Section: New Results

Application of greedy algorithms

Participants : Sébastien Boyaval, Eric Cancès, Virginie Ehrlacher, Tony Lelièvre.

Model reduction techniques are very important tools for applications. They consist in deriving from a high-dimensional problem, a low-dimensional model, which gives very quickly reliable results. We are in particular interested in two techniques: Proper Generalized Decomposition (greedy algorithms) and Reduced Basis techniques.

Concerning the Proper Generalized Decomposition, current research concerns the approximation of high-dimensional spectral problems, see [38] . Prototypical applications include electronic structure calculations or the computation of buckling modes in mechanics. We also explored in the PhD of J. Infante Acevedo the application of these techniques to option pricing problems, see [45] .

Finally, in [40] , Fabien Casenave (CERMICS), Alexandre Ern (CERMICS), Guillaume Sylvand (EADS IW) and Tony Lelièvre propose a new non intrusive implementation of the reduced basis technique using the Empirical Interpolation Method. The interest if the method is illustrated on aeroacoustic problems.