The initial guess of the original system is already used in the RHS creation. To stay consistent, i.e. using the solution as initial guess results in immediate convergence, the initial guess for the constraint system has to be set to zero.

this requires an MPI all-to-all communication, not sure if that could be handled otherwise

before this was O(#neighbour_id * (#local_id + log(#neighbor_id)), now it should be O(#local_id + #neighbor_id)