Franco,
 

> [...]
> As I didn't find a 1:1 correspondence between the two namespaces, I've 
> resorted to remove Trilinos classes as best as I could, for instance, 
> TrilinosWrappers::BlockSparseMatrix exists but in PETSc there is only 
> PETScWrappers::MPI::BlockSparseMatrix that I know of. And the two seem to 
> be not exactly equivalent.
>

step-40 tries to allow switching between Trilinos and PETSc as easy as 
possible by using the deal.II/lac/generic_linear_algebra.h header and the 
defining the LA::MPI namespace.
 

> [...]
> std::shared_ptr<PETScWrappers::PreconditionILU> Amg_preconditioner;
>
 
This looks inappropriate. Probably it should rather be 
PETScWrappers::PreconditionBoomerAMG;

Best,
Daniel

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