A PETSc parallel-in-time solver based on MGRIT algorithm

We address the development of a modular implementation of the MGRIT (MultiGrid-In-Time) algorithm to solve linear and nonlinear systems that arise from the discretization of evolutionary models with a parallel-in-time approach in the context of the PETSc (the Portable, Extensible Toolkit for Scientific computing) library. Our aim is to give the opportunity of predicting the performance gain achievable when using the MGRIT approach instead of the Time Stepping integrator (TS). To this end, we analyze the performance parameters of the algorithm that provide a-priori the best number of processing elements and grid levels to use to address the scaling of MGRIT, regarded as a parallel iterative algorithm proceeding along the time dimension