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