Transient inverse heat conduction problem solutions via Newton's method

International Journal of Heat and Mass Transfer

Volumn 40, Issue 17, 1997, Pages 4115-4127

  Dorai, Gregory A ^a   Tortorelli, Daniel A ^a  

^a United States of America   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; INVERSE PROBLEMS;

BROYTON FLETCHER GOLDFARB SHANNO (BFGS) METHOD; INVERSE HEAT CONDUCTION PROBLEM (IHCP);

HEAT CONVECTION;

EID: 0031250331     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0017-9310(97)00044-6     Document Type: Article

References (42)

1. Schnur, D. S. and Zabaras, N., Finite element solution of two-dimensional inverse elasticity problems using spatial smoothing. International Journal for Numerical Methods in Engineering, 1990, 30, 57-75.
2. Nishmoura, D. and Kobayashi, S., A boundary integral equation method for an inverse problem related to crack detection. International Journal for Numerical Methods in Engineering, 1991, 32, 1371-1387.
3. Beck, J. V., Blackwell, B. and St. Clair, C. R. Jr., Inverse Heat Conduction - Ill Posed Problems. Wiley, New York, 1985.
4. Reinhardt, H. J. and Valencia, L., The numerical solution of inverse heat conduction problems with applications to reactor technology. In SMIRT Conference, 1987, pp. B25-30.
5. Cannon, J. R., Numerical Solutions of Nonlinear Differential Equations. Wiley, New York, 1966.
6. Stolz, G. Jr., Numerical solutions to an inverse problem of heat conduction for simple shapes. Transactions of the ASME, Journal of Heat Transfer, 1960, 82c, 20-26.
7. Özişik, M. N., Heat Conduction. Wiley, New York, 1980.
8. Beck, J. V., Surface heat flux determination using an integral method. Nuclear Engineering Design, 1968, 7, 170-178.
9. Sparrow, E. M., Haji-Sheihk and Lundgren, T. S., The inverse problem in transient heat conduction. Transactions of the ASME, Journal of Heat Transfer, 1964, 86E, 369-375.
10. Frank, I., An application of least square method to the solution of the inverse problems of heat conduction. Journal of Heat Transfer, Transactions of the ASME, 1963, 83(4), 378-379.
11. Beck, J. V., Nonlinear estimation applied to the non-linear heat conduction problem. International Journal of Heat and Mass Transfer, 1970, 13, 703-716.
12. Beck, J. V., Litkouhi, B. and St. Clair, C. R., Efficient sequential solution of the nonlinear inverse heat conduction problem. Numerical Heat Transfer, 1982, 5, 275-286.
13. Liu, J., A stability analysis on beck's procedure for inverse heat conduction problems. Journal of Computational Physics, 1995, 123, 65-73.
14. Reinhardt, H. J., A numerical method for the solution of two-dimensional inverse heat conduction problem. International Journal for Numerical Methods in Engineering, 1991, 32, 363-383.
15. Tikhnov, A. N. and Arsenini, V. Y., Solution of Ill-Posed Problems. V. H. Winston and Sons, Washington, 1977.
16. Alifanov, O. M. and Artyukhin, E. A., Regularized numerical solution of nonlinear inverse heat conduction problem. Journal of Engineering Physics, 1975, 29(1), 934-938.
17. Alifanov, O. M. and Mikhailov, V. V., Solution of the nonlinear inverse thermal conductivity problem by the iteration method. Journal of Engineering Physics, 1978, 35(6), 1501-1506.
18. Beck, J. V. and Murio, D. A., Combined function specification-regularization procedure for solution of inverse heat conduction problem. AIAA Journal, 1986, 24, 180-185.
19. Maniatty, A. M. and Zabaras, N. J., Investigation of regularization parameters and error estimating in inverse elasticity problems. International Journal for Numerical Methods in Engineering, 1994, 37, 1039-1052.
