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Volumn 31, Issue 1-2 SPEC., 2003, Pages 179-191

Efficient model reduction in non-linear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods

Author keywords

Dual weighted residual methods; Error estimates; Karhunen Lo ve expansion; Model reduction; Non linear dynamics

Indexed keywords

COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; NUMERICAL METHODS;

EID: 0037481177     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-002-0404-1     Document Type: Article
Times cited : (152)

References (51)
  • 1
    • 0017970146 scopus 로고
    • Automatic choice of global shape functions in structural analysis
    • Almroth BO, Stern P, Brogan FA (1978) Automatic choice of global shape functions in structural analysis. AIAA J. 16(5): 525-528
    • (1978) AIAA J. , vol.16 , Issue.5 , pp. 525-528
    • Almroth, B.O.1    Stern, P.2    Brogan, F.A.3
  • 2
    • 0033309866 scopus 로고    scopus 로고
    • Finite element approximation of the acoustic wave equation: Error control and mesh adaptation
    • Bangert W, Rannacher R (1999) Finite element approximation of the acoustic wave equation: Error control and mesh adaptation. East-West J. Numer. Math. 7(4): 263-282
    • (1999) East-West J. Numer. Math. , vol.7 , Issue.4 , pp. 263-282
    • Bangert, W.1    Rannacher, R.2
  • 3
    • 0026391155 scopus 로고
    • Aerodynamic sensitivity analysis methods for the compressible Euler equations
    • Baysal O, Eleshaky ME (1991) Aerodynamic sensitivity analysis methods for the compressible Euler equations. J. Fluids Eng. 113: 681-688
    • (1991) J. Fluids Eng. , vol.113 , pp. 681-688
    • Baysal, O.1    Eleshaky, M.E.2
  • 4
    • 0030383153 scopus 로고    scopus 로고
    • A feed-back approach to error control in finite element methods: Basic analysis and examples
    • Becker R, Rannacher R (1996) A feed-back approach to error control in finite element methods: Basic analysis and examples. East-West J. Numer. Math. 4: 237-264
    • (1996) East-West J. Numer. Math. , vol.4 , pp. 237-264
    • Becker, R.1    Rannacher, R.2
  • 5
    • 0004236610 scopus 로고    scopus 로고
    • Weighted a posteriori error control in finite element methods
    • Technical report, Universität Heidelberg
    • Becker R, Rannacher R (1996) Weighted a posteriori error control in finite element methods. Technical report, Universität Heidelberg
    • (1996)
    • Becker, R.1    Rannacher, R.2
  • 6
    • 85022001969 scopus 로고    scopus 로고
    • An optimal control approach to a posteriori error estimation in finite elements
    • Becker R, Rannacher R (2001) An optimal control approach to a posteriori error estimation in finite elements. Acta Numerica 10: 1-102
    • (2001) Acta Numerica , vol.10 , pp. 1-102
    • Becker, R.1    Rannacher, R.2
  • 7
    • 12044259644 scopus 로고
    • The proper orthogonal decomposition in the analysis of turbulent flows
    • Berkooz G, Holmes P, Lumley JL (1993) The proper orthogonal decomposition in the analysis of turbulent flows. Ann. Rev. Fluid Mech. 25:539-575
    • (1993) Ann. Rev. Fluid Mech. , vol.25 , pp. 539-575
    • Berkooz, G.1    Holmes, P.2    Lumley, J.L.3
  • 8
    • 0038548023 scopus 로고    scopus 로고
    • Stabilization of explicit time integration by modal reduction
    • In: Wall W A, Bletzinger KU, Schweizerhof K (eds); Barcelona, CIMNE
    • Bucher C (2001) Stabilization of explicit time integration by modal reduction. In: Wall W A, Bletzinger KU, Schweizerhof K (eds), Trends in Computational Structural Mechanics, Barcelona, CIMNE.
    • (2001) Trends in Computational Structural Mechanics
    • Bucher, C.1
  • 9
    • 0002650095 scopus 로고
    • Error bounds for dynamic responses in forced vibration problems
