Estimation of constant thermal conductivity by use of Proper Orthogonal Decomposition

Computational Mechanics

Volumn 37, Issue 1, 2005, Pages 52-59

  Ostrowski, Ziemowit ^a   Białecki, Ryszard A ^a   Kassab, Alain J ^b  

^a SILESIAN UNIVERSITY OF TECHNOLOGY   (Poland)

^b University of Central Florida   (United States)

Author keywords

Decomposition; Heat conductivity; Heat transfer; Inverse problems; Proper Orthogonal; Regularization

Indexed keywords

COMPUTATIONAL METHODS; DECOMPOSITION; HEAT TRANSFER; INVERSE PROBLEMS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

ORTHOGONAL VECTORS; POD ANALYSIS; PROPER ORTHOGONAL; REGULARIZATION;

THERMAL CONDUCTIVITY;

EID: 27244459402     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-005-0697-y     Document Type: Conference Paper

References (21)

1. Atwell JA, King BB (2001) Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations. Mathematical and Computer Modelling 33:1-19
2. Aubry N, Lian WY, Titi ES (1993) Preserving symmetries in the proper orthogonal decomposition. SIAM J Sci Comput 14(2):483-505
3. Azeez MF, Vakakis AF (2001) Proper orthogonal decomposition (POD) of a class of vibroimpact oscillations. J Sound Vibrations 240(5):859-889
4. Ball KS, Sirovich L, Keefe LR (1991) Dynamical eigenfunction decomposition of turbulent channel flow. Int J Numer Meth Fluids 12:585-604
5. Beck JV, Blackwell B, St. Clair CR, (1985) Inverse heat conduction: Ill-posed problems. John Willey and Sons, New York
6. Berkooz G, Holmes P, Lumley JL (1993) The proper orthogonal decomposition in the analysis of turbulent flows. Annu Rev Fluids Mech 25(N5):539-575
7. Bialecki RA, Kassab AJ, Ostrowski Z (2003) Application of the proper orthogonal decomposition in steady state inverse problems, In: Inverse problems in engineering mechanics IV. Masa. Tanaka (ed) Elsevier BV Amsterdam-Boston, pp. 3-12
8. Goldberg DE (1989) Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Reading, MA
9. Hardy RL (1971) Multiquadric equations of topolography and other irregular surfaces. J Geophys Res 76:1905-1915
10. Hardy RL (1990) Theory and applications of the multiquadricbiharmonic method: 20 years of discovery 1968-1988. Comput Math Appl 19(8-9):163-208
11. Holems P, Lumley JL, Berkooz G (1996) Turbulence, coherent structures, dynamical systems and symmetry. Cambridge Monographs on Mechanics, Cambridge University Press
12. Hotelling H (1983) Analysis of complex of statistical variables into principal components. J Educ Psychol 24:417-441
13. Karhunen K (1946) Ueber lineare Methoden der Wahrscheinigkeitsrechnung. Ann Acad Sci Fennicae AI Math Phys 37:3-79
14. Liang YC, Lee HP, Lim SP, Lin WZ, Lee KH, Wu CG (2002) Proper orthogonal decompositopn and its applications - Part I: Theory. J Sound and Vibration 252(3):527-544
15. Loeve MM (1955) Probability theory. Van Nostrand, Princeton NY
16. Ly HV, Tran HT (2001) Modeling and control of physical processes using proper orthogonal decomposition. Math Comput Model 33:223-236
17. Özisik MN, Orlande HRB (2000) Inverse heat transfer: Fundamentals and applications. Taylor & Francis, New York
18. Pearson K (1901) On lines planes of closes fit to system of points in space. Lond Edinb Dublin Philos Magazine J Sci 2:559-572
19. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipies in FORTRAN: the art of scientific computing. Cambridge University Press, Cambridge
20. Tikhonov AN, Arsenin VA (1994) Solution of ill-posed problems. John Willey and Sons, New York
21. Wu CG, Liang YC, Lin WZ, Lee HP, Lim SP (2003) A note on equivalence of proper orthogonal decomposition methods. J Sound Vibration 265:1103-1110