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__Parallel-in-time integrators for Hamiltonian systems__

F. Legoll, X. Dai, C. LeBris and Y. Maday

**Abstract**

In this talk, we will describe some recent advances for the integration of Hamiltonian systems using parareal-type algorithms. In this specific context, structure-preserving algorithms are preferably employed, because they show interesting numerical properties, in particular excellent preservation of the total energy of the system. We will describe here several structure-preserving variants of the original plain parareal algorithm. Numerical tests on several model systems illustrate the properties of the proposed algorithms over long integration times.
This is joint work with X. Dai (Univ. Paris 6 and Chinese Academy of Sciences), C. Le Bris (ENPC and INRIA) and Y. Maday (Univ. Paris 6 and Brown Univ.).

**Bibliography**

[1]
X. Dai, C. Le Bris, F. Legoll and Y. Maday, Symmetric parareal algorithms for Hamiltonian systems, Mathematical Modelling and Numerical Analysis, 47 (2013), pp. 717-742.