Dear Bruno,
Thanks, that definitely answers my questions.
I would have a final slightly related question. 
Would I see significant performance gain for a GMRES + ILU preconditioning 
setup by going from AztecOO to the Tpetra or Belos stack?
I guess that the best parallel performance increase I could get would be by 
using the AMG from ML, but I think this will require some experiments 
before I can set-up the parameters correctly. My system is not elliptic and 
can be quite ugly at times due to stabilization.

Thank you for everything.

On Monday, 4 March 2019 09:03:24 UTC-5, Bruno Turcksin wrote:
>
> Le lun. 4 mars 2019 à 08:44, Bruno Blais <blais...@gmail.com <javascript:>> 
> a écrit : 
> > I'm using the wrapper, so I guess by default that means it is using the 
> AztecOO stack of solvers? 
>
> Yes, that's right. You won't get any speedup using OpenMP with 
> AztecOO, you need to switch to the Tpetra stack and Belos to use 
> OpenMP (but we don't have wrappers for the all Tpetra stack) 
>
> >>   2) Why do you think that OpenMP would be faster than MPI? MPI is 
> usually faster than OpenMP unless you are very careful about your data 
> management. 
> > My original idea was that since in shared memory parallelism you could 
> precondition a larger chunk of the matrix as a whole, that the ILU 
> preconditioning would be more efficient in a shared-memory context than in 
> a distributed one. Thus you would need less GMRES iterations to solve > 
> your system. It seems I am wrong :) ? 
>
> Using larger blocks for ILU preconditioning will decrease the number 
> of GMRES iterations but you will spend more time in ILU, so it's hard 
> to say if it's worth it. 
>
> Best, 
>
> Bruno 
>

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