[petsc-users] DMPlex Interpolation

Sun Aug 28 16:35:55 CDT 2022

Thank you for the reply.

I think it can be more helpful for me if the attached sample code
(DMInterpolation_Mod.tar) could be checked by you. If you run the sample
code, basically, you would get "VertexField_Map_from_Cell.vtu" file which
displays a solution vector field defined on each vertex, which is mapped
from another solution field defined on each cell-centroid. The vertex
solution field in the vtu file should match with "x-coordinate" value in
the same file. Basically, the attached code tries to reproduce vertex's
x-coordinate value using cell-centroid's x-coordinate value by means of
finite-element space mapping between Q0 and Q1.
>From the vtu file, it is obvious that at the physical boundaries (left,
right, top, and bottom) x-coordinate value is not properly mapped from
cell-centroid, whereas interior vertex's solution seems okay. What I do not
understand is why the boundary vertices cannot have properly mapped
coordinate values? I believe I am doing something wrong and I was
suspicious about the ghost cell, which I do not have. But your comment
seems to say that the problem is not related to the ghost cell. What am I
doing wrong?

Does your section mark these unknowns as constrained?
--> Yes, as shown in the code, I defined one section for each dmplex, one
for vertex and one for cell, respectively, with 1-dof for each (See code
line from 91 to 124).

You should not get 0 unless you constrained these variables in the section.
If not, you should see it use the constant values in the cell.
--> Yes, you are correct. Now I do not have zero value at the physical
boundaries, however, it is still not proper value and seems underscaled,
compared to the proper answer (i.e., compared with the properly mapped
interior values).

Thanks,

> On Sun, Aug 28, 2022 at 12:11 PM Mike Michell <mi.mike1021 at gmail.com>
> wrote:
>
>> Thank you for the reply.
>>
>> *I cannot quite understand. Are you saying that you have inhomogeneous
>> Dirichlet conditions on the boundary, and a 0 guess in the interior, and
>> you get all zeros from interpolation? Yes, we have no way of getting
>> boundary values into the operator. You could conceivably make an operator
>> that mapped between local vectors, but it is hard to see why you would want
>> this. In the solver, we usually  just care about the unknowns we are
>> solving for. Did I understand your question, or is it about something else?*
>> --> It is not imposing a physical boundary condition (Dirichlet condition
>> for example), but my solver needs to import an external solution vector
>> field resolved to each cell-centroid, then I need to map it to a vertex
>> field in which my solver is resolved for solving governing equations. Then,
>> my code solves its equations. After my solver is done solving the
>> equations, the vertex field should be re-map into cell-field and then push
>> back the cell field to the external code. With this context, I have zero
>> values returned at the vertices on the physical boundaries
>>
>
> Does your section mark these unknowns as constrained?
>
>
>> if I try mapping from cell-center to vertex field without having ghost
>> cell layers inside physical boundaries. For interior vertices, I get
>> reasonable mapped values, although the mapping accuracy seems to be able to
>> be improved as I mentioned in the earlier email.
>>
>
> As I replied, I think this is not true.
>
>
>> If dmplex for cell-center field would be defined to have ghost cell
>> layer, and fill it (it meant import ghost cell values as well from the
>> external code), and map it to vertex-field, can it be possible to fill
>> vertex points on the physical boundaries?
>>
>
> You should not get 0 unless you constrained these variables in the
> section. If not, you should see it use the constant values in the cell.
>
>   Thanks,
>
>      Matt
>
>
>> I was trying to test this strategy, but it
>> seems DMPlexComputeCellGeometryFVM() gives NaN values if dmplex has ghost
>> cell by calling DMPlexConstructGhostCells(). In detail,
>> DMPlexComputeCellGeometryFVM() gives zero area for each cell, and returns
>> NaN values for cell centroids and normals for the ghost cells.
>>
>> Thanks,
>>
>>
>>> On Sun, Aug 28, 2022 at 8:51 AM Mike Michell <mi.mike1021 at gmail.com>
>>> wrote:
>>>
>>>> Hi, thank you for the reply.
>>>>
>>>> I was able to manage mapping from cell-center to vertex. Basically, in
>>>> Fortran, it seems DMCreateInterpolation() requires the optional scaling
>>>> vector as a mandatory argument, which is strange.
>>>>
>>>
>>> It needs a custom Fortran wrapper to check for the NULL input from
>>> Fortran.
>>>
>>>
>>>> My dmplex has zero overlap layer over the procs, and there is no ghost
>>>> cell inside physical boundary. In this case, it seems mapping between cell
>>>> center to vertex returns zero (in case the global cell vector initialized
>>>> to zero) value at the nodes, which are located at physical boundary. To
>>>> manage this problem, is it mandatory to have ghost cells. Is this correct
>>>> understanding?
>>>>
>>>
>>> I cannot quite understand. Are you saying that you have inhomogeneous
>>> Dirichlet conditions on the boundary, and a 0 guess in the interior, and
>>> you get all zeros from interpolation? Yes, we have no way of getting
>>> boundary values into the operator. You could conceivably make an operator
>>> that mapped between local vectors, but it is hard to see why you would want
>>> this. In the solver, we usually  just care about the unknowns we are
>>> solving for.
>>>
>>> Did I understand your question, or is it about something else?
>>>
>>>
>>>> Also, my mapping accuracy itself seems to be improved. For simple test,
>>>> cell-center's x-coordinate value of each cell mapped to node and printed to
>>>> the vertex field as .vtu format, and the mapped x-vertex-coordinate is
>>>> quite different with the actual nodal coordinate values what PETSc
>>>> intrinsically provides through DMGetCoordinatesLocal(). I believe I am
>>>> doing something wrong, probably arguments in PetscFECreateLagrange() can
>>>> improve the mapping accuracy in finite-element space?
>>>>
>>>
>>> Yes, a cellwise field is much less accurate than a linear field. Pushing
>>> the values up to a linear field does not make them more accurate.
>>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>>
>>>> Thanks,
>>>>
>>>>
>>>>> On Thu, Aug 25, 2022 at 7:12 PM Mike Michell <mi.mike1021 at gmail.com>
>>>>> wrote:
>>>>>
>>>>>> Hi, this is a duplication of
>>>>>>
>>>>>> https://lists.mcs.anl.gov/pipermail/petsc-users/2022-August/046746.html
>>>>>>
>>>>>> for in-depth question.
>>>>>>
>>>>>> I wrote a short code as attached to test interpolation between two
>>>>>> DMPlex objects. Goal is to map solution field defined on
>>>>>> cell-centroid(DMPlex-1) into vertex(DMPlex-2) field or vice versa.
>>>>>>
>>>>>> Basically, DMCreateInterpolation() fails in the example code and it
>>>>>> was not allowed to get useful error messages. The DMPlex is created by
>>>>>> loading a 2D square box in Gmsh. Can I get some comments on that?
>>>>>>
>>>>>
>>>>> Sure, I am looking at it.
>>>>>
>>>>>   Thanks,
>>>>>
>>>>>      Matt
>>>>>
>>>>>
>>>>>> Thanks,
>>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> 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/>
>>>>>
>>>>
>>>
>>> --
>>> 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/>
>>>
>>
>
> --
> 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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