메뉴 건너뛰기




Volumn 200, Issue 23-24, 2011, Pages 2032-2047

On the verification of model reduction methods based on the proper generalized decomposition

Author keywords

Constitutive relation error; Error estimation; Model reduction; Proper generalized decomposition; Separated representation; Verification

Indexed keywords

CONSTITUTIVE RELATION ERRORS; ERROR ESTIMATION; MODEL REDUCTION; PROPER GENERALIZED DECOMPOSITION; SEPARATED REPRESENTATION;

EID: 79953888465     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2011.02.019     Document Type: Article
Times cited : (116)

References (41)
  • 2
    • 13244260949 scopus 로고    scopus 로고
    • Proper orthogonal decomposition and modal analysis for acceleration of transient FEM thermal analysis
    • Bialecki R.A., Kassab A.J., Fic A. Proper orthogonal decomposition and modal analysis for acceleration of transient FEM thermal analysis. International Journal for Numerical Methods in Engineering 2005, 62(6):774-797.
    • (2005) International Journal for Numerical Methods in Engineering , vol.62 , Issue.6 , pp. 774-797
    • Bialecki, R.A.1    Kassab, A.J.2    Fic, A.3
  • 3
    • 69749114337 scopus 로고    scopus 로고
    • A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable robin coefficient
    • Boyaval S., Le Bris C., Maday Y., Nguyen N.C., Patera A.T. A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable robin coefficient. Computer Methods in Applied Mechanics and Engineering 2009, 198(41-44):3187-3206.
    • (2009) Computer Methods in Applied Mechanics and Engineering , vol.198 , Issue.41-44 , pp. 3187-3206
    • Boyaval, S.1    Le Bris, C.2    Maday, Y.3    Nguyen, N.C.4    Patera, A.T.5
  • 5
    • 0742317141 scopus 로고    scopus 로고
    • Computational quantum chemistry: a primer Handbook of numerical analysis
    • P. Ciarlet, C. Le Bris (Eds.)
    • Cances E., Defranceschi M., Kutzelnigg W., Le Bris C., Maday Y. Computational quantum chemistry: a primer Handbook of numerical analysis. Handbook of Numerical Analysis 2003, vol. 10:3-270. P. Ciarlet, C. Le Bris (Eds.).
    • (2003) Handbook of Numerical Analysis , vol.10 , pp. 3-270
    • Cances, E.1    Defranceschi, M.2    Kutzelnigg, W.3    Le Bris, C.4    Maday, Y.5
  • 6
    • 0011075775 scopus 로고    scopus 로고
    • An introduction to the proper orthogonal decomposition
    • Chatterjee A. An introduction to the proper orthogonal decomposition. Current Science 2000, 78(7):808-817.
    • (2000) Current Science , vol.78 , Issue.7 , pp. 808-817
    • Chatterjee, A.1
  • 7
    • 34548675800 scopus 로고    scopus 로고
    • Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods
    • Chamoin L., Ladevèze P. Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods. International Journal for Numerical Methods in Engineering 2007, 71(12):1387-1411.
    • (2007) International Journal for Numerical Methods in Engineering , vol.71 , Issue.12 , pp. 1387-1411
    • Chamoin, L.1    Ladevèze, P.2
  • 8
    • 36849058122 scopus 로고    scopus 로고
    • A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems
    • Chamoin L., Ladevèze P. A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems. Computer Methods in Applied Mechanics and Engineering 2008, 197(9-12):994-1014.
    • (2008) Computer Methods in Applied Mechanics and Engineering , vol.197 , Issue.9-12 , pp. 994-1014
    • Chamoin, L.1    Ladevèze, P.2
  • 10
    • 79955481777 scopus 로고    scopus 로고
    • Proper generalized decomposition in extreme simulations: towards a change of paradigm in computational mechanics?
    • Chinesta F., Ladevèze P., Ammar A., Cueto E., Nouy A. Proper generalized decomposition in extreme simulations: towards a change of paradigm in computational mechanics?. IACM Expressions 2009, 26/09:2-7.
    • (2009) IACM Expressions , pp. 2-7
    • Chinesta, F.1    Ladevèze, P.2    Ammar, A.3    Cueto, E.4    Nouy, A.5
  • 11
    • 78549239497 scopus 로고    scopus 로고
    • Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models
