[petsc-users] Parallel Graph Coloring

[Peter Brune]

On Tue, Nov 5, 2013 at 11:07 AM, Gaetan Kenway <gaetank at gmail.com> wrote:

> Hi Peter
>
> Thanks for the info. I actually already have a coloring that is done
> through the discretrization that is near optimal. The issue is that I have
> a funny interprocessor dependence that is tricky to do my own sequential
> coloring. So I was looking at doing it in a global, parallel sense. For
> interest, I tried using the matGetColor() on my assembled matrix just to
> see how many colors it would take. My discretrization coloring has 35
> colors (for a stencil with 33 cells) and the matGetColor() resulted in
> approximately 78 colors or about twice as many.
>

Jacobian coloring requires a column, or distance-2 coloring of the matrix.
 The distance-2 colorings we get from the serial algorithms aren't that
bad, so I suspect that you might be doing a 1-coloring from your mesh; I
assume that you mean that your residual/Jacobian stencil has 33 entries
rather than some distance-2 thing?  How did the problems with your coloring
manifest themselves?

- Peter


>
> Thanks,
>
> Gaetan
>
>
> On Tue, Nov 5, 2013 at 11:39 AM, Peter Brune <brune at mcs.anl.gov> wrote:
>
>>
>>
>>
>> On Tue, Nov 5, 2013 at 10:29 AM, Gaetan Kenway <gaetank at gmail.com> wrote:
>>
>>> Hi
>>>
>>> I have a quick question regarding the MatGetColoring() function.
>>> According to the documentation,
>>>
>>>  "For parallel matrices currently converts to sequential matrix and uses
>>> the sequential coloring on that."
>>>
>>>
>> The meaning of this is that it transfers the parallel matrix to a single
>> processor and does the coloring there, not that it only considers
>> on-processor entries.  What comes out is therefore a valid column coloring
>> of the whole matrix.  Parallel matrix coloring is in development but is not
>> quite ready for public consumption.  Anecdotal evidence suggests that the
>> serial coloring does not become a bottleneck on small parallel runs.
>>
>> A good option is to provide the coloring through your discretization.
>>  This will often be more efficient than the matrix colorings, as you know
>> the structure of your problem.
>>
>> - Peter
>>
>>
>>> I am wondering does this give actually give a valid parallel coloring?
>>> My application is a cell centered multi-block finite volume code, (with
>>> block-based decomposition)  and the communications are done using a two
>>> level exchange of halo cells. I would like to use FD (actually forward mode
>>> AD to compute the jacbian matrix). So, what I'm wondering is, if a cell
>>> with color 0 is perturbed on processor 0, is it guaranteed that a residual
>>> on processor 1, that is influenced by the 0-colored cell on proc zero is
>>> *only* influenced by the color 0 from proc 0 and not a 0-colored cell on
>>> proc 1?
>>>
>>> I hope that is clear
>>>
>>> Thank you,
>>>
>>> Gaetan Kenway
>>>
>>>
>>>
>>>
>>>
>>>
>>
>
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