Hi,

I want to compare different implementations of multigrid solvers for Nvidia 
GPUs using the poisson problem (starting from ksp tutorial example ex45.c).
Therefore I am trying to get runtime results comparable to hpgmg-cuda 
(finite-volume), i.e. using multiple warmup and measurement solves and avoiding 
measuring setup time.
For now I am using -log_view with added stages:

PetscLogStageRegister("Solve Bench", &solve_bench_stage);
  for (int i = 0; i < BENCH_SOLVES; i++) {
    PetscCall(KSPSetComputeInitialGuess(ksp, ComputeInitialGuess, NULL)); // 
reset x
    PetscCall(KSPSetUp(ksp)); // try to avoid setup overhead during solve
    PetscCall(PetscDeviceContextSynchronize(dctx)); // make sure that 
everything is done

    PetscLogStagePush(solve_bench_stage);
    PetscCall(KSPSolve(ksp, NULL, NULL));
    PetscLogStagePop();
  }

This snippet is preceded by a similar loop for warmup.

When profiling this using Nsight Systems, I see that the very first solve is 
much slower which mostly correspods to H2D (host to device) copies and e.g. 
cuBLAS setup (maybe also paging overheads as mentioned in the docs, but 
probably insignificant in this case). The following solves have some overhead 
at the start from a H2D copy of a vector (the RHS I guess, as the copy is 
preceeded by a matrix-vector product) in the first MatResidual call (callchain: 
KSPSolve->MatResidual->VecAYPX->VecCUDACopyTo->cudaMemcpyAsync). My 
interpretation of the profiling results (i.e. cuBLAS calls) is that that vector 
is overwritten with the residual in Daxpy and therefore has to be copied again 
for the next iteration.

Is there an elegant way of avoiding that H2D copy? I have seen some examples on 
constructing matrices directly on the GPU, but nothing about vectors. Any 
further tips for benchmarking (vs profiling) PETSc solvers? At the moment I am 
using jacobi as smoother, but I would like to have a CUDA implementation of SOR 
instead. Is there a good way of achieving that, e.g. using PCHYPREs boomeramg 
with a single level and "SOR/Jacobi"-smoother  as smoother in PCMG? Or is the 
overhead from constantly switching between PETSc and hypre too big?

Thanks,
Paul

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