    • Chinesta F., Ammar A., Cueto E. Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models. Archives of Computational Methods in Engineering 2010, 17(4):327-350.
    • (2010) Archives of Computational Methods in Engineering , vol.17 , Issue.4 , pp. 327-350
    • Chinesta, F.1    Ammar, A.2    Cueto, E.3
  • 12
    • 79955475851 scopus 로고    scopus 로고
    • Réduction dynamique par décomposition orthogonale aux valeurs propres (POD). OCET
    • L. Cordier, M. Bergmann, Réduction dynamique par décomposition orthogonale aux valeurs propres (POD). OCET, 2006.
    • (2006)
    • Cordier, L.1    Bergmann, M.2
  • 13
    • 67650233442 scopus 로고    scopus 로고
    • Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method
    • Cottereau R., Diez P., Huerta A. Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method. Computational Mechanics 2009, 44(4):533-547.
    • (2009) Computational Mechanics , vol.44 , Issue.4 , pp. 533-547
    • Cottereau, R.1    Diez, P.2    Huerta, A.3
  • 15
    • 15744385753 scopus 로고    scopus 로고
    • A posteriori error bounds for reduced-basis approximation of parametrized parabolic partial differential equations
    • Grepl M.A., Patera A.T. A posteriori error bounds for reduced-basis approximation of parametrized parabolic partial differential equations. ESAIM-Mathematical Modelling and Numerical Analysis (M2AN) 2005, 39(1):157-181.
    • (2005) ESAIM-Mathematical Modelling and Numerical Analysis (M2AN) , vol.39 , Issue.1 , pp. 157-181
    • Grepl, M.A.1    Patera, A.T.2
  • 20
    • 0035540055 scopus 로고    scopus 로고
    • Galerkin proper orthogonal decomposition methods for parabolic problems
    • Kunish K., Volkwein S. Galerkin proper orthogonal decomposition methods for parabolic problems. Numerische Mathematik 2001, 90(1):148-177.
    • (2001) Numerische Mathematik , vol.90 , Issue.1 , pp. 148-177
    • Kunish, K.1    Volkwein, S.2
  • 21
    • 0000397449 scopus 로고
    • The large time increment method for the analysis of structures with nonlinear constitutive relation described by internal variables
    • (in french)
    • Ladevèze P. The large time increment method for the analysis of structures with nonlinear constitutive relation described by internal variables. Comptes Rendus Académie des Sciences, Paris 1989, 309(II):1095-1099. (in french).
    • (1989) Comptes Rendus Académie des Sciences, Paris , vol.309 , Issue.2 , pp. 1095-1099
    • Ladevèze, P.1
  • 23
    • 42449155099 scopus 로고    scopus 로고
    • Strict upper error bounds for calculated outputs of interest in computational structural mechanics
    • Ladevèze P. Strict upper error bounds for calculated outputs of interest in computational structural mechanics. Computational Mechanics 2008, 42(2):271-286.
    • (2008) Computational Mechanics , vol.42 , Issue.2 , pp. 271-286
    • Ladevèze, P.1
  • 24
    • 0001585002 scopus 로고
    • Error estimate procedure in the finite element method and application
    • Ladevèze P., Leguillon D. Error estimate procedure in the finite element method and application. SIAM Journal of Numerical Analysis 1983, 20(3):485-509.
    • (1983) SIAM Journal of Numerical Analysis , vol.20 , Issue.3 , pp. 485-509
    • Ladevèze, P.1    Leguillon, D.2
  • 29
    • 73449133715 scopus 로고    scopus 로고
    • A new non-intrusive technique for the construction of admissible stress fields in model verification
    • Ladevèze P., Chamoin L., Florentin E. A new non-intrusive technique for the construction of admissible stress fields in model verification. Computer Methods in Applied Mechanics and Engineering 2010, 199(9-12):766-777.
    • (2010) Computer Methods in Applied Mechanics and Engineering , vol.199 , Issue.9-12 , pp. 766-777
    • Ladevèze, P.1    Chamoin, L.2    Florentin, E.3
  • 30
    • 78649679229 scopus 로고    scopus 로고
    • Calculation of strict error bounds for finite element approximations of non-linear pointwise quantities of interest
