메뉴 건너뛰기




Volumn 242, Issue , 2013, Pages 623-647

The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows

Author keywords

CFD; Gappy POD; GNAT; Mesh sampling; Nonlinear model reduction; Petrov Galerkin

Indexed keywords

BIT ERROR RATE; COMPUTATIONAL EFFICIENCY; DEGREES OF FREEDOM (MECHANICS); ERROR ANALYSIS; GALERKIN METHODS; MESH GENERATION; NONLINEAR SYSTEMS; STRUCTURAL DYNAMICS; TURBULENT FLOW;

EID: 84876458320     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2013.02.028     Document Type: Article
Times cited : (609)

References (52)
  • 1
    • 79952654642 scopus 로고    scopus 로고
    • Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations
    • Carlberg K., Bou-Mosleh C., Farhat C. Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations. International Journal for Numerical Methods in Engineering 2011, 86:155-181.
    • (2011) International Journal for Numerical Methods in Engineering , vol.86 , pp. 155-181
    • Carlberg, K.1    Bou-Mosleh, C.2    Farhat, C.3
  • 5
    • 53749107686 scopus 로고    scopus 로고
    • Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
    • Rozza G., Huynh D.B.P., Patera A.T. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Archives of Computational Methods in Engineering 2008, 15:229-275.
    • (2008) Archives of Computational Methods in Engineering , vol.15 , pp. 229-275
    • Rozza, G.1    Huynh, D.B.P.2    Patera, A.T.3
  • 6
    • 79955736755 scopus 로고    scopus 로고
    • A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations
    • AIAA Paper 2003-3847, in: 16th AIAA Computational Fluid Dynamics Conference, Orlando, FL
    • K. Veroy, C. Prud'homme, D.V. Rovas, A.T. Patera, A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations, AIAA Paper 2003-3847, in: 16th AIAA Computational Fluid Dynamics Conference, Orlando, FL, 2003.
    • (2003)
    • Veroy, K.1    Prud'homme, C.2    Rovas, D.V.3    Patera, A.T.4
  • 7
    • 15744376916 scopus 로고    scopus 로고
    • Certified real-time solution of parametrized partial differential equations
    • Springer, Netherlands, S. Yip (Ed.)
    • Ngoc Cuong N., Veroy K., Patera A.T. Certified real-time solution of parametrized partial differential equations. Handbook of Materials Modeling 2005, 1529-1564. Springer, Netherlands. S. Yip (Ed.).
    • (2005) Handbook of Materials Modeling , pp. 1529-1564
    • Ngoc Cuong, N.1    Veroy, K.2    Patera, A.T.3
  • 8
    • 15744406041 scopus 로고    scopus 로고
    • Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds
    • Veroy K., Patera A.T. Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds. International Journal for Numerical Methods in Fluids 2005, 47:773-788.
    • (2005) International Journal for Numerical Methods in Fluids , vol.47 , pp. 773-788
    • Veroy, K.1    Patera, A.T.2
  • 9
    • 0038028696 scopus 로고    scopus 로고
    • Reduced-order modelling of unsteady small-disturbance flows using a frequency-domain proper orthogonal decomposition technique
    • AIAA Paper 99-16520, in: 37th Aerospace Sciences Meeting and Exhibit, Reno, NV
    • K.C. Hall, J.P. Thomas, E.H. Dowell, Reduced-order modelling of unsteady small-disturbance flows using a frequency-domain proper orthogonal decomposition technique, AIAA Paper 99-16520, in: 37th Aerospace Sciences Meeting and Exhibit, Reno, NV, 1999.
    • (1999)
    • Hall, K.C.1    Thomas, J.P.2    Dowell, E.H.3
  • 10
    • 23544437012 scopus 로고    scopus 로고
    • Airfoil design optimization using reduced order models based on proper orthogonal decomposition
    • AIAA Paper 2000-25450, in: Fluids 2000 Conference and Exhibit, Denver, CO
    • P.A. LeGresley, J.J. Alonso, Airfoil design optimization using reduced order models based on proper orthogonal decomposition, AIAA Paper 2000-25450, in: Fluids 2000 Conference and Exhibit, Denver, CO, 2000.
    • (2000)
    • LeGresley, P.A.1    Alonso, J.J.2
  • 11
    • 0034298665 scopus 로고    scopus 로고
    • Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows
    • Hall K.C., Thomas J.P., Dowell E.H. Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows. AIAA Journal 2000, 38:1853-1862.
