lundi 17 janvier 15h30

Title: Parametric Model Reduction - Another Instance of
-----    Multiparametric Function Approximation

by: 
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Peter Benner, Max Planck Institute for Dynamics of Complex
Technical Systems

Abstract:
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Model reduction has become an ubiquitous tool in simulation and
control for dynamical systems arising in various engineering
disciplines.  Often, models of physical processes contain parameters
describing material properties and geometry variations, or arising from
changing boundary conditions.  For purposes of design and
optimization, it is often desirable to preserve these parameters as
symbolic quantities in the reduced-order model (ROM).  This allows the
re-use of the ROM after changing the parameter so that the repeated
computation of reduced-order models can be avoided.  Significant
savings in simulation times for full parameter sweeps or within
optimization algorithms can be achieved this way.

In this talk, we study several approaches for computing ROMs for
linear parametric systems.  Parameter dependencies can be linear,
polynomial, or nonlinear in general.  In any case, frequency domain
representations lead to the task of approximating multiparametric,
possibly matrix-valued, functions that are rational with respect to
the one complex parameter representing frequency and may be nonlinear
with respect to the real (design) parameters.

We study methods based on multi-moment matching.  We provide an
interpretation of these methods as rational interpolation methods and
combine them with optimal H_2 model reduction.  A further approach
based on a combination of balanced truncation and sparse grid
interpolation will also be discussed. Numerical results illustrate the
performance of all the methods under consideration.