    • Ladevèze P., Chamoin L. Calculation of strict error bounds for finite element approximations of non-linear pointwise quantities of interest. International Journal for Numerical Methods in Engineering 2010, 84:1638-1664.
    • (2010) International Journal for Numerical Methods in Engineering , vol.84 , pp. 1638-1664
    • Ladevèze, P.1    Chamoin, L.2
  • 31
    • 78549276796 scopus 로고    scopus 로고
    • Proper generalized decomposition for multiscale and multiphysics problems
    • Néron D., Ladevèze P. Proper generalized decomposition for multiscale and multiphysics problems. Archives of Computational Methods in Engineering 2010, 17(4):351-372.
    • (2010) Archives of Computational Methods in Engineering , vol.17 , Issue.4 , pp. 351-372
    • Néron, D.1    Ladevèze, P.2
  • 32
    • 34548290926 scopus 로고    scopus 로고
    • A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations
    • Nouy A. A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations. Computer Methods in Applied Mechanics and Engineering 2007, 196(45-48):4521-4537.
    • (2007) Computer Methods in Applied Mechanics and Engineering , vol.196 , Issue.45-48 , pp. 4521-4537
    • Nouy, A.1
  • 33
    • 53549096783 scopus 로고    scopus 로고
    • Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms
    • Nouy A. Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms. Computer Methods in Applied Mechanics and Engineering 2008, 197:4718-4736.
    • (2008) Computer Methods in Applied Mechanics and Engineering , vol.197 , pp. 4718-4736
    • Nouy, A.1
  • 34
    • 77951238456 scopus 로고    scopus 로고
    • A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations
    • Nouy A. A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations. Computer Methods in Applied Mechanics and Engineering 2010, 199(23-24):1603-1626.
    • (2010) Computer Methods in Applied Mechanics and Engineering , vol.199 , Issue.23-24 , pp. 1603-1626
    • Nouy, A.1
  • 35
    • 33751113713 scopus 로고    scopus 로고
    • Multiscale computational strategy with time and space homogenization: a radial-type approximation technique for solving microproblems
    • Nouy A., Ladevèze P. Multiscale computational strategy with time and space homogenization: a radial-type approximation technique for solving microproblems. International Journal for Multiscale Computational Engineering 2004, 2(4):557-574.
    • (2004) International Journal for Multiscale Computational Engineering , vol.2 , Issue.4 , pp. 557-574
    • Nouy, A.1    Ladevèze, P.2
  • 37
    • 77954958688 scopus 로고    scopus 로고
    • A scalable time-space multiscale domain decomposition method: adaptive time scales separation
    • Passieux J.C., Ladevèze P., Néron D. A scalable time-space multiscale domain decomposition method: adaptive time scales separation. Computational Mechanics 2010, 46(4):621-633.
    • (2010) Computational Mechanics , vol.46 , Issue.4 , pp. 621-633
    • Passieux, J.C.1    Ladevèze, P.2    Néron, D.3
  • 38
    • 79955468184 scopus 로고    scopus 로고
    • On the techniques for constructing admissible stress fields in model verification: performances on engineering examples
    • online
    • Pled F., Chamoin L., Ladevèze P. On the techniques for constructing admissible stress fields in model verification: performances on engineering examples. International Journal for Numerical Methods in Engineering 2010, online.
    • (2010) International Journal for Numerical Methods in Engineering
    • Pled, F.1    Chamoin, L.2    Ladevèze, P.3
  • 39
  • 40
    • 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
  • 41
    • 79955467709 scopus 로고    scopus 로고
    • Efficient mold danscooling optimization by using model reduction, Technical Report, University of Toulouse
    • F. Schmidt, N. Pirc, M. Mongeau, F. Chinesta, Efficient mold danscooling optimization by using model reduction, Technical Report, University of Toulouse, 2010.
    • (2010)
    • Schmidt, F.1    Pirc, N.2    Mongeau, M.3    Chinesta, F.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.