, CMES: Computer Modeling in Engn. & Sciences, 4: 637-648.
15. Sladek, J.; Sladek, V.; Zhang, Ch. (2003c): Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method. Comput. Material Science, 28: 494-504.
16. Sladek, J.; Sladek, V.; Krivacek, J.; Zhang, Ch. (2003d): Local BIEM for transient heat conduction analysis in 3-D axisymmetric functionally graded solids. Comput. Mech., 32: 169-176.
17. Stehfest, H. (1970): Algorithm 368: numerical inversion of Laplace transform. Comm. Assoc. Comput. Mach., 13: 47-49.
18. Sutradhar, A.; Paulino, G. H.; Gray, L. J. (2002): Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method. Engn. Analysis with Boundary Elements, 26: 119-132.
19. Zhu, T.; Zhang, J. D.; Atluri, S. N. (1998): A Local Boundary Integral Equation (LBIE) Method in Computational Mechanics, and a Meshless Discretization Approach, Computational Mechanics, 21: pp. 223-235.