Parallel-in-time Parareal implementation using PETSc

This work presents implementation details of the Parareal method using PETSc in a distributed and multicore architecture, which is used for the resolution of a parabolic optimal control problem. To this end, this optimization problem is discretized yielding a large KKT linear system. In the context of this work, the Parareal method allows not only to reach problem sizes which normally can not be solved using a single computer, but also allows to speed up the computational resolution time. The implementation developed in this work offers a parallelization relative efficiency for the strong scaling of approximately 70% each time the processes count doubles, while for the weak scaling it is 75 % each time the processes count doubles for a constant solution size per process and 96% each time the processes count doubles for a constant data size per process.