论文信息 - Robust control of PGD-based numerical simulations

Robust control of PGD-based numerical simulations

In this paper, we develop an error estimator that enables to control effectively the quality of numerical solutions obtained using proper generalised decomposition. The method is based on the Constitutive Relation Error and the construction of associated admissible fields. It takes all error sources (discretisations, truncation of the modal representation, etc.) into account and can be used, introducing adjoint-based techniques, for goal-oriented error estimation. Furthermore, specific indicators can be derived to split error contributions and thus drive adaptive procedures in an optimal manner.

Pierre Ladevèze | Ludovic Chamoin | P. Ladevèze | L. Chamoin

[1] P. Ladevèze. Nonlinear Computational Structural Mechanics: New Approaches and Non-Incremental Methods of Calculation , 1998 .

[2] Pierre Ladevèze,et al. Strict upper error bounds on computed outputs of interest in computational structural mechanics , 2008 .

[3] Pierre Ladevèze,et al. On the verification of model reduction methods based on the proper generalized decomposition , 2011 .

[4] Pedro Díez,et al. An error estimator for separated representations of highly multidimensional models , 2010 .

[5] Pierre Ladevèze,et al. Error Estimate Procedure in the Finite Element Method and Applications , 1983 .

[6] Francisco Chinesta,et al. Recent Advances and New Challenges in the Use of the Proper Generalized Decomposition for Solving Multidimensional Models , 2010 .

[7] A. Nouy. A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations , 2010 .

[8] Pierre Ladevèze,et al. New advances on a posteriori error on constitutive relation in f.e. analysis , 1997 .

[9] Pierre Ladevèze,et al. Mastering Calculations in Linear and Nonlinear Mechanics , 2004 .

[10] Pierre Ladevèze,et al. Calculation of strict error bounds for finite element approximations of non‐linear pointwise quantities of interest , 2010 .

[11] P. Ladevèze,et al. The LATIN multiscale computational method and the Proper Generalized Decomposition , 2010 .