20. Busby, H. R. and Trujillo, D. M., Numerical solution to a two-dimensional inverse heat conduction problem. International Journal for Numerical Methods in Engineering, 1985, 21, 349-359.
21. Murio, D. A., The mollification method and the numerical solution of an inverse heat conduction problem. SIAM Journal of Science Statistics in Computing, 1981, 2, 17-34.
22. Murio, D. A., The mollification method and the numerical solution of the inverse heat conduction problem by finite differences. Computing Mathematics Applications, 1989, 17, 1385-1396.
23. Burggraf, O. R., An exact solution of the inverse problem in heat conduction theory and application. Transactions of ASME, Journal of Heat Transfer, 1964, 86C, 373-382.
24. Beck, J. V., Criteria for comparison of methods of solution of the inverse heat conduction problem. Nuclear Engineering and Design, 1977, 53, 11-22.
25. Alifanov, O. M., Solution of an inverse problem of heat conduction by iteration methods. Journal of Engineering Physics, 1974, 26(4), 471-476.
26. Jarny, Y., Özişik, M. N. and Bardon, J. P., A general optimization method using adjoint equation for solving multidimensional inverse heat conduction. International Journal of Heat and Mass Transfer, 1991, 34(11), 2911-2919.
27. Huang, C. H. and Özişik, M. N., Inverse problem of determining unknown wall heat flux in laminar flow through a parallel plate duct. Numerical Heat Transfer - Part A, 1992, 21, 55-70.
28. Scheuing, J. E. and Tortorelli, D. A., Inverse heat conduction problem solutions via second-order design sensitivities and Newton's method. Inverse Problems in Engineering, 1996, 2, 227-262.
29. Vanderplaats, G. N., Numerical Optimization Techniques for Engineering Design: With Applications. McGraw-Hill, New York, 1984.
30. Tortorelli, D. A. and Michaleris, P., Design sensitivity analysis: overview and review. Inverse Problems in Engineering, 1994, 1, 71-105.
31. Michaleris, P., Tortorelli, D. A. and Vidal, C. A., Tangent operators and design sensitivity formulations for transient nonlinear coupled problems with applications to elasto-plasticity. International Journal for Numerical Methods in Engineering, 1995, 37(2), 71-105.
32. Truffart, B., Jarny, Y. and Bourouga, B., A general approach to solve 2-d inverse heat conduction problems. In Proceedings of the Seventh Inverse Problems in Engineering, Ohio, 1995.
33. Belegundu, A. D., The direct and adjoint methods of design sensitivity analysis. ASME Paper, 1984, 84-DET, 211.
34. Haftka, R. T. and Mróz, Z., First- and second-order sensitivity analysis of linear and nonlinear structures. AIAA Journal, 1986, 24(7), 1187-1192.
35. Incropera, F. D. and DeWitt, D. P., Fundamentals of Heat and Mass Transfer, 3rd edn. Wiley, New York, 1990.
36. Bathe, K. J., Finite Element Procedures in Engineering Analysis. Prentice-Hall, Englewood Cliffs, New Jersey, 1982.
37. Rogers, David F. and Adams, J. Alan., Mathematical Elements for Computer Graphics. McGraw-Hill Company, New York, 1937.
38. Gill, P. E., Murray, W. and Wright, M. H., Practical Optimization, 9th edn. Academic Press, New York, 1992.
39. Papalambros, P. Y. and Wilde, D. J., Principles of Optimal Design. Cambridge University Press, New York, 1988.
40. VMA Engineering. DOT User's Manual, Version 3.00. Vanderplaats, Miura and Associates, Goleta, CA, 1992.
41. Strang, G., Linear Algebra and Its Applications, 3rd edn. Harcourt Brace Jovanovich College Publishers, New York, 1988.
42. Beck, J. V. and Arnold, K. J., Parameter Estimation in Engineering and Science. Wiley, New York, 1977.