[petsc-users] Element connectivity of a DMPlex

Tue Jun 17 12:42:15 CDT 2025

On Tue, Jun 17, 2025 at 12:43 PM Noam T. <dontbugthedevs at proton.me> wrote:

> Thank you.  For now, I am dealing with vertices only.
>
> Perhaps I did not explain myself properly, or I misunderstood your
> response.
> What I meant to say is, given an element of order higher than one, the
> connectivity matrix I obtain this way only contains as many entries as the
> first order element: 3 for a triangle, 4 for a tetrahedron, etc.
>
> Looking at the closure of any cell in the mesh, this is also the
> case.However, the nodes are definitely present; e.g. from
>
> DMPlexGetCellCoordinates(dm, cell, NULL, nc, NULL, NULL)
>
> nc returns the expected value (12 for a 2nd order 6-node planar triangle,
> 30 for a 2nd order 10-node tetrahedron, etc).
>
> The question is, are the indices of these extra nodes obtainable in a
> similar way as with the code shared before? So that one can have e.g.  [0,
> 1, 2, 3, 4, 5] for a second order triangle, not just [0, 1, 2].
>

I am having a hard time understanding what you are after. I think this is
because many FEM approaches confuse topology with analysis.

The Plex stores topology, and you can retrieve adjacencies between any two
mesh points.

The PetscSection maps mesh points (cells, faces, edges , vertices) to sets
of dofs. This is how higher order elements are implemented. Thus, we do not
have to change topology to get different function spaces.

The intended interface is for you to call DMPlexVecGetClosure() to get the
closure of a cell (or face, or edge). You can also call
DMPlexGetClosureIndices(), but index wrangling is what I intended to
eliminate.

What exactly are you looking for here?

