Massimo,

we are intending to add Tpetra support in deal.II but this is not yet 
available.
Currently, CUDA can be used through cuSPARSE 
wrappers(https://www.dealii.org/9.0.0/doxygen/deal.II/classCUDAWrappers_1_1SparseMatrix.html,
https://www.dealii.org/9.0.0/doxygen/deal.II/classLinearAlgebra_1_1CUDAWrappers_1_1Vector.html)
or using matrix-free methods 
(https://www.dealii.org/9.0.0/doxygen/deal.II/classCUDAWrappers_1_1MatrixFree.html).
The latter one also supports MPI (using 
https://www.dealii.org/developer/doxygen/deal.II/classLinearAlgebra_1_1distributed_1_1Vector.html
with MemorySpace::CUDA).

Best,
Daniel

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