Dear Rajat,

After the mesh partitioning is done, in a 
parallel::distributed::Triangulation the local meshes are independent of 
each other. In particular, moving a vertex on one process does not change 
anything for all the other processes.
Therefore, it is necessary to move the vertices of a given face on all 
processes that have a cell that has this face as it is done in step-42.

Of course, there is as well 
parallel::distributed::communicate_locally_moved_vertices[1] to synchronize 
changes in vertex positions if you don't keep track of this yourself.

Best,
Daniel

[1] 
https://www.dealii.org/8.4.0/doxygen/deal.II/classparallel_1_1distributed_1_1Triangulation.html#a247598f1323a9f847832e60d6c840469

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