    • Cabos C (1994) Error bounds for dynamic responses in forced vibration problems. SIAM J. Scientific Comput. 15(1): 1-15
    • (1994) SIAM J. Scientific Comput. , vol.15 , Issue.1 , pp. 1-15
    • Cabos, C.1
  • 10
    • 0037871748 scopus 로고    scopus 로고
    • Reduction methods in structural dynamics
    • In: Meskouris K, Wittek U (eds); Balkema
    • Dinkler D (1997) Reduction methods in structural dynamics. In: Meskouris K, Wittek U (eds), Aspects in Modern Computational Structural Analysis, Balkema pp. 19-31
    • (1997) Aspects in Modern Computational Structural Analysis , pp. 19-31
    • Dinkler, D.1
  • 11
    • 0009522795 scopus 로고
    • Introduction to adaptive methods for differential equations
    • Eriksson K, Estep D, Hansbo P, Johnson C (1995) Introduction to adaptive methods for differential equations. Acta Numerica 4: 105-158
    • (1995) Acta Numerica , vol.4 , pp. 105-158
    • Eriksson, K.1    Estep, D.2    Hansbo, P.3    Johnson, C.4
  • 12
    • 0004094896 scopus 로고    scopus 로고
    • Computational differential equations
    • Cambridge University Press, Cambridge
    • Eriksson K, Estep D, Hansbo P, Johnson C (1996) Computational Differential Equations. Cambridge University Press, Cambridge
    • (1996)
    • Eriksson, K.1    Estep, D.2    Hansbo, P.3    Johnson, C.4
  • 13
    • 0001164460 scopus 로고
    • A posteriori error bounds and global error control for approximations of ordinary differential equations
    • Estep D (1995) A posteriori error bounds and global error control for approximations of ordinary differential equations. SIAM J. Numer. Anal. 32: 1-48
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1-48
    • Estep, D.1
  • 14
    • 0004599093 scopus 로고
    • On the discretization error of parameterized nonlinear equations
    • Fink JP, Rheinboldt WC (1983) On the discretization error of parameterized nonlinear equations. SIAM J. Numer. Anal. 20(4): 732-746
    • (1983) SIAM J. Numer. Anal. , vol.20 , Issue.4 , pp. 732-746
    • Fink, J.P.1    Rheinboldt, W.C.2
  • 15
    • 0020547404 scopus 로고
    • On the error behaviour of the reduced basis technique for nonlinear finite element approximations
    • Fink JP, Rheinboldt WC (1983) On the error behaviour of the reduced basis technique for nonlinear finite element approximations. ZAMM 63: 21-28
    • (1983) ZAMM , vol.63 , pp. 21-28
    • Fink, J.P.1    Rheinboldt, W.C.2
  • 17
    • 0038160418 scopus 로고    scopus 로고
    • Flexible multibody dynamics, a finite element approach
    • John Wiley & Sons, Chichester
    • Géradin M, Cardona A (2001) Flexible Multibody Dynamics, A Finite Element Approach. John Wiley & Sons, Chichester
    • (2001)
    • Géradin, M.1    Cardona, A.2
  • 18
    • 0003406531 scopus 로고
    • Modern factor analysis
    • University of Chicago Press, Chicago
    • Harman H (1960) Modern Factor Analysis. University of Chicago Press, Chicago
    • (1960)
    • Harman, H.1
  • 19
    • 0003851376 scopus 로고    scopus 로고
    • Turbulence, coherent structures, dynamical systems and symmetry
    • Cambridge University Press, Cambridge
    • Holmes P, Lumley JL, Berkooz G (1996) Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press, Cambridge
    • (1996)
    • Holmes, P.1    Lumley, J.L.2    Berkooz, G.3
  • 20
    • 58149421595 scopus 로고
    • Analysis of complex statistical variables in principal components
    • Hotelling H (1953) Analysis of complex statistical variables in principal components. J. Experi. Psychol. 24: 417
    • (1953) J. Experi. Psychol. , vol.24 , pp. 417
    • Hotelling, H.1
  • 21
    • 0022077232 scopus 로고
    • A reduction method for nonlinear structural dynamic analysis
    • Idelson SR, Cardona A (1985) A reduction method for nonlinear structural dynamic analysis. Comput. Meth. Appl. Mech. Eng. 49: 253-279
