Doctoral courses on Model Reduction in
Transcription
Doctoral courses on Model Reduction in
D OCTORAL COURSES ON M ODEL R EDUCTION IN NONLINEAR DYNAMICS OF FLUIDS AND STRUCTURES Planning Registration (free) : [email protected], Confirmed spearkers : R. Abgrall (Univerisité de Zurich), F. Daim (ESI group), L. Blanc (EC Lyon), J. Fehr (Stuttgart University), A. Hamdouni (Université de La Rochelle), Y. Maday (Paris VI), D. Néron (ENS Cachan), O. Thomas (ENSAM), D. Ryckelynck (MINES ParisTech), J. Salomon (Université de Paris Dauphine). Program Jour Monday 25th january 9:00-10:30 10:45-12:15 14:00-15:30 15:45-17:15 POD for parametric partial differential equations Proper Generalized Decomposition POD in fluid mechanics (A. Hamdouni) (D. Néron) (D.Amsallem, J. Salomon) Tuesday 26th january Wednesday 27th january Empirical Interpolation Methods Hyper-reduction in mechanics of materials (Y. Maday) (D. Ryckelynck) Reduced variational inequalities Recent advances in model reduction for nonlinear vibrations. (J. Salomon) Geometrical methods Gappy POD and GNAT methods (A. Hamdouni) (D. Amsallem D. Ryckelyncl) Nonlinear normal modes in vibration Numerical exercices (J. Salomon) (O. Thomas) (L. Blanc) Thursday 28th january Error estimation and adaptivity (D. Ryckelynck) Hyper-reduction for crash simulations (F. Daim) Model reduction in flexible multibody dynamics Web applications (J. Bellec) (J. Fehr) Friday 29th january Reduced-basis interpolation (D. Amsallem D. Ryckelynck) Recent advances in model reduction for fluid dynamics. (R. Abgrall) Réduction de modèle en mécanique non linéaire 3-7 février 2014 Réduction d’ordre de modèles 2/3 Motivations Reduced basis methods 1 2 are particularly attractive to use in order to diminish the number of degrees of freedom associated with the numerical approximation to a set of partial differential equations ; the computational complexity can be reduced to a level where potentially very complex systems can be simulated, or where highly repetitive use of the underlying model becomes feasible, e.g., for design, optimization and real time control. The main idea is to construct basis functions with a large information content in order to reduce the number of basis coefficients needed to reach a certain level of accuracy in the outputs of interest. All physical parameters are preserved by model reduction methods. 1. B.O. Almroth, P. Stern, and F.A. Brogan, “Automatic choice of global shape functions in structural analysis,” AIAA J., 16, 525–528, 1978. 2. Noor, A. K., and Peters, J. M. (1980). Reduced basis technique for nonlinear analysis of structures. AIAA J. 18(4), 455–462. Réduction de modèle en mécanique non linéaire 3-7 février 2014 Réduction d’ordre de modèles 3/3