| Abstract: |
| Several numerical schemes have been proposed to speed-up the time propagation of evolution equations, among which the parareal algorithm. It is based on a decomposition of the time interval into subintervals, and on a predictor-corrector strategy, where the propagations over each subinterval for the corrector stage are concurrently performed on the different processors that are available.
This method has been shown to perform well in many situations. The next step is to use it for problems with geometrical structure, such as Hamiltonian dynamics, where symplectic schemes are needed. Since the plain parareal iterations do not give rise to a symplectic scheme, several proposals have been put forward to correct for this drawback. After a short review of previous works, we present in this talk our new approach, together with theoretical and numerical evidence supporting it.
Joint work with Y. Maday (Paris 6) and G. Turinici (Paris 9). |
|