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

Matthew Knepley knepley at gmail.com
Thu Jan 12 20:14:34 CST 2023 

On Thu, Jan 12, 2023 at 4:10 PM Dave May <dave.mayhem23 at gmail.com> wrote:

> On Thu 12. Jan 2023 at 17:58, Blaise Bourdin <bourdin at mcmaster.ca> wrote:
>
>> Out of curiosity, what is the rationale for _reading_ high order gmsh
>> meshes?
>>
>
> GMSH can use a CAD engine like OpenCascade. This provides geometric
> representations via things like BSplines. Such geometric representation are
> not exposed to the users application code, nor are they embedded in any
> mesh format GMSH emits. The next best thing is to use a high order
> representation of the mesh geometry and project the CAD geometry (say a
> BSpline) into this higher order function space. The projection of the
> geometry is a quantity that can be described with the .msh format.
>

Note that PETSc can directly read CAD files now and mesh over them.


> Is it so that one can write data back in native gmsh format?
>>
>
> No.
>
> Cheers,
> Dave
>
>>
>
>
>
>> Regards,
>> Blaise
>>
>>
>> On Jan 12, 2023, at 7:13 PM, Matthew Knepley <knepley at gmail.com> wrote:
>>
>> On Thu, Jan 12, 2023 at 1:33 PM Jed Brown <jed at jedbrown.org> wrote:
>>
>>> 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(),
>>
>>
>> Perhaps as a switch, but there is no way I am getting rid of the current
>> periodicity. As we have discussed before, breaking the topological relation
>> is a non-starter for me.
>>
>> It does look like higher order Gmsh does read as DG. We can just project
>> that to CG for non-periodic stuff.
>>
>>   Thanks,
>>
>>     Matt
>>
>> 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$
>>> >
>>> >>
>>>
>>
>>
>> --
>> 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/>
>>
>>
>> —
>> Canada Research Chair in Mathematical and Computational Aspects of Solid
>> Mechanics (Tier 1)
>> Professor, Department of Mathematics & Statistics
>> Hamilton Hall room 409A, McMaster University
>> 1280 Main Street West, Hamilton,
>> <https://www.google.com/maps/search/1280+Main+Street+West,+Hamilton,+Ontario+L8S+4K1,+Canada?entry=gmail&source=g>
>>  Ontario L8S 4K1, Canada
>> <https://www.google.com/maps/search/1280+Main+Street+West,+Hamilton,+Ontario+L8S+4K1,+Canada?entry=gmail&source=g>
>>
>> https://www.math.mcmaster.ca/bourdin | +1 (905) 525 9140 ext. 27243
>>
>>

-- 
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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