  Thanks,

      Matt

> Thank you.
> Noam
> On Friday, June 13th, 2025 at 3:05 PM, Matthew Knepley <knepley at gmail.com>
> wrote:
>
> On Thu, Jun 12, 2025 at 4:26 PM Noam T. <dontbugthedevs at proton.me> wrote:
>
>>
>> Thank you for the code; it provides exactly what I was looking for.
>>
>> Following up on this matter, does this method not work for higher order
>> elements? For example, using an 8-node quadrilateral, exporting to a
>> PETSC_VIEWER_HDF5_VIZ viewer provides the correct matrix of node
>> coordinates in geometry/vertices
>>
>
> If you wanted to include edges/faces, you could do it. First, you would
> need to decide how you would number things For example, would you number
> all points contiguously, or separately number cells, vertices, faces and
> edges. Second, you would check for faces/edges in the closure loop. Right
> now, we only check for vertices.
>
> I would say that this is what convinced me not to do FEM this way.
>
> Thanks,
>
> Matt
>
>> (here a quadrilateral in [0, 10])
>> 5.0, 5.0
>> 0.0, 0.0
>> 10.0, 0.0
>> 10.0, 10.0
>> 0.0, 10.0
>> 5.0, 0.0
>> 10.0, 5.0
>> 5.0, 10.0
>> 0.0, 5.0
>>
>> but the connectivity in viz/topology is
>>
>> 0 1 2 3
>>
>> which are likely the corner nodes of the initial, first-order element,
>> before adding extra nodes for the higher degree element.
>>
>> This connectivity values [0, 1, 2, 3, ...] are always the same, including
>> for other elements, whereas the coordinates are correct
>>
>> E.g. for 3rd order triangle in [0, 1], coordinates are given left to
>> right, bottom to top
>> 0, 0
>> 1/3, 0,
>> 2/3, 0,
>> 1, 0
>> 0, 1/3
>> 1/3, 1/3
>> 2/3, 1/3
>> 0, 2/3,
>> 1/3, 2/3
>> 0, 1
>>
>> but the connectivity (viz/topology/cells) is [0, 1, 2].
>>
>> Test meshes were created with gmsh from the python API, using
>> gmsh.option.setNumber("Mesh.ElementOrder", n), for n = 1, 2, 3, ...
>>
>> Thank you.
>> Noam
>> On Friday, May 23rd, 2025 at 12:56 AM, Matthew Knepley <knepley at gmail.com>
>> wrote:
>>
>> On Thu, May 22, 2025 at 12:25 PM Noam T. <dontbugthedevs at proton.me>
>> wrote:
>>
>>> Hello,
>>>
>>> Thank you the various options.
>>>
>>> Use case here would be obtaining the exact output generated by option
>>> 1), DMView() with PETSC_VIEWER_HDF5_VIZ; in particular, the matrix
>>> generated under /viz/topology/cells.
>>>
>>> There are several ways you might do this. It helps to know what you are
>>> aiming for.
>>>
>>> 1) If you just want this output, it might be easier to just DMView()
>>> with the PETSC_VIEWER_HDF5_VIZ format, since that just outputs the
>>> cell-vertex topology and coordinates
>>>
>>>
>>> Is it possible to get this information in memory, onto a Mat, Vec or
>>> some other Int array object directly? it would be handy to have it in order
>>> to manipulate it and/or save it to a different format/file. Saving to an
>>> HDF5 and loading it again seems redundant.
>>>
>>>
>>> 2) You can call DMPlexUninterpolate() to produce a mesh with just cells
>>> and vertices, and output it in any format.
>>>
>>> 3) If you want it in memory, but still with global indices (I don't
>>> understand this use case), then you can use DMPlexCreatePointNumbering()
>>> for an overall global numbering, or DMPlexCreateCellNumbering() and
>>> DMPlexCreateVertexNumbering() for separate global numberings.
>>>
>>>
>>> Perhaps I missed it, but getting the connectivity matrix in
>>> /viz/topology/cells/ did not seem directly trivial to me from the list of
>>> global indices returned by DMPlexGetCell/Point/VertexNumbering() (i.e. I
>>> assume all the operations done when calling DMView()).
>>>
>>
>> Something like
>>
>> DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
>> DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
>> DMPlexGetVertexNumbering(dm, &globalVertexNumbers);
>> ISGetIndices(globalVertexNumbers, &gv);
>> for (PetscInt c = cStart; c < cEnd; ++c) {
>> PetscInt *closure = NULL;
>>
>> DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &Ncl, &closure);
>> for (PetscInt cl = 0; c < Ncl * 2; cl += 2) {
>> if (closure[cl] < vStart || closure[cl] >= vEnd) continue;
>> const PetscInt v = gv[closure[cl]] < 0 ? -(gv[closure[cl]] + 1) :
>> gv[closure[cl]];
>>
>> // Do something with v
>> }
>> DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &Ncl, &closure);
>> }
>> ISRestoreIndices(globalVertexNumbers, &gv);
>> ISDestroy(&globalVertexNumbers);
>>
>> Thanks,
>>
>> Matt
>>
>> Thanks,
>>> Noam.
>>>
>>
>>
>> --
>> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!buGhhRYyQDY3kig5GA6tIzeIOCoCAtlZzIz_UTAH1bZ-05GXENI3VZos9r4s6fXhktg7wUl--lMKoG-FNuUV$ 
>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!buGhhRYyQDY3kig5GA6tIzeIOCoCAtlZzIz_UTAH1bZ-05GXENI3VZos9r4s6fXhktg7wUl--lMKoHYcPmhy$ >
>>
>>
>>
>
> --
> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!buGhhRYyQDY3kig5GA6tIzeIOCoCAtlZzIz_UTAH1bZ-05GXENI3VZos9r4s6fXhktg7wUl--lMKoG-FNuUV$ 
> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!buGhhRYyQDY3kig5GA6tIzeIOCoCAtlZzIz_UTAH1bZ-05GXENI3VZos9r4s6fXhktg7wUl--lMKoHYcPmhy$ >
>
>
>

-- 
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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!buGhhRYyQDY3kig5GA6tIzeIOCoCAtlZzIz_UTAH1bZ-05GXENI3VZos9r4s6fXhktg7wUl--lMKoG-FNuUV$  <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!buGhhRYyQDY3kig5GA6tIzeIOCoCAtlZzIz_UTAH1bZ-05GXENI3VZos9r4s6fXhktg7wUl--lMKoHYcPmhy$ >
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