A meshless method based on RBFs method for nonhomogeneous backward heat conduction problem

Engineering Analysis with Boundary Elements

Volumn 34, Issue 9, 2010, Pages 785-792

  Li, Ming ^a   Jiang, Tongsong ^b,c   Hon, Y C ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b LINYI UNIVERSITY   (China)

^c SHANDONG UNIVERSITY   (China)

Author keywords

BHCP; Ill posed problem; Meshless methods; RBF

Indexed keywords

PROBLEM SOLVING; RADIAL BASIS FUNCTION NETWORKS;

BACKWARD HEAT CONDUCTIONS; BHCP; ILL POSED PROBLEM; INITIAL TEMPERATURES; MESH-LESS METHODS; MESHLESS COMPUTATIONAL METHODS; METHOD OF PARTICULAR SOLUTION; RADIAL BASIS FUNCTIONS;

HEAT CONDUCTION;

EID: 79951514568     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2010.03.010     Document Type: Article

References (29)

1. Chang JR, Liu CS, Chang CW. A new shooting method for quasi-boundary regularization of backward heat conduction problems. International Journal of Heat and Mass Transfer 2007;50:2325-32.
2. Chen LY, Chen JT, Hong HK, Chen CH. Application of cesaro mean and the L-curve for the deconvolution problem. Soil Dynamics and Earthquake Engineering 1995;14:361-73. (Pubitemid 26456023)
3. Cheng AHD, Cabral JJSP. Direct solution of ill-posed boundary value problems by radial basis function collocation method. International Journal for Numerical Methods in Engineering 2005;64(1):45-64. (Pubitemid 41300194)
4. Feng XL, Qian Z, Fu CL Numerical approximation of solution of nonhomo-geneous backward heat conduction problem in bounded region. Mathematics and Computers in Simulation 2008;79:177-88.
5. Fredman TP. A boundary identification method for an inverse heat conduction problem with an application in ironmaking. International Journal of Heat and Mass Transfer 2004;41:95-103. (Pubitemid 40003315)
6. Hadamard J. Lectures on Cauchy problems in linear partial differential equations. New Haven, CT: Yale University Press; 1923.
7. Han H, Ingham DB, Yuan Y. The boundary element method for the solution of the back ward heat conduction equation. Journal of Computational Physics 1995;116:292-9.
8. Hansen PC. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review 1992;34:561-80.
9. Hansen PC. Numerical tools for analysis and solution of Fredholm integral equations of the first kind. Inverse Problems 1992;8:849-72.
10. Hansen PC. The L-curve and its use in the numerical treatment of inverse problems. In: Johnston P, editor. Computational inverse problems in electrocardiology, advances in computational bioengineering series, vol. 4. Southampton: WIT Press; 2000. p. 119-42.
11. Hansen PC. Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems. Numerical Algorithms 1994;6:1-35.
12. Hansen PC, O'Leary DP. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM Journal on Scientific Computing 1993;14:1487-503.
13. Hao DN. A mollification method for ill-posed problem. Numerische Mathematik 1994;68:469-506.
14. Hon YC, Li M. A discrepancy principle for the source points location in using the MFS for solving the BHCP. International Journal of Computational Methods 2008;6(2):181-97.
15. Hon YC, Wei T. A fundamental solution method for inverse heat conduction problem. Engineering Analysis with Boundary Elements 2004;28:489-95.
16. Hon YC, Wei T. Numerical computation for multidimensional inverse heat conduction problem. Computer Modeling in Engineering & Sciences 2005;7(2):119-32. (Pubitemid 40401833)
17. Huang CS, Lee CF, Cheng AHD. Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method. Engineering Analysis with Boundary Elements 2007;31(7):614-23.
18. Jourhmane M, Mera NS. An iterative algorithm for the backward heat conduction problem based on variable relaxation factors. Inverse Problems in Engineering 2002;10:293-308.
19. Lattes R, Lions JL. The method of quasi-reversibility. New York: American Elsevier Publisher; 1969.
20. Lawson CL, Hanson RJ. Solving least squares problems. Englewood Cliffs: Prentice-Hall Inc.; 1974.
21. Lesnic D, Elliott L, Ingham DB. An iterative boundary element method for solving the back ward heat conduction problem using an elliptic approximation. Inverse Problems in Engineering 1998;6:255-79.
22. Lijima K. Numerical solution of backward heat conduction problems by a high order lattice-free finite difference method. Journal of the Chinese Institute of Engineers 2004;27(4):611-20.
23. Mera NS. The method of fundamental solutions for the backward heat conduction problem. Inverse Problems in Science and Engineering 2005;13(1):65-78. (Pubitemid 40119911)
24. Miranker WL. A well posed problem for the backward heat equation. Proceedings of the American Mathematical Society 1961;12:243-7.
25. Payne LE. Improperly posed problems in partial differential equations. Philadelphia: Society for Industrial and Applied Mathematics; 1975.
26. Shidfar A, Zakeri A. A numerical technique for backward inverse heat conduction problems in one-dimensional space. Applied Mathematics and Computation 2005;171(2):1016-24. (Pubitemid 43131089)
27. Tautenhahn U, Hämarik U. The use of monotonicity for choosing the regularization parameter in ill-posed problems. Inverse Problems 1999;15:1487-505. (Pubitemid 129655864)
28. Tikhonov AN, Arsenin VY. The Solution of Ill-posed problems. New York: John Wiley and Sons; 1977.
29. Zhou DY, Wei T. The method of fundamental solutions for solving a Cauchy problem of Laplace's equation in a multi-connected domain. Inverse Problems in Science and Engineering 2008;16(3):389-411. (Pubitemid 351571291)