A comparison of generalized eigensystem, truncated singular value decomposition, and Tikhonov regularization for the steady inverse heat conduction problem

Inverse Problems in Engineering

Volumn 8, Issue 3, 2000, Pages 193-227

  Olson, Lorraine ^a   Throne, Robert ^a  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

Generalized Eigensystem Method; Heat conduction; Inverse boundary value problem; SVD; Tikhonov

Indexed keywords

EID: 0004209531     PISSN: 10682767     EISSN: None     Source Type: Journal    
DOI: 10.1080/174159700088027728     Document Type: Review

References (33)

1. Martin, T. J., Halderman, J. D. and Dulikravich, G. S. (1995). "An inverse method for finding unknown surface tractions and deformations in elastostatics", Computers and Structures, 56, 825-835.
2. Martin, T. J. and Dulikravich, G. S. (1995). "Finding unknown surface temperatures and heat fluxes in steady heat conduction", IEEE Transactions on Components, Packaging, and Manufacturing Technology-Part A, 18, 540-545.
3. Martin, T. J. and Dulikravich, G. S. (1996). "Inverse determination of boundary conditions and sources in steady heat conduction with heat generation", Journal of Heat Transfer, 118, 546-554.
4. Martin, T. J. and Dulikravich, G. S. (1998). "Inverse determination of steady heat convection coefficient distributions", Journal of Heat Transfer, 120, 328-334.
5. Dulikravich, G. S. and Martin, T. J. (1997). "Inverse shape and boundary condition problems and optimization in heat conduction", Advances in Numerical Heat Transfer, 1, 381-426.
6. Dennis, B. H. and Dulikravich, G. S. (1998). "A finite element formulation for the detection of boundary conditions in elasticity and heat transfer", Proceedings of the International Symposium on Inverse Problems in Engineering Mechanics -ISIP'98. Tanaka, M. and Dulikravich, G. S., editors, Nagano, Japan, March 24-27, Elsevier Science, 61-70.
7. Dennis, B. H. and Dulikravich, G. S. (1998). "Simultaneous determination of temperatures, heat fluxes, deformations, and tractions on inaccessible boundaries", Computational Methods for Solution of Inverse Problems in Mechanics, Olson, L. G. and Saigal, S., editors, Anaheim, CA, November 15-20. ASME AMD-Vol 228, 1-10.
8. Maillet, D., Degiovanni, A. and Pasquetti, R. (1991). "Inverse heat conduction applied to the measurement of heat transfer coefficient on a cylinder: Comparison between and analytical and a boundary element technique", Journal of Heat Transfer, 113, 549-557.
9. Truffart, B., Jarny, Y. and Delaunay, D. (1993). "A general optimization algorithm to solve 2-D boundary inverse heat conduction problems using finite elements", Inverse Problems in Engineering: Theory and Practice, Zabaras, N., Woodbury, K. A. and Raynaud, M., editors, Palm Coast, FL, June 13-18. ASME, 53-60.
10. Huang, C.-H. and Chen, C.-W. (1998). "A boundary-element-based inverse problem of estimating boundary conditions in an irregular domain with statistical analysis", Numerical Heat Transfer, Part B, 33, 251-268.
11. Ingham, D. B., Yuan, Y. and Han, H. (1991). "The boundary element method for an improperly posed problem", IMA Journal of Applied Mathematics, 47, 61-79.
12. Schnur, D. S. and Zabaras, N. (1990). "Finite element solution of two-dimensional inverse elastic problems using spatial smoothing", International Journal for Numerical Methods in Engineering, 30, 57-75.
13. Maniatty, A., Zabaras, N. and Stelson, K. (1989). "Finite element analysis of some inverse elasticity problems", Journal of Engineering Mechanics, 115, 1303-1317.
