Modelling parareal convergence in 2D drift wave plasma turbulence

Abstract

Parareal [1] is a recent time parallelization algorithm based on a predictor-corrector scheme. On the predictor stage, a fast coarse solver gives an approximate solution for all the simulation time. On the correction stage, the fine solver is used for correcting the result. The process is iterated until convergence. A successful application of parareal to an specific problem depend strongly on finding a good coarse solver. In particular, the algorithm has been successfully applied by some of the authors to fully developed two dimensional drift wave plasma turbulence [2]. Here we study the convergence of the parareal for that turbulence case from a physical point of view [3]. As a second stage, it is built a framework for studying the convergence. The framework is strongly based on the physics of the problem, and aims to generalize the knowledge to other problems. The final objective is to help on the process of finding an adequate coarse solver for similar problems or give new ideas for other cases.