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

Computer Methods in Applied Mechanics and Engineering - Tập 200 - Trang 2032-2047 - 2011
Pierre Ladevèze1,2, Ludovic Chamoin1
1LMT-Cachan (ENS Cachan/CNRS/Paris 6 Univ./PRES UniverSud Paris), 61 Avenue du Président Wilson, 94235 Cachan Cedex, France
2EADS Foundation Chair ‘Advanced Computational Structural Mechanics’, France

Tài liệu tham khảo

Ammar, 2010, An error estimator for separated representations of highly multidimensional models, Computer Methods in Applied Mechanics and Engineering, 199, 1872, 10.1016/j.cma.2010.02.012 Bialecki, 2005, Proper orthogonal decomposition and modal analysis for acceleration of transient FEM thermal analysis, International Journal for Numerical Methods in Engineering, 62, 774, 10.1002/nme.1205 Boyaval, 2009, 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, 198, 3187, 10.1016/j.cma.2009.05.019 Bungartz, 2004, Sparse grids, Acta Numerica, 13, 1, 10.1017/S0962492904000182 Cances, 2003, Computational quantum chemistry: a primer Handbook of numerical analysis, vol. 10, 3 Chatterjee, 2000, An introduction to the proper orthogonal decomposition, Current Science, 78, 808 Chamoin, 2007, Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods, International Journal for Numerical Methods in Engineering, 71, 1387, 10.1002/nme.1978 Chamoin, 2008, 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, 197, 994, 10.1016/j.cma.2007.09.021 Chinesta, 2008, Alleviating mesh constraints: model reduction, parallel time integration and high resolution homogenization, Computer Methods in Applied Mechanics and Engineering, 197, 400, 10.1016/j.cma.2007.07.022 Chinesta, 2009, Proper generalized decomposition in extreme simulations: towards a change of paradigm in computational mechanics?, IACM Expressions, 26/09, 2 Chinesta, 2010, Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models, Archives of Computational Methods in Engineering, 17, 327, 10.1007/s11831-010-9049-y L. Cordier, M. Bergmann, Réduction dynamique par décomposition orthogonale aux valeurs propres (POD). OCET, 2006. Cottereau, 2009, Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method, Computational Mechanics, 44, 533, 10.1007/s00466-009-0388-1 Golub, 1996 Grepl, 2005, A posteriori error bounds for reduced-basis approximation of parametrized parabolic partial differential equations, ESAIM-Mathematical Modelling and Numerical Analysis (M2AN), 39, 157, 10.1051/m2an:2005006 Gunzburger, 2007, Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data, Computer Methods in Applied Mechanics and Engineering, 196, 1030, 10.1016/j.cma.2006.08.004 Jolliffe, 1986 Karhunen, 1946, Zur spektraltheorie stochastisher prozesse, Annales Academiae Scientiarum Fennicae Series, 34 Krysl, 2001, Dimensional model reduction in nonlinear finite element dynamics of solids and structures, International Journal for Numerical Methods in Engineering, 51, 479, 10.1002/nme.167 Kunish, 2001, Galerkin proper orthogonal decomposition methods for parabolic problems, Numerische Mathematik, 90, 148 Ladevèze, 1989, The large time increment method for the analysis of structures with nonlinear constitutive relation described by internal variables, Comptes Rendus Académie des Sciences, Paris, 309, 1095 Ladevèze, 1998 Ladevèze, 2008, Strict upper error bounds for calculated outputs of interest in computational structural mechanics, Computational Mechanics, 42, 271, 10.1007/s00466-007-0201-y Ladevèze, 1983, Error estimate procedure in the finite element method and application, SIAM Journal of Numerical Analysis, 20, 485, 10.1137/0720033 Ladevèze, 1992, Accuracy and optimal meshes in finite element computation for nearly incompressible materials, Computer Methods in Applied Mechanics and Engineering, 94, 303, 10.1016/0045-7825(92)90057-Q Ladevèze, 1996, A general method for recovering equilibrating element tractions, Computer Methods in Applied Mechanics and Engineering, 137, 111, 10.1016/S0045-7825(96)01067-5 Ladevèze, 2004 Ladevèze, 2009, The LATIN multiscale computational method and the proper generalized decomposition, Computer Methods in Applied Mechanics and Engineering, 199, 1287, 10.1016/j.cma.2009.06.023 Ladevèze, 2010, A new non-intrusive technique for the construction of admissible stress fields in model verification, Computer Methods in Applied Mechanics and Engineering, 199, 766, 10.1016/j.cma.2009.11.007 Ladevèze, 2010, Calculation of strict error bounds for finite element approximations of non-linear pointwise quantities of interest, International Journal for Numerical Methods in Engineering, 84, 1638, 10.1002/nme.2957 Néron, 2010, Proper generalized decomposition for multiscale and multiphysics problems, Archives of Computational Methods in Engineering, 17, 351, 10.1007/s11831-010-9053-2 Nouy, 2007, A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations, Computer Methods in Applied Mechanics and Engineering, 196, 4521, 10.1016/j.cma.2007.05.016 Nouy, 2008, Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms, Computer Methods in Applied Mechanics and Engineering, 197, 4718, 10.1016/j.cma.2008.06.012 Nouy, 2010, A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations, Computer Methods in Applied Mechanics and Engineering, 199, 1603, 10.1016/j.cma.2010.01.009 Nouy, 2004, Multiscale computational strategy with time and space homogenization: a radial-type approximation technique for solving microproblems, International Journal for Multiscale Computational Engineering, 2, 557, 10.1615/IntJMultCompEng.v2.i4.40 Pares, 2006, Subdomain-based flux-free a posteriori error estimators, Computer Methods in Applied Mechanics and Engineering, 195, 297, 10.1016/j.cma.2004.06.047 Passieux, 2010, A scalable time–space multiscale domain decomposition method: adaptive time scales separation, Computational Mechanics, 46, 621, 10.1007/s00466-010-0504-2 Pled, 2010, On the techniques for constructing admissible stress fields in model verification: performances on engineering examples, International Journal for Numerical Methods in Engineering Rovas, 2006, Reduced-basis output bound methods for parabolic problems, IMA Journal of Numerical Analysis, 26, 423, 10.1093/imanum/dri044 Ryckelynck, 2005, A priori hyperreduction method: an adaptive approach, Journal of Computational Physics, 202, 346, 10.1016/j.jcp.2004.07.015 F. Schmidt, N. Pirc, M. Mongeau, F. Chinesta, Efficient mold danscooling optimization by using model reduction, Technical Report, University of Toulouse, 2010.