[petsc-users] DMPlexCreateFromDAG for P2 elements

[Matthew Knepley]

On Wed, Oct 9, 2019 at 9:59 AM Asitav Mishra <asitav at gmail.com> wrote:

> Matt,
>
> Please excuse me for not having stated it clearly. Of course, ultimately
> residuals/Jacobians are what I'd need to evaluate using higher-order nodes.
> I just meant my first concern is to create a mesh graph structure that can
> be appropriately partitioned (and hopefully re-distributed) among multiple
> processors without losing the higher order topological information of the
> geometry, such as those in curved (higher-order) elements.
>

Okay, that is clear.

So its turns out there is no topological difference between low order and
high order geometry (that is actually
that point, a teacup and a donut are topologically equivalent). As Stefano
says, you need to treat the coordinates
as just another field. Sp exactly as if you were making a solution field,
you create the coordinate field you want.
Then that coordinate field should be able to be input to the DM using

  DMGetCoordinateDM(dm, &cdm);
  <Set field information into cdm instead of dm>
 DMCreateLocalVector(cdm, &coordinatesLocal);
 <Fill in higher order coordinate values>
 DMSetCoordinatesLocal(dm, coordinatesLocal);

You will probably use a DMProject*(cdm, ...) to fill in the coordinate
values.

This has not been extensively tested. I will look for the example I have of
this.

  Thanks,

     Matt


> Thanks,
> Asitav
>
> On Wed, Oct 9, 2019 at 12:25 AM Matthew Knepley <knepley at gmail.com> wrote:
>
>> On Tue, Oct 8, 2019 at 4:45 PM Asitav Mishra via petsc-users <
>> petsc-users at mcs.anl.gov> wrote:
>>
>>> Stefano,
>>>
>>> Thanks a lot for your prompt response. I have a higher-order mesh, so
>>> will need to create my own PetscSection to add the local coordinates looks
>>> like.
>>> At this point, FEM residuals and Jacobian computations are not as
>>> important. But, could you direct me to any examples in creating
>>> PetscSection for such elements?
>>>
>>
>> Asitav,
>>
>> What do you want to do with higher oder coordinate embeddings, if not
>> calculate residuals and Jacobians?
>> Are you absolutely certain that is what you need, since this is not
>> normally called P2.
>>
>>   Thanks,
>>
>>      Matt
>>
>>
>>> Thanks,
>>> Asitav
>>>
>>> On Tue, Oct 8, 2019 at 3:18 PM Stefano Zampini <
>>> stefano.zampini at gmail.com> wrote:
>>>
>>>> DMPlex abstracts the mesh topology. PetscSection defines the dofs
>>>> associated to the mesh entities.
>>>> Why do you need P2 elements? For the discrete solution or because you
>>>> have a high order mesh?
>>>>
>>>> If it is only for the solution, you should create a linear mesh
>>>> (cell-vertex only), interpolate the mesh, and then use
>>>> PetscFECreateDefault (
>>>> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/FE/PetscFECreateDefault.htm
>>>> )
>>>> +
>>>> DMAddField (
>>>> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/DMAddField.html
>>>> )
>>>> +
>>>> DMCreateDS (
>>>> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/DMCreateDS.html
>>>> )
>>>>
>>>> Instead, if you have a high-order mesh, you should create a linear
>>>> mesh, and then manipulate yourself the PetscSection defining the local
>>>> coordinates.
>>>> However, I’m not sure how complete is the support for high-order meshes
>>>> when it comes to compute FEM residuals and assemble Jacobians
>>>>
>>>>
>>>> On Oct 8, 2019, at 9:54 PM, Asitav Mishra via petsc-users <
>>>> petsc-users at mcs.anl.gov> wrote:
>>>>
>>>> Hi,
>>>>
>>>> Does Petsc support DMPlexCreateFromDAG for 2nd order (P2) elements, or
>>>> any orders higher than one (P1) for that matter? I know it is possible to
>>>> create DMPlex mesh from GMSH files with P2 elements, but not sure how the
>>>> 'cone/support' structures are built. One approach is to ignore the higher
>>>> order nodes in an element to create the 'cones', but is there a way to
>>>> preserve the P2 element information in the 'cones'?
>>>>
>>>> For example: how would the depth=1 cone structure look like for a mesh
>>>> with two P2 triangles sharing a face?
>>>>             2
>>>>           / | \
>>>>         /   |   \
>>>>      6     |     8
>>>>     /       |       \
>>>>   /         |         \
>>>> 0   0    5    1    3
>>>>   \         |         /
>>>>     \       |       /
>>>>      4     |     7
>>>>         \   |   /
>>>>           \ | /
>>>>            1
>>>>
>>>> Higher order nodes: [4, 5, 6, 7, 8]. Can we construct cones with
>>>> cells-to-nodes (depth = 1)?:
>>>>
>>>> numPoints = [9, 2];                                             // 9
>>>> nodes instead of just 4?
>>>> coneSizes = [6, 6,    0, 0, 0, 0, 0, 0, 0, 0, 0];
>>>> cones        = [0, 1, 2, 4, 5, 6,    2, 1, 3, 5, 7, 8];
>>>> etc.
>>>>
>>>> Any help would be greatly appreciated.
>>>>
>>>> Thanks,
>>>> Asitav
>>>>
>>>> --
>>>> Asitav Mishra, PhD
>>>> Research Engineer II, NIA
>>>>
>>>>
>>>>
>>>
>>> --
>>> Asitav Mishra, PhD
>>> Research Engineer II, NIA
>>>
>>
>>
>> --
>> 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
>>
>> https://www.cse.buffalo.edu/~knepley/
>> <http://www.cse.buffalo.edu/~knepley/>
>>
>
>
> --
> Asitav Mishra, PhD
> Research Engineer II, NIA
>


-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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