Parallelization of Dependent Iterations in Scientific Computing by the Parareal-in-Time Algorithm

A new field of application by a prominent timeparallel technique, the ‘parareal-in-time’ algorithm, is explored with the perturbative description. The parareal algorithm introduced by Lions, et al. [J. Lions, Y. Maday, and G. Turinici, C. R. Acad. Sci., Ser. I 332, 661–668 (2001)] has been applied to parallelization of time evolutions and is usually implemented by coarsening the width of timesteps. In this contribution, another description based on the concept of perturbation is introduced for this algorithm. It turns out that the new description is more general and suitable for scientific applications, where all kinds of dependent iterations are within the range of applicable calculations. Several examples of the parallel implementations are shown to be feasible for the forthcoming post-peta era.