It looks like data parallel and SPMD solutions for the grid solver problem do not need steps the 3 and 6 in this slide (passing updated cells to other processors) - it is because the first two solutions are all modifying the same global grid (workers/threads can share the same memory space). Meanwhile, in the message-passing solution, threads operate within their own address space and do not update the same grid, thus step 3 and 6 are neccessary to communicate updated new cell values to threads that need them for next round's calculation.

In steps 3 and 6, processors need data that other processors computed in the previous stage. Looking at these stages in particular, blocked assignment requires much less data to be communicated between processors than interleaved assignment.