Most operations in Afivo loop over a number of boxes, for example the leaves at a certain refinement level. All such loops have been parallelized by adding OpenMP statements around them, for example as shown below:

!$omp parallel private(lvl, i, id)
do lvl = 1, tree%highest_lvl
   !$omp do
   do i = 1, size(tree%lvls(lvl)%leaves)
      id = tree%lvls(lvl)%leaves(i)
      call my_procedure(tree%boxes(id))
   end do
   !$omp end do
end do
!$omp end parallel

The parallel speedup that one can get depends on the cost of the algorithm that one is using. The communication cost (updating ghost cells) is always about the same, so that an expensive algorithm will show a better speedup. Furthermore, on a shared memory system, it is not unlikely for an algorithm to be memory-bound instead of CPU-bound. An example of the scaling can be found