Mat-1.3656 Seminar on
numerical analysis and computational science
Monday, September 7, 2009, room
U322 at 14.15, Eirola & Stenberg
Toni Lassila, TKK Mat
Reduced basis method for parametric PDEs in computational fluid and structural mechanics problems
Computational
mechanics problems are often modelled using PDEs with one or more free
parameters. These parameters can be either physical, such as material
constants, or geometric, such as dimensions or even shape parameters.
There is typically an engineering interest in computing outputs of the
model for different parameter values for purposes of sensitivity
analysis, optimization, shape design etc. The outputs are assumed to be
linear functionals of the field solution. The objective is to compute
efficiently and reliably the outputs of the model for many different
parameter values in a real-time or repeated evaluation context.
Since
solving repeatedly the full finite element problem turns out to be too
costly in many cases, a reduced basis method was proposed in the 1980's
to approximate the finite element solution. This method is based on the
use of "snapshot" solutions of the PDE at well-chosen parameter points
as global basis functions, followed by standard Galerkin projection. We
introduce some basic concepts of reduced basis methods and their a
posteriori error estimates. Some examples of reduced basis computations
for computational mechanics problems in haemodynamics and aerodynamic
design are presented.