Pasha,

[...]
> It works fine when using one CPU, however, the mesh is not consistent for 
> a parallel run with more CPUs. How and where I can use 
> Triangulation::communicate_locally_moved_vertices() to solve this issue?
>
You would use Triangulation::communicate_locally_moved_vertices [1] 
directly after your move_mesh function.
Since you are moving all vertices, you can use the return value 
of GridTools::get_locally_owned_vertices [2] as argument for 
Triangulation::communicate_locally_moved_vertices.
Otherwise, an entry of vertex_locally_moved should only be true if the 
vertex is locally owned and moved.
 
Best, Daniel

[1] 
https://www.dealii.org/8.4.0/doxygen/deal.II/classparallel_1_1distributed_1_1Triangulation_3_011_00_01spacedim_01_4.html#a6654e33ba281946895a7a6aa5adec231
 
[2] 
https://www.dealii.org/8.4.0/doxygen/deal.II/namespaceGridTools.html#a33b3f1dcc53c868171f1bb0a3793a96e

>
> Thank you,
> Pasha
>

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