14. Maniatty, A. M. (1993). "A numerical solution with error estimating for inverse elasticity problems", Inverse Problems in Engineering: Theory and Practice, Zabaras, N., Woodbury, K. A. and Raynaud, M., editors, Palm Coast, FL, June 13-18. ASME, 179-185.
15. Hensel, E. and Hills, R. (1989). "Steady-state two-dimensional inverse heat conduction", Numerical Heat Transfer, Part B, 15, 227-240.
16. Tseng, A. A., Chen, T. C. and Zhao, F. Z. (1995). "Direct sensitivity coefficient method for solving two-dimensional inverse heat conduction problems by finite element scheme", Numerical Heat Transfer, Part B, 27, 291-307.
17. Beck, J. V., Blackwell, B. F. and Clair, C. R. S. (1985). Inverse Heat Conduction -Ill-posed Problems. John Wiley and Sons, New York.
18. Al-Najem, N. M., Osman, A. M., El-Refaee, M. M. and Khanafer, K. M. (1998). "Two dimensional steady-state inverse heat conduction problems", International Communications in Heat and Mass Transfer, 25, 541-550.
19. Yang, Y.-T., Hsu, P.-T. and Chen, C.-K. (1997). "A three-dimensional inverse heat conduction problem approach for estimating the heat flux and surface temperature of a hollow cylinder", J. Phys. D: Appl. Phys., 30, 1326-1333.
20. Fang, Z., Xie, D. and Diao, N. (1997). "A new method for solving the inverse conduction problem in steady heat flux measurement", International Journal of Heat and Mass Transfer, 40, 3947-3953.
21. Throne, R. and Olson, L. (1994). "A generalized eigensystem approach to the inverse problem of electrocardiography", IEEE Transactions on Biomedical Engineering, 41, 592-600.
22. Throne, R. D. and Olson, L. G. (1995). "The effects of errors in assumed conductivities and geometry on numerical solutions to the inverse problem of electrocardiography", IEEE Transactions on Biomedical Engineering, 42, 1192-1200.
23. Olson, L. and Throne, R. (1995). "Computational issues arising in multi-dimensional elliptic inverse problems: The inverse problem of electrocardiography", Engineering Computations, 12(4), 343-356.
24. Throne, R. D., Olson, L. G., Hrabik, T. J. and Windle, J. R. (1997). "Generalized eigensystem techniques for the inverse problem of electrocardiography applied to a realistic heart-torso geometry", IEEE Transactions on Biomedical Engineering, 44, 447-454.
25. Throne, R. D., Olson, L. G. and Hrabik, T. J. (1999). "A comparison of higher-order generalized eigensystem techniques and Tikhonov regularization for the inverse problem of electrocardiography", Inverse Problems in Engineering, 7, 143-193.
26. Throne, R. and Olson, L., Algorithms for the inverse problem of electrocardiography. Gordon and Breach Science Publishers, in Press.
27. Throne, R. D. and Olson, L. G., "Fusion of body surface potential and body surface Laplacian signals for electrocardiographic imaging", IEEE Transactions on Biomedical Engineering, In press.
28. Bathe, K. (1982). Finite Element Procedures in Engineering Analysis. Prentice-Hall, Englewood Cliffs, NJ.
29. Wilson, E. (1974). "The static condensation algorithm", International Journal for Numerical Methods in Engineering, 8, 198-203.
30. Baumeister, J. (1987). Stable Solutions of Inverse Problems. Advanced Lectures in Mathematics, Friedr. Vieweg and Sohn, Braunschweig.
31. Phillips, D. L. (1962). "A technique for the numerical solution of certain integral equations of the first kind", J. Assoc. Comput. Mach., 9, 84-97.
32. Varah, J. (1979). "A practical examination of some numerical methods for linear discrete ill-posed problems", SIAM Review, 21, 100-111.
33. Colli-Franzone, P. (1980). "Regularization methods applied to an inverse problem in electrocardiography", Computing Methods in Applied Sciences and Engineering, North-Holland Publishing Company.