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Volumn 32, Issue 5, 2010, Pages 2737-2764

Nonlinear model reduction via discrete empirical interpolation

Author keywords

Empirical interpolation methods; Nonlinear model reduction; Nonlinear partial differential equations; Proper orthogonal decomposition

Indexed keywords

CONTROL NONLINEARITIES; INTERPOLATION; NONLINEAR ANALYSIS; NONLINEAR EQUATIONS; NONLINEAR SYSTEMS; ONE DIMENSIONAL; PARTIAL DIFFERENTIAL EQUATIONS; PRINCIPAL COMPONENT ANALYSIS;

EID: 78149314237     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/090766498     Document Type: Article
Times cited : (1767)

References (42)
  • 1
    • 8744274501 scopus 로고    scopus 로고
    • Fast reduced order modeling technique for large scale LTV systems
    • P. Astrid, Fast reduced order modeling technique for large scale LTV systems, in Proceedings of the 2004 American Control Conference, Vol.1, 2004, pp. 762-767.
    • (2004) Proceedings of the 2004 American Control Conference , vol.1 , pp. 762-767
    • Astrid, P.1
  • 5
    • 56549095007 scopus 로고    scopus 로고
    • Missing point estimation in models described by proper orthogonal decomposition
    • P. Astrid, S. Weiland, K. Willcox, and T. Backx, Missing point estimation in models described by proper orthogonal decomposition, IEEE Trans. Automat. Control, 53 (2008), pp. 2237-2251.
    • (2008) IEEE Trans. Automat. Control , vol.53 , pp. 2237-2251
    • Astrid, P.1    Weiland, S.2    Willcox, K.3    Backx, T.4
  • 6
    • 0036776433 scopus 로고    scopus 로고
    • Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
    • Z. Bai, Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems, Appl. Numer. Math., 43 (2002), pp. 9-44.
    • (2002) Appl. Numer. Math. , vol.43 , pp. 9-44
    • Bai, T.1
  • 7
    • 15744385841 scopus 로고    scopus 로고
    • An "empirical interpolation" method: Application to efficient reduced-basis discretization of partial differential equations
    • M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera, An "empirical interpolation" method: Application to efficient reduced-basis discretization of partial differential equations, C. R. Math. Acad. Sci. Paris, 339 (2004), pp. 667-672.
    • (2004) C. R. Math. Acad. Sci. Paris , vol.339 , pp. 667-672
    • Barrault, M.1    Maday, Y.2    Nguyen, N.C.3    Patera, A.T.4
  • 8
    • 78149309764 scopus 로고    scopus 로고
    • Nonlinear model order reduction in nanoelectronics: Combination of POD and TPWL
    • T. Bechtold, M. Striebel, K. Mohaghegh, and E. J. W. ter Maten, Nonlinear model order reduction in nanoelectronics: Combination of POD and TPWL, Proc. Appl. Math. Mech., 8 (2008), pp. 10057-10060.
    • (2008) Proc. Appl. Math. Mech. , vol.8 , pp. 10057-10060
    • Bechtold, T.1    Striebel, M.2    Mohaghegh, K.3    Ter Maten, E.J.W.4
  • 9
    • 4344609077 scopus 로고    scopus 로고
    • Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition
    • T. Bui-Thanh, M. Damodaran, and K. Willcox, Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition, AIAA J., 42 (2004), pp. 1505-1516.
    • (2004) AIAA J. , vol.42 , pp. 1505-1516
    • Bui-Thanh, T.1    Damodaran, M.2    Willcox, K.3
  • 10
    • 70449707083 scopus 로고    scopus 로고
    • Linearized reduced-order models for subsurface flow simulation
    • M. A. Cardoso and L. J. Durlofsky, Linearized reduced-order models for subsurface flow simulation, J. Comput. Phys., 229 (2010), pp. 681-700.
    • (2010) J. Comput. Phys. , vol.229 , pp. 681-700
    • Cardoso, M.A.1    Durlofsky, L.J.2
  • 11
    • 60949093256 scopus 로고    scopus 로고
    • Development and application of reducedorder modeling procedures for subsurface flow simulation
    • M. A. Cardoso, L. J. Durlofsky, and P. Sarma, Development and application of reducedorder modeling procedures for subsurface flow simulation, Internat. J. Numer. Methods Engrg., 77 (2009), pp. 1322-1350.
    • (2009) Internat. J. Numer. Methods Engrg. , vol.77 , pp. 1322-1350
    • Cardoso, M.A.1    Durlofsky, L.J.2    Sarma, P.3
  • 12
    • 79960903533 scopus 로고    scopus 로고
    • Application of POD and DEIM to dimension reduction of nonlinear miscible viscous fingering in porous media
    • to appear
    • S. Chaturantabut and D. C. Sorensen, Application of POD and DEIM to dimension reduction of nonlinear miscible viscous fingering in porous media, Math. Comput. Model. Dyn. Syst., to appear.
    • Math. Comput. Model. Dyn. Syst.
