On dynamic mode decomposition: Theory and applications
Pages: 391  421,
Issue 2,
December
2014
doi:10.3934/jcd.2014.1.391 Abstract
References
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Jonathan H. Tu  Dept. of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, United States (email)
Clarence W. Rowley  Dept. of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, United States (email)
Dirk M. Luchtenburg  Dept. of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, United States (email)
Steven L. Brunton  Dept. of Applied Mathematics, University of Washington, Seattle, WA 98195, United States (email)
J. Nathan Kutz  Dept. of Applied Mathematics, University of Washington, Seattle, WA 98195, United States (email)
1 
S. Bagheri, Koopmanmode decomposition of the cylinder wake, J. Fluid Mech., 726 (2013), 596623. 

2 
B. A. Belson, J. H. Tu and C. W. Rowley, A Parallelized Model Reduction Library, ACM T. Math. Software, 2013 (accepted). 

3 
M. B. Blumenthal, Predictability of a coupled oceanatmosphere model, J. Climate, 4 (1991), 766784. 

4 
K. K. Chen, J. H. Tu and C. W. Rowley, Variants of dynamic mode decomposition: Boundary condition, Koopman, and Fourier analyses, J. Nonlinear Sci., 22 (2012), 887915. 

5 
T. Colonius and K. Taira, A fast immersed boundary method using a nullspace approach and multidomain farfield boundary conditions, Comput. Method Appl. M., 197 (2008), 21312146. 

6 
D. Duke, D. Honnery and J. Soria, Experimental investigation of nonlinear instabilities in annular liquid sheets, J. Fluid Mech., 691 (2012), 594604. 

7 
D. Duke, J. Soria and D. Honnery, An error analysis of the dynamic mode decomposition, Exp. Fluids, 52 (2012), 529542. 

8 
P. J. Goulart, A. Wynn and D. Pearson, Optimal mode decomposition for high dimensional systems, In Proceedings of the 51st IEEE Conference on Decision and Control, 2012 (2012), 49654970. 

9 
M. Grilli, P. J. Schmid, S. Hickel and N. A. Adams, Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction, J. Fluid Mech., 700 (2012), 1628. 

10 
K. Hasselmann, PIPs and POPs: The reduction of complex dynamicalsystems using Principal Interaction and Oscillation Patterns, J. Geophys. Res.Atmos., 93 (1988), 1101511021. 

11 
B. L. Ho and R. E. Kalman, Effective construction of linear statevariable models from input/output data, Proceedings of the Third Annual Allerton Conference on Circuit and System Theory, (1965), 449459. 

12 
P. J. Holmes, J. L. Lumley, G. Berkooz and C. W. Rowley, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, Cambridge, UK, 2nd edition, 2012. 

13 
H. Hotelling, Analysis of a complex of statistical variables into principal components, J. Educ. Psychol., 24 (1933), 417441. 

14 
H. Hotelling, Analysis of a complex of statistical variables into principal components, J. Educ. Psychol., 24 (1933), 498520. 

15 
M. R. Jovanović, P. J. Schmid and J. W. Nichols, Sparsitypromoting dynamic mode decomposition, Phys. Fluids, 26 (2014), 024103, arXiv:1309.4165v1. 

16 
J. N. Juang and R. S. Pappa, An eigensystem realizationalgorithm for modal parameteridentification and modelreduction, J. Guid. Control Dynam., 8 (1985), 620627. 

17 
E. N. Lorenz, Empirical orthogonal functions and statistical weather prediction, Technical report, Massachusetts Institute of Technology, Dec. 1956. 

18 
Z. Ma, S. Ahuja and C. W. Rowley, Reducedorder models for control of fluids using the eigensystem realization algorithm, Theor. Comp. Fluid Dyn., 25 (2011), 233247. 

19 
L. Massa, R. Kumar and P. Ravindran, Dynamic mode decomposition analysis of detonation waves, Phys. Fluids, 24, June 2012. 

20 
I. Mezić, Spectral properties of dynamical systems, model reduction and decompositions, Nonlin. Dynam., 41 (2005), 309325. 

21 
I. Mezić, Analysis of fluid flows via spectral properties of the Koopman operator, Annu. Rev. Fluid Mech., 45 (2013), 357378. 

22 
T. W. Muld, G. Efraimsson and D. S. Henningson, Flow structures around a highspeed train extracted using proper orthogonal decomposition and dynamic mode decomposition, Comput. Fluids, 57 (2012), 8797. 

