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Volumn 80, Issue 8, 2009, Pages 1025-1057

Reduced-order modeling of parameterized PDEs using time-space-parameter principal component analysis

Author keywords

Design optimization; Fluid dynamics problems; Metamodel; Parameterized partial differential equation (PDE); Physics based model; Proper orthogonal decomposition (POD); Radial basis functions (RBF); Reduced order model (ROM); Surrogate

Indexed keywords

DESIGN OPTIMIZATION; METAMODEL; PARAMETERIZED PARTIAL DIFFERENTIAL EQUATION (PDE); PHYSICS-BASED MODEL; PROPER ORTHOGONAL DECOMPOSITION (POD); RADIAL BASIS FUNCTIONS (RBF); REDUCED-ORDER MODEL (ROM); SURROGATE;

EID: 70350393816     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2540     Document Type: Article
Times cited : (118)

References (39)
  • 3
    • 0003097075 scopus 로고
    • Uber lineare methoden in der wahrscheinlichkeitsrechnung
    • Series A-1, (Mathematica-Physica)
    • Karhumen K. Uber lineare methoden in der wahrscheinlichkeitsrechnung. Annales Academiaé Scientiarum Fennicaé, Series A-1 (Mathematica-Physica) 1946; 37
    • (1946) Annales Academiaé Scientiarum Fennicaé , pp. 37
    • Karhumen, K.1
  • 7
    • 0002708045 scopus 로고
    • The structure of inhomogeneous turbulent flow
    • Yaglom AM, Tatarski VI (eds). Nauka: Moscow
    • Lumley JL. The structure of inhomogeneous turbulent flow. In Atmospheric Turbulence and Wave Propagation, Yaglom AM, Tatarski VI (eds). Nauka: Moscow, 1967; 166-178
    • (1967) Atmospheric Turbulence and Wave Propagation , pp. 166-178
    • Lumley, J.L.1
  • 9
    • 0000246863 scopus 로고
    • Dynamics and the coherence of turbulent structures, Parts I-III
    • Sirovich L. Dynamics and the coherence of turbulent structures, Parts I-III. Quaterly of Applied Mathematics 1987; XLV(3):561-590
    • (1987) Quaterly of Applied Mathematics , vol.45 , Issue.3 , pp. 561-590
    • Sirovich, L.1
  • 10
    • 0034327551 scopus 로고    scopus 로고
    • A reduced order approach to optimal control of fluids using proper orthogonal decomposition
    • Ravindran SS. A reduced order approach to optimal control of fluids using proper orthogonal decomposition. International Journal for Numerical Methods in Fluids 2000; 34:425-448
    • (2000) International Journal for Numerical Methods in Fluids , vol.34 , pp. 425-448
    • Ravindran, S.S.1
  • 16
    • 0037906854 scopus 로고    scopus 로고
    • A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations
    • Maday Y, Patera AT, Turinici G. A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations. Journal of Scientific Computing 2002; 17:437-446
    • (2002) Journal of Scientific Computing , vol.17 , pp. 437-446
    • Maday, Y.1    Patera, A.T.2    Turinici, G.3
  • 18
    • 15744406041 scopus 로고    scopus 로고
    • Certified real-time solution of the parameterized steady incompressible Navier-Stokes equations: Rigorous reduced-basis a posteriori error bounds
    • Veroy K, Patera AT. Certified real-time solution of the parameterized 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
  • 19
    • 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(1):346-366
    • (2005) Journal of Computational Physics , vol.202 , Issue.1 , pp. 346-366
    • Ryckelynck, D.1
  • 21
    • 70350429142 scopus 로고    scopus 로고
    • Physics-based surrogate modeling of parameterized PDEs for optimization and uncertainty analysis
    • Structural Dynamics, and Materials Con- ference, Denver, CO, AIAA Paper 2002-1586
    • Nair PB. Physics-based surrogate modeling of parameterized PDEs for optimization and uncertainty analysis. Proceedings of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures. Structural Dynamics, and Materials Con- ference, Denver, CO, 2002; AIAA Paper 2002-1586
    • (2002) Proceedings of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures
    • Nair, P.B.1
  • 22
    • 0000473317 scopus 로고
    • On the systematic search in a hypercube
    • Sobol IM. On the systematic search in a hypercube. SIAM Journal on Numerical Analysis 1979; 16(5):790-793
    • (1979) SIAM Journal on Numerical Analysis , vol.16 , Issue.5 , pp. 790-793
    • Sobol, I.M.1
  • 23
    • 0022954116 scopus 로고
    • Algorithm 647: Implementation and relative efficiency of quasirandom sequence generators
    • Fox B. Algorithm 647: implementation and relative efficiency of quasirandom sequence generators. ACM Transactions on Mathematical Software 1986; 12:362-376