    • Chaturantabut, S.1    Sorensen, D.C.2
  • 14
    • 0013237778 scopus 로고    scopus 로고
    • Master's thesis, Massachusetts Institute of Technology, Cambridge, MA
    • Y. Chen, Model Order Reduction for Nonlinear Systems, Master's thesis, Massachusetts Institute of Technology, Cambridge, MA, 1999.
    • (1999) Model Order Reduction for Nonlinear Systems
    • Chen, Y.1
  • 16
    • 0042134784 scopus 로고    scopus 로고
    • Piecewise polynomial nonlinear model reduction
    • IEEE Computer Society, Los Alamitos, CA
    • N. Dong and J. Roychowdhury, Piecewise polynomial nonlinear model reduction, in Proceedings of the Design Automation Conference, IEEE Computer Society, Los Alamitos, CA, 2003, pp. 484-489.
    • (2003) Proceedings of the Design Automation Conference , pp. 484-489
    • Dong, N.1    Roychowdhury, J.2
  • 17
    • 75649118920 scopus 로고    scopus 로고
    • Non-linear model reduction for uncertainty quantification in large-scale inverse problems
    • D. Galbally, K. Fidkowski, K. Willcox, and O. Ghattas, Non-linear model reduction for uncertainty quantification in large-scale inverse problems, Internat. J. Numer. Methods Engrg., 81 (2010), pp. 1581-1608.
    • (2010) Internat. J. Numer. Methods Engrg. , vol.81 , pp. 1581-1608
    • Galbally, D.1    Fidkowski, K.2    Willcox, K.3    Ghattas, O.4
  • 18
    • 0033540943 scopus 로고    scopus 로고
    • Optimal control of vortex shedding using loworder models. Part I-Open-loop model development
    • W. R. Graham, J. Peraire, and K. Y. Tang, Optimal control of vortex shedding using loworder models. Part I-Open-loop model development, Internat. J. Numer. Methods Engrg., 44 (1999), pp. 945-972.
    • (1999) Internat. J. Numer. Methods Engrg. , vol.44 , pp. 945-972
    • Graham, W.R.1    Peraire, J.2    Tang, K.Y.3
  • 19
    • 34547943108 scopus 로고    scopus 로고
    • Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
    • M. A. Grepl, Y. Maday, N. C. Nguyen, and A. T. Patera, Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations, M2AN Math. Model. Numer. Anal., 41 (2007), pp. 575-605.
    • (2007) M2AN Math. Model. Numer. Anal. , vol.41 , pp. 575-605
    • Grepl, M.A.1    Maday, Y.2    Nguyen, N.C.3    Patera, A.T.4
  • 20
    • 33750977082 scopus 로고    scopus 로고
    • Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control
    • Springer, Berlin
    • M. Hinze and S. Volkwein, Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control, in Dimension Reduction of Large-Scale Systems, Lect. Notes Comput. Sci. Eng. 45, Springer, Berlin, 2005, pp. 261-306.
    • (2005) Dimension Reduction of Large-Scale Systems, Lect. Notes Comput. Sci. Eng. , vol.45 , pp. 261-306
    • Hinze, M.1    Volkwein, S.2
  • 22
    • 0033177060 scopus 로고    scopus 로고
    • Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
    • K. Kunisch and S. Volkwein, Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition, J. Optim. Theory Appl., 102 (1999), pp. 345-371.
    • (1999) J. Optim. Theory Appl. , vol.102 , pp. 345-371
    • Kunisch, K.1    Volkwein, S.2
  • 23
    • 0038693394 scopus 로고    scopus 로고
    • Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics
    • K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics, SIAM J. Numer. Anal., 40 (2002), pp. 492-515.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 492-515
    • Kunisch, K.1    Volkwein, S.2
  • 25
  • 26
    • 0037906854 scopus 로고    scopus 로고
    • A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations
    • Y. Maday, A. T. Patera, and G. Turinici, A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations, J. Sci. Comput., 17 (2002), pp. 437-446.
    • (2002) J. Sci. Comput. , vol.17 , pp. 437-446
    • Maday, Y.1    Patera, A.T.2    Turinici, G.3
  • 27
    • 38349195074 scopus 로고    scopus 로고
    • A "best points" interpolation method for efficient approximation of parametrized functions
    • N. C. Nguyen, A. T. Patera, and J. Peraire, A "best points" interpolation method for efficient approximation of parametrized functions, Internat. J. Numer. Methods Engrg., 73 (2007), pp. 521-543.
    • (2007) Internat. J. Numer. Methods Engrg. , vol.73 , pp. 521-543
    • Nguyen, N.C.1    Patera, A.T.2    Peraire, J.3
  • 28
    • 53749102512 scopus 로고    scopus 로고
    • An efficient reduced-order modeling approach for non-linear parametrized partial differential equations
