The parareal in time iterative solver: A further direction to parallel implementation

Abstract

This paper is the basic one of the series resulting from the minisymposium entitled "Recent Advances for the Parareal in Time Algorithm" that was held at DD15. The parareal in time algorithm is presented in its current version (predictor-corrector) and the combination of this new algorithm with other more classical iterative solvers for parallelization which makes it possible to really consider the time direction as fertile ground to reduce the time integration costs.