Mapping between vertex DoF indices in serial and fully distributed Triangulation

[James Shi]

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