    • (2000) AIAA Journal , vol.38 , pp. 1853-1862
    • Hall, K.C.1    Thomas, J.P.2    Dowell, E.H.3
  • 12
    • 0036849510 scopus 로고    scopus 로고
    • Balanced model reduction via the proper orthogonal decomposition
    • Willcox K., Peraire J. Balanced model reduction via the proper orthogonal decomposition. AIAA Journal 2002, 40:2323-2330.
    • (2002) AIAA Journal , vol.40 , pp. 2323-2330
    • Willcox, K.1    Peraire, J.2
  • 13
    • 0042944156 scopus 로고    scopus 로고
    • A parametric analysis of reduced order models of viscous flows in turbomachinery
    • Epureanu B.I. A parametric analysis of reduced order models of viscous flows in turbomachinery. Journal of Fluids and Structures 2003, 17:971-982.
    • (2003) Journal of Fluids and Structures , vol.17 , pp. 971-982
    • Epureanu, B.I.1
  • 14
    • 0037866713 scopus 로고    scopus 로고
    • Three-dimensional transonic aeroelasticity using proper orthogonal decomposition-based reduced order models
    • Thomas J.P., Dowell E.H., Hall K.C. Three-dimensional transonic aeroelasticity using proper orthogonal decomposition-based reduced order models. Journal of Aircraft 2003, 40:544-551.
    • (2003) Journal of Aircraft , vol.40 , pp. 544-551
    • Thomas, J.P.1    Dowell, E.H.2    Hall, K.C.3
  • 15
    • 29544443507 scopus 로고    scopus 로고
    • Aeroelastic model reduction for affordable computational fluid dynamics-based flutter analysis
    • Kim T., Hong M., Bhatia K.B., SenGupta G. Aeroelastic model reduction for affordable computational fluid dynamics-based flutter analysis. AIAA Journal 2005, 43:2487-2495.
    • (2005) AIAA Journal , vol.43 , pp. 2487-2495
    • Kim, T.1    Hong, M.2    Bhatia, K.B.3    SenGupta, G.4
  • 17
    • 34347218566 scopus 로고    scopus 로고
    • Adaptation of aeroelastic reduced-order models and application to an F-16 configuration
    • Lieu T., Farhat C. Adaptation of aeroelastic reduced-order models and application to an F-16 configuration. AIAA Journal 2007, 45:1244-1269.
    • (2007) AIAA Journal , vol.45 , pp. 1244-1269
    • Lieu, T.1    Farhat, C.2
  • 18
    • 47749108243 scopus 로고    scopus 로고
    • An interpolation method for adapting reduced-order models and application to aeroelasticity
    • Amsallem D., Farhat C. An interpolation method for adapting reduced-order models and application to aeroelasticity. AIAA Journal 2008, 46:1803-1813.
    • (2008) AIAA Journal , vol.46 , pp. 1803-1813
    • Amsallem, D.1    Farhat, C.2
  • 19
    • 77957173096 scopus 로고    scopus 로고
    • Toward real-time CFD-based aeroelastic computations using a database of reduced-order information
    • Amsallem D., Cortial J., Farhat C. Toward real-time CFD-based aeroelastic computations using a database of reduced-order information. AIAA Journal 2010, 48:2029-2037.
    • (2010) AIAA Journal , vol.48 , pp. 2029-2037
    • Amsallem, D.1    Cortial, J.2    Farhat, C.3
  • 20
    • 8744227253 scopus 로고    scopus 로고
    • A priori hyperreduction method: an adaptive approach
    • Ryckelynck D. A priori hyperreduction method: an adaptive approach. Journal of Computational Physics 2005, 202:346-366.
    • (2005) Journal of Computational Physics , vol.202 , pp. 346-366
    • Ryckelynck, D.1
  • 22
    • 15744385841 scopus 로고    scopus 로고
    • An 'empirical interpolation' method: application to efficient reduced-basis discretization of partial differential equations
    • Barrault M., Maday Y., Nguyen N.C., Patera A.T. An 'empirical interpolation' method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus Mathématique Académie des Sciences 2004, 339:667-672.
    • (2004) Comptes Rendus Mathématique Académie des Sciences , vol.339 , pp. 667-672
    • Barrault, M.1    Maday, Y.2    Nguyen, N.C.3    Patera, A.T.4
  • 24
    • 53749102512 scopus 로고    scopus 로고
    • An efficient reduced-order modeling approach for non-linear parametrized partial differential equations
    • Nguyen N.C., Peraire J. An efficient reduced-order modeling approach for non-linear parametrized partial differential equations. International Journal for Numerical Methods in Engineering 2008, 76:27-55.
