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In this paper, we are concerned with the micro-macro Parareal algorithm forthe simulation of initial-value problems. In this algorithm, a coarse (fast)solver is applied sequentially over the time domain, and a fine(time-consuming) solver is applied as a corrector in parallel over smallerchunks of the time interval. Moreover, the coarse solver acts on a reducedstate variable, which is coupled to the fine state variable through appropriatecoupling operators. We first provide a contribution to the convergence analysisof the micro-macro Parareal method for multiscale linear ordinary differentialequations (ODEs). Then, we extend a variant of the micro-macro Pararealalgorithm for scalar stochastic differential equations (SDEs) tohigher-dimensional SDEs.

Micro-macro Parareal, from ODEs to SDEs and back again