A new look at proper orthogonal decomposition

SIAM Journal on Numerical Analysis

Volumn 41, Issue 5, 2003, Pages 1893-1925

  Rathinam, Muruhan ^a   Petzold, Linda R ^b  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Dynamical systems; Model reduction; Numerical methods; Proper orthogonal decomposition

Indexed keywords

DYNAMICAL SYSTEMS; MODEL REDUCTION; PROPER ORTHOGONAL DECOMPOSITION;

COMPUTATIONAL COMPLEXITY; DATA REDUCTION; DATA STRUCTURES; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; SENSITIVITY ANALYSIS;

DATA COMPRESSION;

EID: 9244228981     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142901389049     Document Type: Conference Paper

References (29)

1. R. ABRAHAM, J. E. MARSDEN, AND T. RATIU, Manifolds, Tensor Analysis and Applications, 2nd ed., Springer-Verlag, New York, 1988.
2. V. ALGAZI AND D. SAKRISON, On the optimality of Karhunen-Loève expansion, IEEE Trans. Inform. Theory, 15 (1969), pp. 319-321.
3. N. AUBRY, W. LIAN, AND E. TITI, Preserving symmetries in the proper orthogonal decomposition, SIAM J. Sci. Comput., 14 (1993), pp. 483-505.
4. G. BERKOOZ AND E. TITI, Galerkin projections and the proper orthogonal decomposition for equivariant equations, Phys. Lett. A, 174 (1993), pp. 94-102.
5. C. BISCHOF, A. CARLE, P. HOVLAND, P. KHADEMI, AND A. MAUER, Adifor 2.0 Users' Guide (Revision D), Technical report CRPC-95516-S, Center for Research on Parallel Computation, Houston, TX, 1995.
6. W. BOOTHBY, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd ed., Academic Press, New York, 1994.
7. Y. CAO AND L. R. PETZOLD, A Note on Model Reduction for Analysis of Cascading Failures in Power Systems, manuscript.
8. E. A. CHRISTENSEN, M. BRØNS, AND J. N. SØRENSEN, Evaluation of proper orthogonal decomposition-based decomposition techniques applied to parameter-dependent nonturbulent flows, SIAM J. Sci. Comput., 21 (2000), pp. 1419-1434.
9. A. CURTIS, M. POWELL, AND J. REID, On the estimation of sparse Jacobian matrices, J. Inst. Math. Appl., 13 (1974), pp. 117-120.
10. S. GLAVASKI, J. E. MARSDEN, AND R. MURRAY, Model reduction, centering, and the Karhunen-Loève expansion, in Proceedings of the IEEE Conference on Decision and Control, Tampa, FL, 1998, pp. 2071-2076.
11. G. GOLUB AND C. VAN LOAN, Matrix Computations, Johns Hopkins University Press, Baltimore, MD, 1996.
12. M. GRAHAM AND I. KEVREKIDIS, Alternative approaches to the Karhunen-Loève decomposition for model reduction and data analysis, Computers and Chemical Engineering, 20 (1996), pp. 495-506.
13. E. HAIRER, S. NORSETT, AND G. WANNER, Solving Ordinary Differential Equations I: Nonstiff Problems, Springer-Verlag, New York, 1980.
14. P. HOLMES. J. LUMLEY, AND G. BERKOOZ, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, Cambridge, UK, 1996.
15. S. LALL, P. KRYSL, AND J. E. MARSDEN, Structure-preserving model reduction for mechanical systems, Phys. D, 184 (2003), pp. 304-318.
16. S. LALL, J. E. MARSDEN, AND S. GLAVASKI, Empirical model reduction of controlled nonlinear systems, in Proceedings of the IFAC World Congress, Beijing, 1999, pp. 473-478.
17. B. MOORE, Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE Trans. Automat. Control, 26 (1981), pp. 17-31.
18. P. PARRILO, F. PAGANINI, G. VERGHESE, B. LESIEUTRE, AND J. E. MARSDEN, Model reduction for analysis of cascading failures in power systems, in Proceedings of the American Control Conference, San Diego, CA, 1999, pp. 4028-4212.
19. K. PEARSON, On lines and planes of closest fit to a system of points in space, Philosophical Magazine, 2 (1833), pp. 609-629.
20. M. RATHINAM AND L. R. PETZOLD, Dynamic iteration using reduced order models: A method for simulation of large scale modular systems, SIAM J. Numer. Anal., 40 (2002), pp. 1446-1474.
21. M. RATHINAM AND L. PETZOLD, An iterative method for simulation of large scale modular systems using reduced order models, in Proceedings of the IEEE Conference on Decision and Control, Sydney, Australia, 2000, pp. 4630-4635.
22. A. ROSENFELD AND A. KAK, Digital Picture Processing, Academic Press, New York, 1982.
23. C. ROWLEY AND J. E. MARSDEN, Reconstruction equations and the Karhunen-Loève expansion for systems with symmetry, Phys. D, 142 (2000), pp. 1-19.
24. L. F. SHAMPINE AND M. W. REICHELT, The MATLAB ODE suite, SIAM J. Sci. Comput., 18 (1997), pp. 1-22.
25. S. SHVARTSMAN AND I. KEVREKIDIS, Low-dimensional approximation and control of periodic solutions in spatially extended systems, Phys. Rev. E(3), 58 (1998), pp. 361-368.
26. S. SHVARTSMAN, C. THEODOROPOULOS, R. RICO-MARTINEZ, I. KEVREKIDIS, E. TITI, AND T. MOUNTZIARIS, Order reduction for nonlinear dynamic models of distributed reacting systems, J. Process Control, 10 (2000), pp. 177-184.
27. L. SIROVICH, Turbulence and the dynamics of coherent structures, I, Quart. Appl. Math., 45 (1987), pp. 561-571.
28. L. SIROVICH, Turbulence and the dynamics of coherent structures, II, Quart. Appl. Math., 45 (1987), pp. 573-582.
29. L. SIROVICH, Turbulence and the dynamics of coherent structures, III, Quart. Appl. Math., 45 (1987), pp. 583-590.