[petsc-users] Grid Partitioning with ParMetis
Mohammad Mirzadeh
mirzadeh at gmail.com
Fri Jul 29 00:11:55 CDT 2011
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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