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

Thu Jan 12 20:10:38 CST 2023

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.

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
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>
> https://www.math.mcmaster.ca/bourdin | +1 (905) 525 9140 ext. 27243
>
>
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