Praveen,

I solve a PDE in serial and save the solution to file.
>
Do you mean that your triangulation is not a 
parallel::distributed::Triangulation or that you are simply running with 
one process?
 

> Is there a way to now read this solution into a 
> TrilinosWrappers::MPI::Vector object ?
>
If you already save the solution from a TrilinosWrappers::MPI::Vector 
object, then parallel::distributed::SolutionTransfer should work for you as 
well.
Note that you are allowed to choose the number of processes when reading 
different from the number of processes you used for writing.
If your original vector is not a TrilinosWrappers::MPI::Vector object, how 
did you write the vector to a file?

Best,
Daniel

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