Hi folks,

I'm wondering if there's somewhere I can look to get a broad overview of 
the different parallelization schemes available in deal.II for various 
pieces of the library, and maybe what people's experiences have been. As I 
understand it, any matrix/vector assembly can be done with a 
shared-parallel scheme with the threads framework, but I'm less sure about 
solvers (which are typically the bottleneck in my applications). To relay 
my understanding so far (and ask some specific questions):

Matrix-based AMG methods:

   - PETSc and Trilinos Epetra only use MPI distributed parallelism
   - Trilinos Tpetra with MueLu is hybrid, but requires Kokkos. Do the 
   Tpetra wrappers have associated solvers? And how do they work with Kokkos 
   via CUDA?

Matrix-based GMG methods:

   - Use deal.II's own distributed vector, and wraps a regular deal.II 
   solver (although perhaps uses a Trilinos smoother). Are any of the solvers 
   hybrid-parallelized? And are there deal.II-specific smoothers to avoid 
   copying to Epetra vectors?

Matrix-free GMG methods:

   - Use deal.II's distributed vector and wrap regular solver. 
   Additionally, the matrix multiplication is done via a matrix-free operator. 
   Is it possible (or easy) to write a custom matrix-free operator which takes 
   advantage of shared parallelism? And will the solver take advantage of 
   shared-memory parallelism when (say) adding vectors?

Matrix-free GMG methods with hp-adaptivity:

   - The only example that I've seen is step-75, and that uses Trilinos AMG 
   for the coarse solver, which I think is limited to MPI distributed 
   parallelism. Could the coarse solver be adapted to use shared parallelism, 
   and are the other aspects of this solver able to be parallelized?

As a final question: which of these aspects are eligible for handling by 
CUDA, MPI-3.0 shared memory, and Kokkos? And have folks found a significant 
speed-up by implementing any of these tools in their code?

Thanks so much for any insight,
Lucas

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