[petsc-users] Grid Partitioning with ParMetis
Matthew Knepley
knepley at gmail.com
Fri Jul 29 00:01:04 CDT 2011
On Fri, Jul 29, 2011 at 4:52 AM, Mohammad Mirzadeh <mirzadeh at gmail.com>wrote:
> Thank you Matt. Indeed I have looked into p4est and also Dendro. p4est uses
> parallel octrees/quadtrees but for what I intend to do I only need to
> distribute a single tree that is created in serial among processors.
> I definitely like to have the tree data-structure in parallel but that would
> be another project. I also looked into Dendro and they kind of follow the
> same strategy. i.e every single processor has a local copy of the whole
> tree. What they do differently, however, is they somehow manage to use DA
> instead of a general unstructured numbering which is quite interesting but I
> still don't know how they do it. Unfortunately, they do not handle (as far
> as I understood from their manual) non-graded trees which are the ones I
> work with.
>
> So, all I need to do is to somehow distribute my grid among processors and
> since each one has a local copy of data-structure I could get around the
> problem. Just anotehr question. If the partitioning is not unique, do you at
> least get a better numbering than the tree you start with?
>
You should, which is why I suggested that you are not giving the input you
think you are.
Matt
> Mohammad
>
>
> On Thu, Jul 28, 2011 at 9:25 PM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> On Fri, Jul 29, 2011 at 3:49 AM, Mohammad Mirzadeh <mirzadeh at gmail.com>wrote:
>>
>>> Hi all,
>>>
>>> I am trying to write a code to do parallel computation on quadtree
>>> adaptive grids and to do so , I need to distribute the grid in parallel. I
>>> have selected a general unstructured framework for telling PETSc about my
>>> node numbering. An example of such grid is schematically shown below.
>>>
>>
>> 0) If you are doing this, I think you should at least look at the p4est
>> package before proceeding.
>>
>>
>>>
>>> 1 16 7 3
>>> +---------------+---------------+------------------------------+
>>> | | | |
>>> | | | |
>>> |14 | 15 | 17 |
>>> +---------------+---------------+ |
>>> | | | |
>>> | | | |
>>> | 4 | 12 | 6 |8
>>> +---------------+---------------+------------------------------+
>>> | | | |
>>> | | | |
>>> | 9 | 11 | 13 |
>>> +---------------+---------------+ |
>>> | | | |
>>> | | | |
>>> | 0 | 10 |5 | 2
>>> +---------------+---------------+------------------------------+
>>>
>>>
>>> To distribute this in parallel I am using the ParMetis interface via MatPartitioning object and I follow(more or less) the example in $PETSC_DIR/src/dm/ao/examples/tutorials/ex2.c; To make the initial distribution, I choose nodal based partitioning by creating the adjacency matrix, for which I create ia and ja arrays accordingly. once the grid is processed and the new orderings are generated, I follow all required steps to generate the AO needed to map between PETSc ordering and the new global numbering and this is the result:
>>>
>>>
>>> Number of elements in ordering 18
>>> PETSc->App App->PETSc
>>> 0 9 0 1
>>> 1 0 1 3
>>> 2 10 2 4
>>> 3 1 3 7
>>> 4 2 4 12
>>> 5 11 5 14
>>> 6 12 6 15
>>> 7 3 7 16
>>> 8 13 8 17
>>> 9 14 9 0
>>> 10 15 10 2
>>> 11 16 11 5
>>> 12 4 12 6
>>> 13 17 13 8
>>> 14 5 14 9
>>> 15 6 15 10
>>> 16 7 16 11
>>> 17 8 17 13
>>>
>>> Now I have two questions/concerns:
>>>
>>> 1) Do processors always have the nodes in contiguous chunks of PETSc
>>> ordering? i.e 0-8 on rank 0 and 9-17 on rank 1 ? If so, this particular
>>> ordering does not seem to be "good" for this grid since it seems to cross
>>> too many edges in the graph (here 13 edges) and by just looking at the graph
>>> I can(at least) think of a better distribution with only 6 edge cuts. (if
>>> you are wondering how, having {0,9,4,14,1,10,11,12,15} on rank 0 and rest on
>>> rank 1).
>>>
>>
>> Yes, the PETSc ordering is always contiguous. Perhaps you are not
>> providing the graph you think you are for partitioning.
>>
>>
>>> 2) Isn't it true that the final distribution should be independent of
>>> initial grid numbering? When I try the same grid but with the following
>>> (hand-generated) numbering:
>>>
>>> 14 15 16 17
>>> +---------------+---------------+------------------------------+
>>> | | | |
>>> | | | |
>>> |11 | 12 | 13 |
>>> +---------------+---------------+ |
>>> | | | |
>>> | | | |
>>> | 7 | 8 | 9 |10
>>> +---------------+---------------+------------------------------+
>>> | | | |
>>> | | | |
>>> | 4 | 5 | 6 |
>>> +---------------+---------------+ |
>>> | | | |
>>> | | | |
>>> | 0 | 1 |2 | 3
>>> +---------------+---------------+------------------------------+
>>>
>>> I get the following AO:
>>>
>>> Number of elements in ordering 18
>>> PETSc->App App->PETSc
>>> 0 9 0 9
>>> 1 10 1 10
>>> 2 11 2 11
>>> 3 12 3 12
>>> 4 13 4 13
>>> 5 14 5 14
>>> 6 15 6 15
>>> 7 16 7 16
>>> 8 17 8 17
>>> 9 0 9 0
>>> 10 1 10 1
>>> 11 2 11 2
>>> 12 3 12 3
>>> 13 4 13 4
>>> 14 5 14 5
>>> 15 6 15 6
>>> 16 7 16 7
>>> 17 8 17 8
>>>
>>>
>>> which is simply the initial ordering with a change in the order in which
>>> processors handle nodes. Could it be that the partitioning is not unique
>>> and each time the algorithm only tries to obtain the "best" possible
>>> ordering depending on the initial distribution? If so, how should I know
>>> what ordering to start with?
>>>
>>
>> Yes, ParMetis does not provide a unique "best" ordering, which is at least
>> NP-complete if not worse.
>>
>> Matt
>>
>>
>>> I am really confused and would appreciate if someone could provide some
>>> insights.
>>>
>>> Thanks,
>>> Mohammad
>>>
>>
>>
>>
>> --
>> 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
>>
>
>
--
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
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