A fundamental solution method for inverse heat conduction problem

Engineering Analysis with Boundary Elements

Volumn 28, Issue 5, 2004, Pages 489-495

  Hon, Y C ^a   Wei, T ^a,b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b LANZHOU UNIVERSITY   (China)

Author keywords

Inverse heat conduction problem; Radial basis functions; Tikhonov regularization

Indexed keywords

APPROXIMATION THEORY; CURVE FITTING; INVERSE PROBLEMS; LINEAR SYSTEMS; PROBLEM SOLVING; RADIAL BASIS FUNCTION NETWORKS;

INVERSE HEAT CONDUCTION PROBLEM; TIKHONOV REGULARIZATION;

HEAT CONDUCTION;

EID: 1842842972     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0955-7997(03)00102-4     Document Type: Conference Paper

References (21)

1. Alves CJS, Chen CS, Sǎler B. The method of fundamental solutions for solving Poisson problems. International series on advances in boundary elements, vol. 13. Boundary elements XXIV; 2002. p.67-76.
2. Chen C.S., Golberg M.A., Hon Y.C. The method of fundamental Solutions and Quasi-Monte-Carlo method for diffusion equations. Int J Numer Meth Engng. 43:(8):1998;1421-1435.
3. Frankel J.I., Keyhani M. A global time treatment for inverse heat conduction problems. Int J Heat Transfer. 119:1997;673-683.
4. Hansen P.C. Analysis of discrete ill-posed problems by means of the L -curve. SIAM Rev. 34:1992;561-580.
5. Hansen P.C. Numerical tools for analysis and solution of Fredholm integral equations of the first kind. Inverse Problems. 8:1992;849-872.
6. Hansen P.C. The L -curve and its use in the numerical treatment of inverse problems. Johnston P. Computational inverse problems in electrocardiology. Advances in computational bioengineering series. vol. 4:2000;WIT Press, Southampton.
7. Hansen P.C. Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems. Numer Algorithms. 6:1994;1-35.
8. Hansen P.C., O'Leary D.P. The use of the L -curve in the regularization of discrete ill-posed problems. SIAM J Sci Comput. 14:1993;1487-1503.
9. Hon Y.C., Cheung K.F., Mao X.Z., Kansa E.D. Multiquadric solution for shallow water equations. ASCE J Hydraul Engng. 125:1999;524-533.
10. Hon Y.C., Lu M.W., Xue W.M., Zhou X. A new formulation and computation of the triphasic model for mechano-electrochemical mixtures. Computat Mech. 24:1999;155-165.
11. Hon Y.C., Mao X.Z. A radial basis function method for solving options pricing models. J Financial Engng. 8:1999;31-49.
12. Hon Y.C., Wu Z.M. A numerical computation for inverse boundary determination problem. Engng Anal Bound Elem. 24:2000;599-606.
13. Jonas P., Louis A.K. Approximate inverse for a one-dimensional inverse heat conduction problem. Inverse Problems. 16:2000;175-185.
14. Kansa E.J., Hon Y.C. Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations. Comput Math Appl. 39:2000;123-137.
15. Lawson C.L., Hanson R.J. Solving least squares problems. 1995;SIAM, Philadelphia, PA. First published by Prentice-Hall, 1974.
16. Lesnic D., Elliott L. The decomposition approach to inverse heat conduction. J Math Anal Appl. 232:1999;82-98.
17. Lesnic D., Elliott L., Ingham D.B. Application of the boundary element method to inverse heat conduction problems. Int Commun Heat Mass Transfer. 39:(7):1996;1503-1517.
18. Liu J. A stability analysis on Beck's procedure for inverse heat conduction problem. J Comput Phys. 123:1996;65-73.
19. Shen S.Y. A numerical study of inverse heat conduction problems. Comput Math Appl. 38:1999;173-188.
20. Tikhonov A.N., Arsenin V.Y. On the solution of ill-posed problems. 1977;Wiley, New York.
21. Zerroukat M., Power H., Chen C.S. A numerical method for heat transfer problems using collocation and radial basisfunctions. Int J Numer Meth Engng. 42:1998;1263-1278.