PETSc-dev has some support for running portions of the computation on Nvidia GPUs. See installation. Html for how to install PETSc to use GPUs.
PETSc has a Vec class VECCUSP that performs almost all the vector operations on the GPU. The Mat class MATCUSP performs matrix-vector products on the GPU but does not have matrix assembly on the GPU yet. Both of these classes run in parallel with MPI.
All KPS methods, except KSPIBCGS, run all their vector operations on the GPU thus, for example Jacobi preconditioned Krylov methods run completely on the GPU. Preconditioners are a problem, we could do with some help for these. The example src/snes/examples/tutorials/ex47cu.cu demonstates how the nonlinear function evaluation can be done on the GPU.
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