    • (1986) ACM Transactions on Mathematical Software , vol.12 , pp. 362-376
    • Fox, B.1
  • 24
    • 12044259644 scopus 로고
    • The proper orthogonal decomposition in the analysis of turbulent flows
    • Berkooz G, Holmes P, Lumley JL. The proper orthogonal decomposition in the analysis of turbulent flows. Annual Review of Fluid Mechanics 1993; 25:539-575
    • (1993) Annual Review of Fluid Mechanics , vol.25 , pp. 539-575
    • Berkooz, G.1    Holmes, P.2    Lumley, J.L.3
  • 26
    • 55149091531 scopus 로고    scopus 로고
    • Model reduction for large-scale systems with high-dimensional parametric input space
    • MIT ACDL, ACDL-TR-07-2, August 2007
    • Bui-Thanh T, Willcox K, Ghattas O. Model reduction for large-scale systems with high-dimensional parametric input space. MIT ACDL, ACDL-TR-07-2, August 2007; SIAM Journal on Scientific Computing 2008; 30(6):3270-3288
    • (2008) SIAM Journal on Scientific Computing , vol.30 , Issue.6 , pp. 3270-3288
    • Bui-Thanh, T.1    Willcox, K.2    Ghattas, O.3
  • 27
    • 0141607828 scopus 로고    scopus 로고
    • Some greedy learning algorithms for sparse regression and classification with mercer kernels
    • Nair PB, Choudhury A, Keane AJ. Some greedy learning algorithms for sparse regression and classification with mercer kernels. Journal of Machine Learning Research 2002; 3:781-801
    • (2002) Journal of Machine Learning Research , vol.3 , pp. 781-801
    • Nair, P.B.1    Choudhury, A.2    Keane, A.J.3
  • 31
    • 0242497930 scopus 로고    scopus 로고
    • Time-decomposed parallel time-integrators: Theory and feasability studies for fluid, structure, and fluid-structure applications
    • Farhat C, Chandesris M. Time-decomposed parallel time-integrators: theory and feasability studies for fluid, structure, and fluid-structure applications. International Journal for Numerical Methods in Engineering 2003; 58(9):1397-1434
    • (2003) International Journal for Numerical Methods in Engineering , vol.58 , Issue.9 , pp. 1397-1434
    • Farhat, C.1    Chandesris, M.2
  • 32
    • 34249917362 scopus 로고
    • Spatio-temporal analysis of complex signals: Theory and applications
    • Aubry N, Guyonnet R, Lima R. Spatio-temporal analysis of complex signals: theory and applications. Journal of Statistical Physics 1991; 63:683
    • (1991) Journal of Statistical Physics , vol.63 , pp. 683
    • Aubry, N.1    Guyonnet, R.2    Lima, R.3
  • 35
    • 70350407847 scopus 로고    scopus 로고
    • Physics-based metamodeling for parametrized PDE problems using space-parameter space principal component analysis
    • Lecture Notes. CEA-EDF-INRIA School: INRIA Rocquencourt, France, 8-10 October
    • De Vuyst F, Audouze C. Physics-based metamodeling for parametrized PDE problems using space-parameter space principal component analysis. Model Reduction: Theory and Applications. Lecture Notes. CEA-EDF-INRIA School: INRIA Rocquencourt, France, 8-10 October 2007
    • (2007) Model Reduction: Theory and Applications
    • de Vuyst, F.1    Audouze, C.2
  • 36
    • 70350388835 scopus 로고    scopus 로고
    • State of the art in physics-based metamodeling for CFD problems
    • Research Report ECP/MAS 2007, in press
    • Audouze C, De Vuyst F. State of the art in physics-based metamodeling for CFD problems. Research Report ECP/MAS 2007; Journal of Shanghai University 2007; in press
    • Journal of Shanghai University 2007
    • Audouze, C.1    de Vuyst, F.2
  • 38
    • 15944386355 scopus 로고    scopus 로고
    • Low-order empirical modeling of distributed parameter systems using temporal and spatial eigenfunctions
    • Bleris L, Kothare MV. Low-order empirical modeling of distributed parameter systems using temporal and spatial eigenfunctions. Computer and Chemical Engineering 2005; 29:817-827
    • (2005) Computer and Chemical Engineering , vol.29 , pp. 817-827
    • Bleris, L.1    Kothare, M.V.2
  • 39
    • 41449117770 scopus 로고    scopus 로고
    • Analysis of the parareal time-parallel time-integration method
    • Gander MJ, Vandewalle S. Analysis of the parareal time-parallel time-integration method. SIAM Journal on Scientific Computing 2007; 29(2):556-578
    • (2007) SIAM Journal on Scientific Computing , vol.29 , Issue.2 , pp. 556-578
    • Gander, M.J.1    Vandewalle, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.