Jeudi 23 mars 2017 à 10h (Salle de séminaire du CERMICS)
Ulrich Hetmaniuk (University of Washington)
Reduced-order models (ROMs) have received lots of attention for
simulating dynamical systems at a reduced cost. Numerical simulations
have highlighted the efficiency of model-order reduction for many
applications. When a dimension reduction occurs, estimating the
approximation error between the full-order model and the
reduced-order model solutions is a natural question to address.
This talk will present theoretical results on a priori and a posteriori error estimations and numerical experiments for selecting snapshots adaptively. In particular error bounds for the semi-discrete wave equation will be derived in the continuous setting (when the whole trajectory is known) and in the discrete setting when the Newmark average-acceleration scheme is used on the second-order semi-discrete equation. An a posteriori error indicator for linear time-invariant dynamical systems will be proposed in terms of a Krylov-based exponential integrator and an a posteriori residual-based estimate. An adaptive selection of snapshots will be presented for simulating incompressible Navier-Stokes flows over a range of physical parameters.