    • (2008) International Journal for Numerical Methods in Engineering , vol.76 , pp. 27-55
    • Nguyen, N.C.1    Peraire, J.2
  • 25
    • 68149120541 scopus 로고    scopus 로고
    • A reduced basis method for evolution schemes with parameter-dependent explicit operators
    • Haasdonk B., Ohlberger M., Rozza G. A reduced basis method for evolution schemes with parameter-dependent explicit operators. Electronic Transactions on Numerical Analysis 2008, 32:145-161.
    • (2008) Electronic Transactions on Numerical Analysis , vol.32 , pp. 145-161
    • Haasdonk, B.1    Ohlberger, M.2    Rozza, G.3
  • 27
    • 14244249495 scopus 로고    scopus 로고
    • A Trajectory Piecewise-Linear Approach to Model Order Reduction of Nonlinear Dynamical Systems
    • Ph.D. thesis, Massachusetts Institute of Technology
    • M.J. Rewienski, A Trajectory Piecewise-Linear Approach to Model Order Reduction of Nonlinear Dynamical Systems, Ph.D. thesis, Massachusetts Institute of Technology, 2003.
    • (2003)
    • Rewienski, M.J.1
  • 28
    • 51149118725 scopus 로고    scopus 로고
    • Application of Proper Orthogonal Decomposition (POD) to Design Decomposition Methods
    • Ph.D. thesis, Stanford University
    • P.A. LeGresley, Application of Proper Orthogonal Decomposition (POD) to Design Decomposition Methods, Ph.D. thesis, Stanford University, 2006.
    • (2006)
    • LeGresley, P.A.1
  • 30
    • 8744303647 scopus 로고    scopus 로고
    • Accelerating large-scale non-linear models for monitoring and control using spatial and temporal correlations
    • Bos R., Bombois X., Van den Hof P. Accelerating large-scale non-linear models for monitoring and control using spatial and temporal correlations. Proceedings of the American Control Conference 2004, 4:3705-3710.
    • (2004) Proceedings of the American Control Conference , vol.4 , pp. 3705-3710
    • Bos, R.1    Bombois, X.2    Van Den Hof, P.3
  • 33
    • 84861368452 scopus 로고    scopus 로고
    • Reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation
    • Drohmann M., Haasdonk B., Ohlberger M. Reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation. SIAM Journal on Scientific Computing 2012, 34:A937-A969.
    • (2012) SIAM Journal on Scientific Computing , vol.34
    • Drohmann, M.1    Haasdonk, B.2    Ohlberger, M.3
  • 34
    • 84870571331 scopus 로고    scopus 로고
    • Non-linear Petrov-Galerkin methods for reduced order hyperbolic equations and discontinuous finite element methods
    • Fang F., Pain C., Navon I., Elsheikh A., Du J., Xiao D. Non-linear Petrov-Galerkin methods for reduced order hyperbolic equations and discontinuous finite element methods. Journal of Computational Physics 2013, 234:540-559.
    • (2013) Journal of Computational Physics , vol.234 , pp. 540-559
    • Fang, F.1    Pain, C.2    Navon, I.3    Elsheikh, A.4    Du, J.5    Xiao, D.6
  • 36
    • 84876459194 scopus 로고    scopus 로고
    • Model Reduction of Nonlinear Mechanical Systems via Optimal Projection and Tensor Approximation
    • Ph.D. thesis, Stanford University
    • K. Carlberg, Model Reduction of Nonlinear Mechanical Systems via Optimal Projection and Tensor Approximation, Ph.D. thesis, Stanford University, 2011.
    • (2011)
    • Carlberg, K.1
  • 37
    • 0033895382 scopus 로고    scopus 로고
    • A comparison of three methods for selecting values of input variables in the analysis of output from a computer code
    • McKay M., Beckman R., Conover W. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 2000, 42:55-61.
    • (2000) Technometrics , vol.42 , pp. 55-61
    • McKay, M.1    Beckman, R.2    Conover, W.3
  • 38
    • 15744385753 scopus 로고    scopus 로고
    • A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations
    • Grepl M.A., Patera A.T. A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. ESAIM - Mathematical Modelling and Numerical Analysis (M2AN) 2005, 39:157-181.
    • (2005) ESAIM - Mathematical Modelling and Numerical Analysis (M2AN) , vol.39 , pp. 157-181
    • Grepl, M.A.1    Patera, A.T.2
  • 39
    • 55149091531 scopus 로고    scopus 로고
    • Model reduction for large-scale systems with high-dimensional parametric input space