    • N. C. Nguyen and J. Peraire, An efficient reduced-order modeling approach for non-linear parametrized partial differential equations, Internat. J. Numer. Methods Engrg., 76 (2008), pp. 27-55.
    • (2008) Internat. J. Numer. Methods Engrg. , vol.76 , pp. 27-55
    • Nguyen, N.C.1    Peraire, J.2
  • 29
    • 70349560243 scopus 로고    scopus 로고
    • Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers' equation
    • N. C. Nguyen, G. Rozza, and A. T. Patera, Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers' equation, Calcolo, 46 (2009), pp. 157-185.
    • (2009) Calcolo , vol.46 , pp. 157-185
    • Nguyen, N.C.1    Rozza, G.2    Patera, A.T.3
  • 32
    • 0003321083 scopus 로고    scopus 로고
    • Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods
    • C. Prud'homme, D. V. Rovas, K. Veroy, L. Machiels, Y. Maday, A. T. Patera, and G. Turinici, Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods, J. Fluids Eng., 124 (2002), pp. 70-80.
    • (2002) J. Fluids Eng. , vol.124 , pp. 70-80
    • Prud'homme, C.1    Rovas, D.V.2    Veroy, K.3    Machiels, L.4    Maday, Y.5    Patera, A.T.6    Turinici, G.7
  • 33
    • 0034327551 scopus 로고    scopus 로고
    • A reduced-order approach for optimal control of fluids using proper orthogonal decomposition
    • S. S. Ravindran, A reduced-order approach for optimal control of fluids using proper orthogonal decomposition, Internat. J. Numer. Methods Fluids, 34 (2000), pp. 425-448.
    • (2000) Internat. J. Numer. Methods Fluids , vol.34 , pp. 425-448
    • Ravindran, S.S.1
  • 35
    • 0035212532 scopus 로고    scopus 로고
    • A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices
    • M. Rewienski and J. White, A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices, in Proceedings of the International Conference on Computer-Aided Design, 2001, pp. 252-257.
    • (2001) Proceedings of the International Conference on Computer-Aided Design , pp. 252-257
    • Rewienski, M.1    White, J.2
  • 36
    • 0037322638 scopus 로고    scopus 로고
    • A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices
    • M. Rewienski and J. White, A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., 22 (2003), pp. 155-170.
    • (2003) IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. , vol.22 , pp. 155-170
    • Rewienski, M.1    White, J.2
  • 37
    • 33646125616 scopus 로고    scopus 로고
    • Model order reduction for nonlinear dynamical systems based on trajectory piecewise-linear approximations
    • M. Rewienski and J. White, Model order reduction for nonlinear dynamical systems based on trajectory piecewise-linear approximations, Linear Algebra Appl., 415 (2006), pp. 426-454.
    • (2006) Linear Algebra Appl. , vol.415 , pp. 426-454
    • Rewienski, M.1    White, J.2
  • 38
    • 0842343715 scopus 로고    scopus 로고
    • Model reduction for compressible flows using POD and Galerkin projection
    • C. W. Rowley, T. Colonius, and R. M. Murray, Model reduction for compressible flows using POD and Galerkin projection, Phys. D, 189 (2004), pp. 115-129.
    • (2004) Phys. D , vol.189 , pp. 115-129
    • Rowley, C.W.1    Colonius, T.2    Murray, R.M.3
  • 39
    • 33751510481 scopus 로고    scopus 로고
    • The many proofs of an identity on the norm of oblique projections
    • D. B. Szyld, The many proofs of an identity on the norm of oblique projections, Numer. Algorithms, 42 (2006), pp. 309-323.
    • (2006) Numer. Algorithms , vol.42 , pp. 309-323
    • Szyld, D.B.1
  • 41
    • 14644387249 scopus 로고    scopus 로고
    • A posteriori error estimation for reduced-basis approximation of parametrized elliptic coercive partial differential equations: "Convex inverse" bound conditioners
    • K. Veroy, D. V. Rovas, and A. T. Patera, A posteriori error estimation for reduced-basis approximation of parametrized elliptic coercive partial differential equations: "Convex inverse" bound conditioners, ESAIM Control Optim. Calc. Var., 8 (2002), pp. 1007-1028.
    • (2002) ESAIM Control Optim. Calc. Var. , vol.8 , pp. 1007-1028
    • Veroy, K.1    Rovas, D.V.2    Patera, A.T.3
  • 42
    • 26844464354 scopus 로고    scopus 로고
    • Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition
    • K. Willcox, Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition, Comput. Fluids, 35 (2006), pp. 208-226.
    • (2006) Comput. Fluids , vol.35 , pp. 208-226
    • Willcox, K.1


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