Numerical study of inverse heat conduction problems

Computers and Mathematics with Applications

Volumn 38, Issue 7, 1999, Pages 173-188

  Shen, Shih Yu ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; BOUNDARY VALUE PROBLEMS; ERROR ANALYSIS; LINEAR SYSTEMS; MATRIX ALGEBRA; NUMERICAL METHODS;

CONDITION NUMBERS; INVERSE HEAT CONDUCTION; TIKHONOVS REGULARIZATION;

HEAT CONDUCTION;

EID: 0033204082     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(99)00248-5     Document Type: Article

References (23)

1. M.C. Flemings, Solidification Processing, McGraw-Hill, New York, (1974).
2. D.A. Porter and K.E. Easteling, Phase Transformations in Metals and Alloys, Chapman & Hall, London, (1981).
3. J.A. Emerson, Thermal phenomena during the encapsulation of electronic devices, In Proceedings Intersociety Conference on Thermal Phenomena in the Fabrication and Operation of Electronic Components, IEEE, Los Angeles, CA, (1988).
4. P.C. Duchateau, Inverse problems for parabolic partial differential equations, In Inverse Problems, (Edited by J.R. Connon and U. Hornung), Birkhäuser Verlag, Basel, (1986).
5. O.M. Alifanov, Inverse Heat Transfer Problems, Springer-Verlag, Berlin, (1994).
6. J.V. Beck, B. Blackwell and C.R. Clair, Inverse Heat Conduction, Wiley, New York, (1985).
7. D.A. Popov, E.B. Sokolova and D.V. Sushko, Mathematical models in two-dimensional radon tomography, In Applied Problems of Radon Transform, (Edited by S. Gindikin), AMS, Providence, RI, (1994).
8. A.M. Cormack, Computed tomography: Some history and recent developments, In Computed Tomography, (Edited by L.A. Shepp), AMS, Providence, RI, (1983).
9. F. Scarpa and G. Milano, Kalman smoothing technique applied to the inverse heat conduction problem, Numerical Heat Transfer, Part B 28, 79-96 (1995).
10. M. Raudensk'y, K.A. Woodbury, J. Kral and T. Brezina, Genetic algorithm in solution of inverse heat conduction problems, Numerical Heat Transfer, Part B 28, 293-306 (1995).
11. C.F. Weber, Analysis and solution of ill-posed inverse heat conduction problem, Int. J. Heat Mass Transfer 24, 1783-1792 (1981).
12. J.I. Frankel, Residual-minimization least-square method for inverse heat conduction, Computers Math. Applic. 32 (4), 117-130 (1996).
13. D.B. Ingham, Y. Yuan and H. Han, The boundary element method for an improperly posed problem, IMA J. Appl. Math. 47, 61-79 (1991).
14. D. Lesnic, L. Elliott and D.B. Ingham, Application of the boundary element method to inverse heat conduction problems, Int. J. Heat Mass Transfer 39, 1503-1517 (1996).
15. P. Linz, A new numerical method for ill-posed problems, Inverse Problems 10, L1-L6 (1994).
16. J.M. Varah, Pitfalls in the numerical solution of linear ill-posed problems, SIAM J. Sci. Stat. Comput. 4, 164-176 (1983).
17. J.M. Varah, On the numerical solution of ill-conditioned linear systems with applications to ill-posed problems, SIAM J. Numer Anal. 10, 257-267 (1973).
18. A.N. Tikhonov, A.V. Goncharsky, U.V. Stepanov and A.G. Yagola, Numerical Methods for the Solution Ill-Posed Problems, Kluwer Academic, Dordrecht, (1995).
19. M.T. Nair, M.H. Hegland and R.S. Anderssen, The trade-off between regularity and stability in Tikhonov regularization, Mathematics of Computation 66, 193-206 (1997).
20. J. Kevorkian, Partial Differential Equations, Chapman & Hall, New York, (1990).
21. nd Edition, Wiley, New York, (1992).
22. nd Edition, Johns Hopkins University Press, Baltimore, MD, (1989).
23. H.W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic, Dordrecht, (1996).