23 
B. R. Noack, K. Afanasiev, M. Morzyński, G. Tadmor and F. Thiele, A hierarchy of lowdimensional models for the transient and posttransient cylinder wake, J. Fluid Mech., 497 (2003), 335363. 

24 
B. R. Noack, G. Tadmor and M. Morzyński, Actuation models and dissipative control in empirical Galerkin models of fluid flows, In Proceedings of the American Control Conference, (2004), 57225727. 

25 
K. Pearson, LIII. on lines and planes of closest fit to systems of points in space, Philos. Mag., 2 (1901), 559572. 

26 
C. Penland, Random forcing and forecasting using Principal Oscillation Pattern analysis, Mon. Weather Rev., 117 (1989), 21652185. 

27 
C. Penland and T. Magorian, Prediction of Niño 3 seasurface temperatures using linear inverse modeling, J. Climate, 6 (1993), 10671076. 

28 
C. W. Rowley, Model reduction for fluids, using balanced proper orthogonal decomposition, Int. J. Bifurcat. Chaos, 15 (2005), 9971013. 

29 
C. W. Rowley, I. Mezic, S. Bagheri, P. Schlatter and D. S. Henningson, Spectral analysis of nonlinear flows, J. Fluid Mech., 641 (2009), 115127. 

30 
P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech., 656 (2010), 528. 

31 
P. J. Schmid, Application of the dynamic mode decomposition to experimental data, Exp. Fluids, 50 (2011), 11231130. 

32 
P. J. Schmid, L. Li, M. P. Juniper and O. Pust, Applications of the dynamic mode decomposition, Theor. Comp. Fluid Dyn., 25 (2011), 249259. 

33 
P. J. Schmid and J. Sesterhenn, Dynamic mode decomposition of numerical and experimental data, Journal of Fluid Mechanics, 656 (2010), 528. 

34 
P. J. Schmid, D. Violato and F. Scarano, Decomposition of timeresolved tomographic PIV, Exp. Fluids, 52 (2012), 15671579. 

35 
A. Seena and H. J. Sung, Dynamic mode decomposition of turbulent cavity flows for selfsustained oscillations, Int. J. Heat Fluid Fl., 32 (2011), 10981110. 

36 
O. Semeraro, G. Bellani and F. Lundell, Analysis of timeresolved PIV measurements of a confined turbulent jet using POD and Koopman modes, Exp. Fluids, 53 (2012), 12031220. 

37 
J. R. Singler, Optimality of balanced proper orthogonal decomposition for data reconstruction, Numerical Functional Analysis and Optimization, 31 (2010), 852869. 

38 
L. Sirovich, Turbulence and the dynamics of coherent structures. 2. Symmetries and transformations, Q. Appl. Math., 45 (1987), 573582. 

39 
K. Taira and T. Colonius, The immersed boundary method: A projection approach, J. Comput. Phys., 225 (2007), 21182137. 

40 
L. N. Trefethen and D. Bau III, Numerical Linear Algebra, SIAM, Philadelphia, 1997. 

41 
J. H. Tu, J. Griffin, A. Hart, C. W. Rowley, L. N. Cattafesta III and L. S. Ukeiley, Integration of nontimeresolved PIV and timeresolved velocity point sensors for dynamic estimation of velocity fields, Exp. Fluids, 54 (2013), pp1429. 

42 
J. H. Tu and C. W. Rowley, An improved algorithm for balanced POD through an analytic treatment of impulse response tails, J. Comput. Phys., 231 (2012), 53175333. 

43 
J. H. Tu, C. W. Rowley, E. Aram and R. Mittal, Koopman spectral analysis of separated flow over a finitethickness flat plate with elliptical leading edge, AIAA Paper 201138, 49th AIAA Aerospace Sciences Meeting and Exhibit, Jan. 2011. 

44 
H. von Storch, G. Bürger, R. Schnur and J. S. von Storch, Principal oscillation patterns: A review, J. Climate, 8 (1995), 377400. 

45 
M. O. Williams, I. G. Kevrekidis and C. W. Rowley, A datadriven approximation of the Koopman operator: extending dynamic mode decomposition, arXiv:1408.4408, 2014. 

46 
A. Wynn, D. Pearson, B. Ganapathisubramani and P. J. Goulart, Optimal mode decomposition for unsteady flows, J. Fluid Mech., 733 (2013), 473503. 

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