Parallel-in-time algorithms and long-time integration

Parallel-in-time algorithms and long-time integration

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Claude Le Bris, University of Minnesota
Fine Hall 224

We investigate some issues related to the integration of Hamiltonian systems when using integrators that are parallel in time (the so-called class of parareal integrators, introduced by JL Lions, Y. Maday and G. Turinici in C. R. Acad. Sci., Paris, Sér. I, Math. 332, No.7, 661-668 (2001)). We show that, when appropriately adjusted, this original class of integrators enjoy excellent properties of conservation over long times. We present some elements of numerical analysis that explain the numerical observations. We also present a possible symmetrized version of such algorithms, with similar, agreeable properties. This is joint work with Yvon Maday (University Paris 6) and Frederic Legoll (Ecole des Ponts).