Free Access
Issue
ESAIM: M2AN
Volume 44, Number 3, May-June 2010
Page(s) 509 - 529
DOI https://doi.org/10.1051/m2an/2010011
Published online 04 February 2010
  1. G. Berkooz, P. Holmes and J.L. Lumley, Turbulence, Coherent Structures, Dynamical Systems and SymmetryCambridge Monographes in Mechanics. Cambridge Universtity Press, UK (1996). [Google Scholar]
  2. T. Bui-Thanh, Model-constrained optimization methods for reduction of parameterized systems. Ph.D. Thesis, MIT, USA (2007). [Google Scholar]
  3. T. Bui-Thanh, M. Damodoran and K. Willcox, Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition. AIAA Journal 42 (2004) 1505–1516. [Google Scholar]
  4. T. Bui-Thanh, K. Willcox, O. Ghattas and B. van Bloemen Wanders, Goal-oriented, model-constrained optimization for reduction of large-scale systems. J. Comput Phys. 224 (2007) 880–896. [Google Scholar]
  5. R. Everson and L. Sirovich, The Karhunen-Loeve procedure for gappy data. J. Opt. Soc. Am. 12 (1995) 1657–1664. [CrossRef] [Google Scholar]
  6. K. Fukunaga, Introduction to Statistical Recognition. Academic Press, New York, USA (1990). [Google Scholar]
  7. M.A. Grepl, Y. Maday, N.C. Nguyen and A.T. Patera, Efficient reduced-basis treatment of affine and nonlinear partial differential equations. ESAIM: M2AN 41 (2007) 575–605. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  8. M. Heinkenschloss, Formulation and Analysis of a Sequential Quadratic Programming Method for the Optimal Dirichlet Boundary Control of Navier Stokes Flow – Optimal Control: Theory, Methods and Applications. Kluwer Academic Publisher, B.V. (1998) 178–203. [Google Scholar]
  9. M. Hinze and K. Kunisch, Second order methods for optimal control of time – Dependent fluid flow. SIAM J. Contr. Optim. 40 (2001) 925–946. [Google Scholar]
  10. K. Ito and S.S. Ravindran, A reduced-order method for simulation and control of fluid flows. J. Comput. Phys. 143 (1998) 403–425. [CrossRef] [MathSciNet] [Google Scholar]
  11. T. Kato, Perturbation Theory for Linear Operators. Springer Verlag, Germany (1980). [Google Scholar]
  12. K. Kunisch and S. Volkwein, Control of Burgers' equation by reduced order approach using proper orthogonal decomposition. J. Optim. Theory Appl. 102 (1999) 345–371. [CrossRef] [MathSciNet] [Google Scholar]
  13. K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for parabolic problems. Numer. Math. 90 (2001) 117–148. [CrossRef] [MathSciNet] [Google Scholar]
  14. S. Lall, J.E. Marsden and S. Glavaski, Empirical model reduction of controlled nonlinear systems, in Proceedings of the IFAC Congress, Vol. F (1999) 473–478. [Google Scholar]
  15. H.V. Ly and H.T. Tran, Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor. Quarterly Appl. Math. 60 (2002) 631–656. [Google Scholar]
  16. J. Nocedal and S.J. Wright, Numerical Optimization, Springer Series in Operation Research. Second Edition, Springer Verlag, New York, USA (2006). [Google Scholar]
  17. M. Rathinam and L.R. Petzold, A new look at proper orthogonal decomposition. SIAM J. Numer. Anal. 41 (2003) 1893–1925. [CrossRef] [MathSciNet] [Google Scholar]
  18. S.S. Ravindran, Adaptive reduced-order controllers for a thermal flow system using proper orthogonal decomposition. SIAM J. Sci. Comput. 23 (2002) 1924–1942. [CrossRef] [MathSciNet] [Google Scholar]
  19. C.W. Rowley, Model reduction for fluids using balanced proper orthogonal decomposition. Int. J. Bifur. Chaos 15 (2005) 997–1013. [Google Scholar]
  20. G. Rozza, D.B.P. Huynh and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: Application to transport and continuum mechanics. Arch. Comput. Method. E. 15 (2008) 229–275. [Google Scholar]
  21. R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics. Second edition, Springer, Berlin, Germany (1997). [Google Scholar]
  22. K. Willcox, O. Ghattas, B. von Bloemen Wanders and W. Bader, An optimization framework for goal-oriented, model-based reduction of large-scale systems, in 44th IEEE Conference on Decision and Control, Sevilla, Spain (2005). [Google Scholar]

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