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

[Matthew Knepley]

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://github.com/firedrakeproject/firedrake/issues/982> as it pertains
> to Firedrake but I think this is more an issue at the PETSc level.
>
> This code
> <https://gist.github.com/danshapero/a140daaf951ba58c48285ec29f5973cc>
> 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/ <http://www.cse.buffalo.edu/~knepley/>
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