Solving transient nonlinear heat conduction problems by proper orthogonal decomposition and the finite-element method

Numerical Heat Transfer, Part B: Fundamentals

Volumn 48, Issue 2, 2005, Pages 103-124

  Fic, Adam ^a   Białecki, Ryszard A ^a   Kassab, Alain J ^b  

^a SILESIAN UNIVERSITY OF TECHNOLOGY   (Poland)

^b University of Central Florida   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DECOMPOSITION; DEGREES OF FREEDOM (MECHANICS); ERROR ANALYSIS; FINITE ELEMENT METHOD; FUNCTIONS; GALERKIN METHODS; MATRIX ALGEBRA; ORDINARY DIFFERENTIAL EQUATIONS; STATISTICAL METHODS;

ALGEBRAIC EQUATIONS; PROPER ORTHOGONAL DECOMPOSITION (POD); TIME STEPPING; WEIGHTING FUNCTIONS;

HEAT CONDUCTION;

EID: 23944465416     PISSN: 10407790     EISSN: None     Source Type: Journal    
DOI: 10.1080/10407790590935920     Document Type: Article

References (21)

1. P. Krysl, S. Lall, and J. E. Marsden, Dimensional Model Reduction in Non-linear Finite Element Dynamics of Solids and Structures, Int. J. Numer. Meth. Eng., vol. 51, pp. 479-504, 2001.
2. P. A. LeGresley and J. J. Alonso, Investigation of Non-linear Projection for POD Based Reduced Order Models for Aerodynamics, AIAA Paper 2001-0926, presented at 39th AIAA Aerospace Science Meeting & Exhibit, Reno, NV, January 8-11, 2001.
3. D. Ahlman, F. Söderlund, J. Jackson, A. Kurdila, and W. Shyy, Proper Orthogonal Decomposition for Time-Dependent Lid-Driven Cavity Flows, Numer. Heat Transfer B, vol. 42, pp. 285-306, 2002.
4. R. A. Białecki, A. J. Kassab, and A. Fie, Reduction of the Dimensionality of Transient FEM Solutions Using Proper Orthogonal Decomposition, Proc. 36th AIAA Thermophysics Conf, Orlando, FL, AIAA Paper, 2003-4207, 2003.
5. R. A. Białecki, A. J. Kassab, and A. Fie, Proper Orthogonal Decomposition and Modal Analysis for Acceleration of Transient FEM Thermal Analysis, Int. J. Numer. Meth. Eng., vol. 62, pp. 774-797, 2005.
6. L. Sirovich, Turbulence and Dynamics of Coherent Structures, Part I: Coherent Structures, Q. Appl. Math., vol. XLV, pp. 561-571, 1987.
7. Y. C. Liang, H. P. Lee, S. P. Lim, W. Z. Lin, K. H. Lee, and C. G. WU, Proper Orthogonal Decomposition and Its Applications - Part I: Theory, J. Sound Vibration, vol. 252, no. 3, pp. 527-544, 2002.
8. K. Pearson, On Lines Planes of Closes Fit to System of Points in Space, London Edinburgh Dublin Phil. Mag. J. Science, vol. 2, pp. 559-572, 1901.
9. H. Hotelling, Analysis of Complex of Statistical Variables into Principal Components, J. Educ. Psych., vol. 24, pp. 417-441, 1933.
10. K. Karhunen, Ueber lineare Methoden füer Wahrscheinigkeitsrechnung, Ann. Acad. Sci. Fennicae Ser. Al Math. Phys., vol. 37, pp. 3-79, 1946.
11. M. M. Loeve, Probability Theory, Van Nostrand, Princeton, NJ, 1955.
12. M. Kirby and L. Sirovich, Application of Karhunen-Loeve Procedure for Characterization of Human Faces, IEEE Trans. Pattern Anal. Machine Intell., vol. 12, no. 1, pp. 103-108, 1990.
13. J. A. Atwell and B. B. King, Proper Orthogonal Decomposition for Reduced Basis Feedback Controllers for Parabolic Equations, Math. Comput. Modell., vol. 33, pp. 1-19, 2001.
14. K. S. Ball, L. Sirovich, and L. R. Keefe, Dynamical Eigenfunction Decomposition of Turbulent Channel Flow, Int. J. Numer. Meth. Fluids, vol. 12, pp. 585-604, 1991.
15. V. R. Algazi, K. L. Brown, and M. J. Reddy, Transform Representation of the Spectra of Acoustic Speech Segments with Applications, Part I: General Approach and Application to Speech Recognition, IEEE Trans. Speech Audio Process., vol. 1, pp. 180-195, 1993.
16. S. A. Zahorian and M. Rothenberg, Principal Component Analysis for Low-Redundancy Encoding of Speech Spectra, J. Acoust. Soc. Am., vol. 69, pp. 519-524, 1981.
17. Z. Nenadic, B. K. Gosh, and P. S. Ulinski, Modelling and Estimation Problems in the Turtle Visual Cortex, IEEE Trans. Biomed. Eng., vol. 49, no. 8, pp. 753-762, 2002.
18. R. B. Białecki, A. J. Kassab, and Z. Ostrowski, Application of the Proper Orthogonal Decomposition in Steady State Inverse Problems, in M. Tanaka and G. S. Dulikravich (eds.), Proc. Int. Symp. on Inverse Problems in Engineering Mechanics, Nagano City, Japan, 3-12, Elsevier, Amsterdam, Boston, 2003.
19. Fortran Subroutines for Mathematical Applications Math/Library Volumes 1 and 2, Visual Numerics, 1997. Electronic documentation: www.vni.com/books/docs.
20. H. V. Ly and H. T. Tran, Modeling and Control of Physical Processes Using Proper Orthogonal Decomposition, Math. Comput. Modell., vol. 33, pp. 223-236, 2001.
21. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, vol. 1, McGraw-Hill, London and New York, 1989.