Speaker Affiliation :
Date(s) - 18/02/2020
11 h 00 min - 12 h 00 min
Joackim BERNIER (Institut de Mathématiques de Toulouse)
I will present some general tools to factorize semigroups generated by inhomogeneous quadratic differential operators as product of more elementary semigroups. On the one hand, I will explain how such a factorization can be used to characterize geometrically the regularizing effects of these semigroups. On the other hand, from a numerical point of view, we will see how it can be used to get some efficient and accurate splitting methods. I will highlight the efficiency of these new methods on the examples of the magnetic Schrödinger equations with harmonic potentials and some Fokker-Planck equations. This talk will rely on some joint works with Paul Alphonse, Nicolas Crouseilles, Fernando Casas and Yingzhe Li.