Sambit,

I am trying to move all parallel triangulation nodes by a constant 
> displacement, but that breaks the periodic face pairs match when I 
> call GridTools::collect_periodic_faces(...). I use the following code for 
> the mesh movement. The dftPtr->triangulation has periodicity constraints 
> using add_periodicity(...). 
>
What exactly do you mean by "that breaks the periodic face pairs match"? 
What is the error you are observing?
Can you provide us with a minimal example that shows the problem so we can 
check?

Best,
Daniel

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