It seems, that we should think about, if it is a problem of the initial condition, so because of the use of multiple processes, the random numbers applied vary on the domain. Then it would not be a bug of the solver or a problem with overlap at all. If one changes the term in the main file in line 174 to:
sol[n] = double(n%2)/10.0;
then the initial conditions are the same. This is totally different for a value of 7 instead of 2. We should find a way, that ensures that initial conditions are the same no matter if mpi is used or not, maybe via a loadsolution.