    • Bui-Thanh T., Willcox K., Ghattas O. Model reduction for large-scale systems with high-dimensional parametric input space. SIAM Journal on Scientific Computing 2008, 30:3270-3288.
    • (2008) SIAM Journal on Scientific Computing , vol.30 , pp. 3270-3288
    • Bui-Thanh, T.1    Willcox, K.2    Ghattas, O.3
  • 40
    • 41549118036 scopus 로고    scopus 로고
    • Reduced basis method for finite volume approximations of parametrized linear evolution equations
    • Haasdonk B., Ohlberger M. Reduced basis method for finite volume approximations of parametrized linear evolution equations. ESAIM - Mathematical Modelling and Numerical Analysis 2008, 42:277-302.
    • (2008) ESAIM - Mathematical Modelling and Numerical Analysis , vol.42 , pp. 277-302
    • Haasdonk, B.1    Ohlberger, M.2
  • 41
    • 84861371899 scopus 로고    scopus 로고
    • A state space error estimate for POD-DEIM nonlinear model reduction
    • Chaturantabut S., Sorensen D. A state space error estimate for POD-DEIM nonlinear model reduction. SIAM Journal on Numerical Analysis 2012, 50:46-63.
    • (2012) SIAM Journal on Numerical Analysis , vol.50 , pp. 46-63
    • Chaturantabut, S.1    Sorensen, D.2
  • 42
    • 84861396087 scopus 로고    scopus 로고
    • Reduced basis method for finite volume approximation of evolution equations on parametrized geometries
    • M. Drohmann, B. Haasdonk, M. Ohlberger, Reduced basis method for finite volume approximation of evolution equations on parametrized geometries, in: Proceedings of ALGORITMY, pp. 1-10.
    • Proceedings of ALGORITMY , pp. 1-10
    • Drohmann, M.1    Haasdonk, B.2    Ohlberger, M.3
  • 44
    • 26844464354 scopus 로고    scopus 로고
    • Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition
    • Willcox K. Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition. Computers and Fluids 2006, 35:208-226.
    • (2006) Computers and Fluids , vol.35 , pp. 208-226
    • Willcox, K.1
  • 46
    • 33847118934 scopus 로고    scopus 로고
    • Reduction of process simulation models: a proper orthogonal decomposition approach
    • Ph.D. thesis, Technische Universiteit Eindhoven
    • P. Astrid, Reduction of process simulation models: a proper orthogonal decomposition approach, Ph.D. thesis, Technische Universiteit Eindhoven, 2004.
    • (2004)
    • Astrid, P.1
  • 47
    • 0004263947 scopus 로고
    • Some salient features of the time-averaged ground vehicle wake
    • SAE Paper 840300
    • S.R. Ahmed, G. Ramm, G. Faitin, Some salient features of the time-averaged ground vehicle wake, SAE Paper 840300, 1984.
    • (1984)
    • Ahmed, S.R.1    Ramm, G.2    Faitin, G.3
  • 48
    • 0037345147 scopus 로고    scopus 로고
    • Aeroelastic dynamic analysis of a full F-16 configuration for various flight conditions
    • Geuzaine P., Brown G., Harris C., Farhat C. Aeroelastic dynamic analysis of a full F-16 configuration for various flight conditions. AIAA Journal 2003, 41:363-371.
    • (2003) AIAA Journal , vol.41 , pp. 363-371
    • Geuzaine, P.1    Brown, G.2    Harris, C.3    Farhat, C.4
  • 49
    • 0036390834 scopus 로고    scopus 로고
    • Application of a three-field nonlinear fluid-structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter
    • Farhat C., Geuzaine P., Brown G. Application of a three-field nonlinear fluid-structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter. Computers & Fluids 2003, 32:3-29.
    • (2003) Computers & Fluids , vol.32 , pp. 3-29
    • Farhat, C.1    Geuzaine, P.2    Brown, G.3
  • 51
    • 33644798370 scopus 로고    scopus 로고
    • Large eddy simulation of flow around the Ahmed body
    • Springer, J.R.R. McCallen, F. Browand (Eds.) The Aerodynamics of Heavy Vehicles: Trucks, Buses and Trains
    • Hinterberger C., Garci{dotless}a-Villalba M., Rodi W. Large eddy simulation of flow around the Ahmed body. Lecture Notes in Applied and Computational Mechanics 2004, vol. 19. Springer. J.R.R. McCallen, F. Browand (Eds.).
    • (2004) Lecture Notes in Applied and Computational Mechanics , vol.19
    • Hinterberger, C.1    Garcia-Villalba, M.2    Rodi, W.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.