[petsc-users] petsc4py: parallel matrix-vector multiplication

[Dave May]

On Sun, 6 May 2018 at 10:40, Robert Speck <r.speck at fz-juelich.de> wrote:

> Hi!
>
> I would like to do a matrix-vector multiplication (besides using linear
> solvers and so on) with petsc4py. I took the matrix from this example
>
(https://bitbucket.org/petsc/petsc4py/src/master/demo/kspsolve/petsc-mat.py)


This example only produces a matrix. And from the code the matrix produced
is identical in serial or parallel.



> and applied it to a PETSc Vector. All works well in serial, but in
> parallel (in particular if ordering becomes relevant) the resulting
> vector looks very different.


Given this, the way you defined the x vector in y = A x must be different
when run on 1 versus N mpi ranks.


Using the shell matrix of this example
> (
> https://bitbucket.org/petsc/petsc4py/src/master/demo/poisson2d/poisson2d.py
> )
> helps, but then I cannot use matrix-based preconditioners for KSP
> directly (right?). I also tried using DMDA for creating vectors and
> matrix and for taking care of their ordering (which seems to be my
> problem here), but that did not help either.
>
> So, my question is this: How do I do easy parallel matrix-vector
> multiplication with petsc4py in a way that allows me to use parallel
> linear solvers etc. later on? I want to deal with spatial decomposition
> as little as possible.


What's the context - are you solving a PDE?

Assuming you are using your own grid object (e.g. as you might have if
solving a PDE), and assuming you are not solving a 1D problem, you actually
have to "deal" with the spatial decomposition otherwise performance could
be quite terrible - even for something simple like a 5 point Laplacian on a
structured grid in 2D

What data structures should I use? DMDA or
> PETSc.Vec() and PETSc.Mat() or something else?


The mat vec product is not causing you a problem. Your issue appears to be
that you do not have a way to label entries in a vector in a consistent
manner.

What's the objective? Are you solving a PDE? If yes, structured grid? If
yes again, use the DMDA. It takes care of all the local-to-global and
global-to-local mapping you need.

Thanks,
  Dave


>
> Thanks!
> -Robert-
>
> --
> Dr. Robert Speck
> Juelich Supercomputing Centre
> Institute for Advanced Simulation
> Forschungszentrum Juelich GmbH
> 52425 Juelich, Germany
>
> Tel: +49 2461 61 1644
> Fax: +49 2461 61 6656
>
> Email:   r.speck at fz-juelich.de
> Website: http://www.fz-juelich.de/ias/jsc/speck_r
> PinT:    http://www.fz-juelich.de/ias/jsc/pint
>
>
>
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