Dear deal.II developers,

I have a question regarding fully distributed Triangulations.

I start with a *Triangulation<dim> *on each rank, and partition it using 
*TriangulationDescription::Utilities::create_description_from_triangulation()* 
to 
construct a *parallel::fullydistributed::Triangulation<dim>* across 
multiple MPI ranks.

On the serial Triangulation, I compute some data associated with vertex 
DoFs (i.e., for a Q1 or P1 element, one DoF per vertex), using full mesh 
information. I would now like to transfer this data to the fully 
distributed Triangulation. However, I’ve found that the global indices of 
the same vertices differ between the serial and distributed meshes.

I have tried matching vertices using their Point<dim> coordinates, but I 
would prefer a more robust or built-in solution if available.

Is there a recommended way to obtain or construct a mapping between the 
vertex (or DoF) indices in the serial Triangulation and those in the fully 
distributed Triangulation?

Any suggestions would be greatly appreciated.

Best regards,
James

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