[petsc-users] On unknown ordering

[Matthew Knepley]

On Thu, Nov 15, 2018 at 5:49 AM Appel, Thibaut via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Good morning,
>
> I would like to ask about the importance of the initial choice of ordering
> the unknowns when feeding a matrix to PETSc.
>
> I have a regular grid, using high-order finite differences and I simply
> divide rows of the matrix with PetscSplitOwnership using vertex major,
> natural ordering for the parallelism (not using DMDA)
>
> My understanding is that when using LU-MUMPS, this does not matter because
> either serial or parallel analysis is performed and all the rows are
> reordered ‘optimally’ before the LU factorization. Quality of reordering
> might suffer from parallel analysis.
>
> But if I use the default block Jacobi with ILU with one block per
> processor, the initial ordering seems to have an influence because some
> tightly coupled degrees of freedom might lay on different processes and the
> ILU becomes less powerful. You can change the ordering on each block but
> this won’t necessarily make things better.
>

Yes.


> Are my observations accurate? Is there a recommended ordering type for a
> block Jacobi approach in my case? Could I expect natural improvements in
> fill-in or better GMRES robustness opting for parallelism offered by DMDA?
>

For fill-in, I think yes. The impact of ordering on Krylov methods is
complicated, so I have no idea here.

  Thanks,

     Matt


> Thank you,
>
> Thibaut
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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