    • (1985) Comput. Meth. Appl. Mech. Eng. , vol.49 , pp. 253-279
    • Idelson, S.R.1    Cardona, A.2
  • 22
    • 20544476549 scopus 로고
    • Aerodynamic design via control theory
    • Jameson A (1988) Aerodynamic design via control theory. SIAM J. Sci. Comput. 3: 233-260
    • (1988) SIAM J. Sci. Comput. , vol.3 , pp. 233-260
    • Jameson, A.1
  • 23
    • 0001562231 scopus 로고
    • Error estimates and adaptive time-step control for a class of one-step methods for stiff ordinary differential equations
    • Johnson C (1988) Error estimates and adaptive time-step control for a class of one-step methods for stiff ordinary differential equations. SIAM J. Numer. Anal. 25(4): 908-926
    • (1988) SIAM J. Numer. Anal. , vol.25 , Issue.4 , pp. 908-926
    • Johnson, C.1
  • 24
    • 0024607886 scopus 로고
    • Ritz vectors and generation criteria for mode superposition analysis
    • Joo KJ, Wilson EL, Leger P (1989) Ritz vectors and generation criteria for mode superposition analysis. Earthquake Eng. Struct. Dynam. 18: 149-167
    • (1989) Earthquake Eng. Struct. Dynam. , vol.18 , pp. 149-167
    • Joo, K.J.1    Wilson, E.L.2    Leger, P.3
  • 26
    • 0004021243 scopus 로고    scopus 로고
    • Parameter sensitivity in nonlinear mechanics
    • John Wiley & Sons, Chichester
    • Kleiber M (1997) Parameter Sensitivity in Nonlinear Mechanics. John Wiley & Sons, Chichester
    • (1997)
    • Kleiber, M.1
  • 27
    • 0022889148 scopus 로고
    • Dynamic analysis using a reduced basis of exact modes and Ritz vectors
    • Kline KA (1986) Dynamic analysis using a reduced basis of exact modes and Ritz vectors. AIAA J. 24(12): 2022-2029
    • (1986) AIAA J. , vol.24 , Issue.12 , pp. 2022-2029
    • Kline, K.A.1
  • 28
    • 0030411230 scopus 로고    scopus 로고
    • Analysis of long torsional springs by proper orthogonal decomposition
    • Kreuzer E, Kust O (1996) Analysis of long torsional springs by proper orthogonal decomposition. Arch. Appl. Mech. 67: 68-80
    • (1996) Arch. Appl. Mech. , vol.67 , pp. 68-80
    • Kreuzer, E.1    Kust, O.2
  • 29
    • 0035838104 scopus 로고    scopus 로고
    • Dimensional model reduction in non-linear finite element dynamics of solids and structures
    • Krysl P, Lall S, Marsden JE (2001) Dimensional model reduction in non-linear finite element dynamics of solids and structures. Int. J. Numer. Meth. Eng. 51: 479-504
    • (2001) Int. J. Numer. Meth. Eng. , vol.51 , pp. 479-504
    • Krysl, P.1    Lall, S.2    Marsden, J.E.3
  • 30
    • 0026821122 scopus 로고
    • Non-linear seismic response analysis using vector superposition methods
    • Leger P, Dussault S (1992) Non-linear seismic response analysis using vector superposition methods. Earthquake Eng. Struct. Dynam. 21: 163-176
    • (1992) Earthquake Eng. Struct. Dynam. , vol.21 , pp. 163-176
    • Leger, P.1    Dussault, S.2
  • 31
    • 0012752030 scopus 로고    scopus 로고
    • Multi-adaptive error control for ODEs
    • Preprint 2000-003, Chalmers Finite Element Center
    • Logg A (2000) Multi-adaptive error control for ODEs. Preprint 2000-003, Chalmers Finite Element Center
    • (2000)
    • Logg, A.1
  • 32
    • 0012654166 scopus 로고    scopus 로고
    • A multiadaptive ODE-solver
    • Preprint 2000-002, Chalmers Finite Element Center
    • Logg A (2000) A multiadaptive ODE-solver. Preprint 2000-002, Chalmers Finite Element Center
    • (2000)
    • Logg, A.1
  • 33
    • 0003519658 scopus 로고
    • Empirical orthogonal eigenfunctions and statistical weather prediction
    • Technical report, MIT Report, Department of Meteorology, Cambridge, MA
    • Lorenz EN (1956) Empirical orthogonal eigenfunctions and statistical weather prediction. Technical report, MIT Report, Department of Meteorology, Cambridge, MA
