[petsc-users] coordinate degrees of freedom for 2nd-order gmsh mesh

[Jed Brown]

It's confusing, but this line makes high order simplices always read as discontinuous coordinate spaces. I would love if someone would revisit that, perhaps also using DMPlexSetIsoperiodicFaceSF(), which should simplify the code and avoid the confusing cell coordinates pattern. Sadly, I don't have time to dive in.

https://gitlab.com/petsc/petsc/-/commit/066ea43f7f75752f012be6cd06b6107ebe84cc6d#3616cad8148970af5b97293c49492ff893e25b59_1552_1724

"Daniel R. Shapero" <shapero at uw.edu> writes:

> Sorry either your mail system or mine prevented me from attaching the file,
> so I put it on pastebin:
> https://pastebin.com/awFpc1Js
>
> On Wed, Jan 11, 2023 at 4:54 PM Matthew Knepley <knepley at gmail.com> wrote:
>
>> Can you send the .msh file? I still have not installed Gmsh :)
>>
>>   Thanks,
>>
>>      Matt
>>
>> On Wed, Jan 11, 2023 at 2:43 PM Daniel R. Shapero <shapero at uw.edu> wrote:
>>
>>> Hi all -- I'm trying to read in 2nd-order / piecewise quadratic meshes
>>> that are generated by gmsh and I don't understand how the coordinates are
>>> stored in the plex. I've been discussing this with Matt Knepley here
>>> <https://urldefense.com/v3/__https://github.com/firedrakeproject/firedrake/issues/982__;!!K-Hz7m0Vt54!hL9WLR51ieyHFZx8N9AjhDwJCRpvmQto9CL1XOTkkAxFfUbtsabHuBDOATnWyP6lQszhA2gOStva7A$>
>>> as it pertains to Firedrake but I think this is more an issue at the PETSc
>>> level.
>>>
>>> This code
>>> <https://urldefense.com/v3/__https://gist.github.com/danshapero/a140daaf951ba58c48285ec29f5973cc__;!!K-Hz7m0Vt54!hL9WLR51ieyHFZx8N9AjhDwJCRpvmQto9CL1XOTkkAxFfUbtsabHuBDOATnWyP6lQszhA2hho2eD1g$>
>>> uses gmsh to generate a 2nd-order mesh of the unit disk, read it into a
>>> DMPlex, print out the number of cells in each depth stratum, and finally
>>> print a view of the coordinate DM's section. The resulting mesh has 64
>>> triangles, 104 edges, and 41 vertices. For 2nd-order meshes, I'd expected
>>> there to be 2 degrees of freedom at each node and 2 at each edge. The
>>> output is:
>>>
>>> ```
>>> Depth strata: [(64, 105), (105, 209), (0, 64)]
>>>
>>> PetscSection Object: 1 MPI process
>>>   type not yet set
>>> 1 fields
>>>   field 0 with 2 components
>>> Process 0:
>>>   (   0) dim 12 offset   0
>>>   (   1) dim 12 offset  12
>>>   (   2) dim 12 offset  24
>>> ...
>>>   (  62) dim 12 offset 744
>>>   (  63) dim 12 offset 756
>>>   (  64) dim  0 offset 768
>>>   (  65) dim  0 offset 768
>>> ...
>>>   ( 207) dim  0 offset 768
>>>   ( 208) dim  0 offset 768
>>>   PetscSectionSym Object: 1 MPI process
>>>     type: label
>>>     Label 'depth'
>>>     Symmetry for stratum value 0 (0 dofs per point): no symmetries
>>>     Symmetry for stratum value 1 (0 dofs per point): no symmetries
>>>     Symmetry for stratum value 2 (12 dofs per point):
>>>       Orientation range: [-3, 3)
>>>     Symmetry for stratum value -1 (0 dofs per point): no symmetries
>>> ```
>>>
>>> The output suggests that there are 12 degrees of freedom in each
>>> triangle. That would mean the coordinate field is discontinuous across cell
>>> boundaries. Can someone explain what's going on? I tried reading the .msh
>>> file but it's totally inscrutable to me. I'm happy to RTFSC if someone
>>> points me in the right direction. Matt tells me that the coordinate field
>>> should only be discontinuous if the mesh is periodic, but this mesh
>>> shouldn't be periodic.
>>>
>>
>>
>> --
>> 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/
>> <https://urldefense.com/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!K-Hz7m0Vt54!hL9WLR51ieyHFZx8N9AjhDwJCRpvmQto9CL1XOTkkAxFfUbtsabHuBDOATnWyP6lQszhA2go23tjRg$>
>>