[petsc-users] Grid Partitioning with ParMetis
Mohammad Mirzadeh
mirzadeh at gmail.com
Fri Jul 29 14:52:33 CDT 2011
Matt,
Is ParMetis implementation in PETSc only done via
$PETSC_DIR/src/mat/partition/impls/pmetis/pmetis.c ? I am wondering if PETSc
has interface to ParMETIS_V3_RefineKway function as noted in ParMetis
manual?
Thanks,
Mohammad
On Thu, Jul 28, 2011 at 10:11 PM, Mohammad Mirzadeh <mirzadeh at gmail.com>wrote:
> I see. Thanks for the help Matt
>
>
> On Thu, Jul 28, 2011 at 10:01 PM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> 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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