    • (1956)
    • Lorenz, E.N.1
  • 35
  • 36
    • 0003754415 scopus 로고
    • Adjoint equations and analysis of complex systems
    • Kluwer Academic Publishers, Dordrecht
    • Marchuk GI (1995) Adjoint Equations and Analysis of Complex Systems. Kluwer Academic Publishers, Dordrecht
    • (1995)
    • Marchuk, G.I.1
  • 37
    • 0016871727 scopus 로고
    • Nonlinear dynamics by mode superposition
    • Nickell RE (1976). Nonlinear dynamics by mode superposition. Comput. Meth. Appl. Mech. Eng. 7: 107-129
    • (1976) Comput. Meth. Appl. Mech. Eng. , vol.7 , pp. 107-129
    • Nickell, R.E.1
  • 38
    • 85025237802 scopus 로고
    • Recent advances and applications of reduction methods
    • Noor AK (1994) Recent advances and applications of reduction methods. Appl. Mech. Rev. 47(5): 125-145
    • (1994) Appl. Mech. Rev. , vol.47 , Issue.5 , pp. 125-145
    • Noor, A.K.1
  • 39
    • 0019009732 scopus 로고
    • Reduced basis technique for nonlinear analysis of structures
    • Noor AK, Peters J.M. (1980) Reduced basis technique for nonlinear analysis of structures. AIAA J. 18(4): 455-462
    • (1980) AIAA J. , vol.18 , Issue.4 , pp. 455-462
    • Noor, A.K.1    Peters, J.M.2
  • 40
    • 0021469350 scopus 로고
    • Dynamic analysis of structures using Lanczos co-ordinates
    • Nour-Omid B, Clough RW (1984) Dynamic analysis of structures using Lanczos co-ordinates. Earthquake Eng. Struct. Dynam. 12: 565-577
    • (1984) Earthquake Eng. Struct. Dynam. , vol.12 , pp. 565-577
    • Nour-Omid, B.1    Clough, R.W.2
  • 41
    • 0012656543 scopus 로고    scopus 로고
    • The dual-weighted-residual method for error control and mesh adaptation in finite element methods
    • In: Whiteman JR (ed.); Amsterdam, Elsevier
    • Rannacher R (2000) The dual-weighted-residual method for error control and mesh adaptation in finite element methods. In: Whiteman JR (ed.), MAFELEAP 99, pp. 97-115, Amsterdam, Elsevier
    • (2000) MAFELEAP 99 , pp. 97-115
    • Rannacher, R.1
  • 42
    • 0346244559 scopus 로고
    • On error control in computational fluid mechanics
    • Technical Report 94-13, Universität Heidelberg
    • Rannacher R, Johnson C (1994) On error control in computational fluid mechanics. Technical Report 94-13, Universität Heidelberg
    • (1994)
    • Rannacher, R.1    Johnson, C.2
  • 43
    • 0027222258 scopus 로고
    • Eine modale Reduktionsmethode zur geometrisch nichtlinearen statischen und dynamischen Finite-Element-Berechnung
    • Remke J, Rothert H (1993) Eine modale Reduktionsmethode zur geometrisch nichtlinearen statischen und dynamischen Finite-Element-Berechnung. Arch. Appl. Mech. 63: 101-115
    • (1993) Arch. Appl. Mech. , vol.63 , pp. 101-115
    • Remke, J.1    Rothert, H.2
  • 45
    • 0038209341 scopus 로고    scopus 로고
    • Time integration and reduction methods in nonlinear dynamics of solids
    • Sansour C, Wriggers P, Sansour J (2001) Time integration and reduction methods in nonlinear dynamics of solids. In: GAMM 2001, Zürich
    • (2001) GAMM 2001, Zürich
    • Sansour, C.1    Wriggers, P.2    Sansour, J.3
  • 46
    • 0000246863 scopus 로고
    • Turbulence and the dynamics of coherent structures, Part I-II
    • Sirovitch L (1987) Turbulence and the dynamics of coherent structures, Part I-II. Quart. Appl. Math. 45: 561-590
    • (1987) Quart. Appl. Math. , vol.45 , pp. 561-590
    • Sirovitch, L.1
  • 47
    • 0002250046 scopus 로고
    • Management and analysis of large scientific datasets
    • Sirovitch L, Everson R (1992) Management and analysis of large scientific datasets. Int. J. Supercomp. Appl. 6(1): 50-68
    • (1992) Int. J. Supercomp. Appl. , vol.6 , Issue.1 , pp. 50-68
    • Sirovitch, L.1    Everson, R.2


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