Exposé :

Tony Lelievre, Cermics, Ecole des Ponts ParisTech

Recent results on the reduced basis methods and the greedy algorithms for high-dimensional partial differential equations

Résumé

We will present recent works concerning two numerical methods to solve high-dimensional partial differential equations: greedy algorithms and reduced basis techniques. Concerning greedy algorithms, we will essentially present convergence results for PDEs and eigenvalue problems. Concerning reduced basis techniques, we will focus on improvements to the standard approach in order to make the method less intrusive and more precise, together with some applications to solve aeroacoustic problems.

These are joint works with E. Cancès, F. Casenave, V. Ehrlacher and A. Ern.