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

[Jed Brown]

Robert Speck <r.speck at fz-juelich.de> writes:

> Thanks for your reply and help. Yes, this is going to be a PDE solver
> for structured grids. The first goal would be IDC (or Crank-Nicholson)
> for the heat equation, which would require both solving a linear system
> and application of the matrix.
>
> The code I wrote for testing parallel matrix-vector multiplication can
> be found here:
> https://github.com/Parallel-in-Time/pySDC/blob/petsc/pySDC/playgrounds/PETSc/playground_matmult.py
>
> Both vectors and matrix come from the DMDA, but I guess filling them is
> done in a wrong way? Or do I need to convert global/natural vectors to
> local ones somewhere?

Global and Natural are not the same (see user's manual for details).
The matrix acts on a Global vector.  See
petsc4py/demo/bratu3d/bratu3d.py for examples of efficiently setting
values (and computing residuals) using Global vectors.  It should be
simpler/cleaner code than you currently have.

>
> Best
> -Robert-
>
>
>
> On 06.05.18 14:44, Dave May wrote:
>> On Sun, 6 May 2018 at 10:40, Robert Speck <r.speck at fz-juelich.de
>> <mailto: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 <mailto: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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>
> -- 
> 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