Orateur
Description
Reduced basis methods (RBM) is part of model reduction methods which
are used more and more in the industrial framework for rapid numerical
simulations without a loss of the accuracy. They can be considered as an
additional feature for a more classical simulation tool based on e.g.
finite element or finite volume, since the reduced basis is constructed
from these classical tools. One drawback of these approaches is the fact
that their (offline/online) implementation is intrusive, in the sense
that some elementary RBM bricks of the approximation needs to be
assembled offline from the original code and this requires to modify
lines in the code. Non Intrusive versions are thus interesting if the
user does not want or has not the possibility to "enter" in the original
code. The two-grid process which is a "Non Intrusive Reduced Basis"
(NIRB) method combines the concept of reduced basis methods by
postprocessing a coarse classical approximation. The online part, which
is computed in a short time, proposes a second approximation that is as
accurate as the solution that would have been obtained by using the
reference code on a very fine grid (but without computing it). This
method will first be presented and various follow up results will be
explained both from a theoretical point of view and illustrated
numerically. These results underline that retrieving the fine mesh
accuracy without computing on the fine mesh is possible in a non
intrusive way.
