Application of the boundary element method to inverse heat conduction problems

International Journal of Heat and Mass Transfer

Volumn 39, Issue 7, 1996, Pages 1503-1517

  Lesnic, D ^a   Elliott, L ^a   Ingham, D B ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; HEAT FLUX; INVERSE PROBLEMS; OSCILLATIONS; SENSORS; TEMPERATURE MEASUREMENT; UNSTEADY FLOW;

KINETIC ENERGY; LEAST SQUARES METHOD; REGULARIZATION PROCEDURES;

HEAT CONDUCTION;

EID: 0030150013     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/0017-9310(95)00229-4     Document Type: Article

References (34)

1. J. V. Beck, B. Blackwell and C. R. St Clair Jr, Inverse Heat Conduction. Wiley, New York (1985).
2. R. G. Hills, M. Raynaud and E. Hensel, Surface variance estimates using an adjoint formulation for a one-dimensional nonlinear inverse heat conduction technique, Numer. Heat Transfer 10, 441-461 (1986).
3. J. Hadamard, Lectures on the Cauchy Problem in Linear Partial Differential Equations. Yale University Press, New Haven (1923).
4. O. R. Burggraf, An exact solution of the inverse problem in heat conduction theory and applications, J. Heat Transfer 86C, 373-382.
5. D. Langford, New analytic solutions of the one-dimensional heat equation for temperature and heat flow rate both prescribed at the same fixed boundary (with applications to the phase change problem), Q. Appl. Math. 24, 315-322 (1966).
6. D. M. France and T. Chiang, Analytic solutions to inverse heat conduction problems with periodicity, J Heat Transfer 102, 579-581 (1980).
7. K. Kurpisz and A. J. Nowak, Applying BEM and the sensitivity coefficient concept to inverse heat conduction problems. In Advanced Computational Methods in Heat Transfer (Edited by C. A. Brebbia), pp. 309-321. Springer, New York (1990).
8. C. A. Brebbia, Applications of the boundary element method for heat transfer problems, Proceedings of the Conference Modelisation et Simulation en Thermique, Ensma, Poitiers, pp. 1-18 (1984).
9. C. Le Niliot, C. Papini and R. Pasquetti, Boundary element method for inverse heat conduction problems. In Advanced Computational Methods in Heat Transfer (Edited by C. A. Brebbia), pp. 285-295. Springer, New York (1990).
10. K. Kurpisz and A. J. Nowak, BEM approach to inverse heat conduction problems, Engng Anal. Bound. Elem. 10, 291-297 (1992).
11. Y. Yuan, Application of the boundary element method to nonlinear and improperly posed problems. PhD Thesis, University of Leeds (1993).
12. D. B. Ingham and Y. Yuan, The Boundary Element Method for Solving Improperly Posed Problems (Edited by C. A. Brebbia and J. J. Connor), Vol. 19. Computational Mechanics, Southampton (1994).
13. H. Han, D. B. Ingham and Y. Yuan, The boundary-element method for the solution of the backward heat conduction equation, J. Comput. Phys. 116, 292-299 (1995).
14. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems. Winston-Wiley, WA (1977).
15. C. F. Weber, Analysis and solution of the ill-posed inverse heat conduction problem, Int. J. Heat Mass Transfer 24, 1783-1792 (1981).
16. J. V. Beck, Nonlinear estimation applied to the nonlinear inverse heat conduction problem, Int. J. Heat Mass Transfer 13, 703-716 (1970).
17. 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).
18. J. Skorek, Applying the least squares adjustment technique for solving inverse heat conduction problems, Proceedings of the 8th Conference on Numerical Methods in Laminar and Turbulent Flow (Edited by C. Taylor), pp. 189-198. Pineridge Press, Swansea (1993).
19. O. M. Alifanov, Solution of an inverse problem of heat conduction by iteration methods, J. Engng Phys. 26, 682-687 (1974).
20. D. A. Murio, The Mollification Method and the Numerical Solution of Ill-Posed Problems. Wiley, New York (1993).
21. H. R. Busby and D. M. Trujillo, Numerical solution to a two-dimensional inverse heat conduction problem, Int. J. Numer. Meth. Engng 21, 349-359 (1985).
22. C. A. Brebbia, J. C. F. Telles and L. C. Wrobel, Boundary Element Techniques: Theory and Application in Engineering. Springer, New York (1984).
23. R. Pasquetti and C. Le Niliot, Boundary element approach for inverse heat conduction problems: application to a bidimensional transient numerical experiment, Numer. Heat Transfer 20, 169-189 (1991).
24. A. Morozov, On the solution of functional equations by the method of regularization, Soviet Math. Dokl. 7, 414-417 (1966).
25. H. Han, The finite element method in a family of improperly posed problems, Math. Comput. 38, 55-65 (1982).
26. D. B. Ingham and Y. Yuan, The solution of a nonlinear inverse problem in heat transfer, IMA J. Appl. Math. 50, 113-132 (1993).
27. P. E. Gill, S. J. Hammarling, W. Murray, M. A. Saunders and M. H. Wright, User's guide for LSSOL (version 1.0). Report SOL 86-1, Stanford University (1986).
28. D. L. Philips, A technique for the numerical solution of certain integral equations of the first kind, J. Assoc. Comput. Mach. 9, 84-97 (1962).
29. J. R. Cannon, The One-Dimensional Heat Equation. Addison-Wesley, MA (1984).
30. E. Hensel, Inverse Theory and Applications for Engineers. Prentice Hall, NJ (1991).
31. M. N. Özişik, Boundary Value Problems of Heat Conduction. Dover, New York (1989).
32. R. P. Brent, Algorithm 488, Commun. A.C.M. pp. 704-706 (1974).
33. J. V. Beck, Criteria for comparison of methods of solution of the inverse heat conduction problem, Nucl. Engng Des. 53, 11-22 (1979).
34. D. Lesnic, L. Elliott and D. B. Ingham, Boundary element method and minimal energy technique for the inverse heat conduction problem. In Proceedings of the Second International Conference on Dynamic System Identification and Inverse Problems (Edited by O. M. Alifaniov, V. V. Mickhailov and A. V. Nenarokomov), Vol. 1, pp. A4.1-A4.12. St Petersburg (1994).