[petsc-users] orientation of DMPLEX for tetrehedral meshes

[Matthew Knepley]

On Thu, Jul 2, 2026 at 10:55 AM Matteo Semplice via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Dear PETSc,
>
>     I am a bit puzzled by the 3d tet mesh representations as DMPlex. I
> boiled it down to a mesh of a single tet. More specifically,
>
>    - if a I create the mesh as
>
>   const PetscInt dim=3;
>   const PetscInt numCells=1; // The number of cells, only on process 0
>   const PetscInt numVertices=4; // The number of vertices owned by this
> process, or PETSC_DECIDE, only on process 0
>   const PetscInt numCorners=4; // The number of vertices for each cell,
> only on process 0
>   const PetscBool interpolate=PETSC_TRUE; // should intermediate mesh
> entities (faces, edges) be created?
>   // An array of numCells×numCornersnumCells×numCorners numbers, the
> vertices for each cell, only on process 0
>   const PetscInt cells[] = {0,1,2,3 };
>   const PetscInt spaceDim=3; // The spatial dimension used for coordinates
>   // An array of numVertices×spaceDimnumVertices×spaceDim numbers, the
> coordinates of each vertex, only on process 0
>   const PetscReal vertexCoords[] = { 0,0,0,
>                                      1,0,0,
>                                      0,1,0,
>                                      0,0,1 };
>   PetscCall( DMPlexCreateFromCellListPetsc(MPI_COMM_WORLD, dim,
>              numCells, numVertices, numCorners, interpolate, cells,
>              spaceDim, vertexCoords, dmMesh) );
>
> I get the representation that I would expect:
>
> DM Object: Mesh 1 MPI process
>  type: plex
> Mesh in 3 dimensions:
>  Number of 0-cells per rank: 4
>  Number of 1-cells per rank: 6
>  Number of 2-cells per rank: 4
>  Number of 3-cells per rank: 1
> Labels:
>  celltype: 4 strata with value/size (0 (4), 1 (6), 3 (4), 6 (1))
>  depth: 4 strata with value/size (0 (4), 1 (6), 2 (4), 3 (1))
> Mesh with 1 cells
>
> with DMPlexGetCellCoordinates giving me the coordinates
>
> CELL 0 with vertices at
> ( 0.000,     0, 0.000 )
> ( 1.000,     0, 0.000 )
> ( 0.000,     1, 0.000 )
> ( 0.000,     0, 1.000 )
>
>
>    - on the other hand, if I load the MSH file
>
> $MeshFormat
> 2.2 0 8
> $EndMeshFormat
> $Nodes
> 4
> 1 0.0 0.0 0.0
> 2 1.0 0.0 0.0
> 3 0.0 1.0 0.0
> 4 0.0 0.0 1.0
> $EndNodes
> $Elements
> 1
> 1 4 2 0 1 1 2 3 4
> $EndElements
>
> with DMPlexCreateGmshFromFile, the first and second vertices are swapped
> and I get
>
> DM Object: Mesh 1 MPI process
>  type: plex
> Mesh in 3 dimensions:
>  Number of 0-cells per rank: 4
>  Number of 1-cells per rank: 6
>  Number of 2-cells per rank: 4
>  Number of 3-cells per rank: 1
> Labels:
>  celltype: 4 strata with value/size (0 (4), 1 (6), 3 (4), 6 (1))
>  depth: 4 strata with value/size (0 (4), 1 (6), 2 (4), 3 (1))
>  Cell Sets: 1 strata with value/size (0 (1))
> Mesh with 1 cells
>
> with DMPlexGetCellCoordinates giving me
>
> CELL 0 with vertices at
> ( 1.000,     0, 0.000 )
> ( 0.000,     0, 0.000 )
> ( 0.000,     1, 0.000 )
> ( 0.000,     0, 1.000 )
>
> I understand that this behaviour is somehow consistent with the formulas
> in DMPlexComputeTetrahedronGeometry_Internal, where you compute the
> Jacobians swappnig the order of vertices (and with 0.5 factors that I do
> not understand at all... it looks as if your reference element was not the
> unit simplex)
>
> if (J) {
>      for (d = 0; d < dim; d++) {
>        /* I orient with outward face normals */
>        J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) -
> PetscRealPart(coords[0 * dim + d]));
>        J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) -
> PetscRealPart(coords[0 * dim + d]));
>        J[d * dim + 2] = 0.5 * (PetscRealPart(coords[3 * dim + d]) -
> PetscRealPart(coords[0 * dim + d]));
>      }
> }
>
> but still I am worried by this fact that different ways of creating a mesh
> gives a DMPlex with different orientations.
>
> Can you explain the rationale behind this or refer me to some
> documentation?
>
1. DMPlexCreateFromCellListPetsc() is very low-level, so I let you do
whatever you want, including tell me to use inverted
cells. DMPlexCreateGmshFromFile() is guaranteed to get a properly oriented
simplex from GMsh, so I guarantee that it produces a properly oriented Plex
simplex.

2. Here is the order of vertices, and face vertices, in a Plex tetrahedron.

https://urldefense.us/v3/__https://gitlab.com/petsc/petsc/-/blob/main/src/dm/impls/plex/plexinterpolate.c?ref_type=heads*L194__;Iw!!G_uCfscf7eWS!fu9zsNqFCcOd2B75fjpxQSn9mZeYFR3er6s4FhLRrwVo7aVdS4BgUE7eMN4pq3YHjZRId_sQT8Cq0SjYzs6B$ 

I truly believe the only sensible way to describe a simple is to have every
normal outward facing. The convention in Gmsh is to have some normals
inward and some outward, which I think is ridiculous. It breaks the
inherent symmetry of the simplex.

3. The reference simplex has coordinates 1 and -1, and thus volume 4/3.
This is the convention of FIAT (
https://urldefense.us/v3/__https://www.firedrakeproject.org/fiat/index.html__;!!G_uCfscf7eWS!fu9zsNqFCcOd2B75fjpxQSn9mZeYFR3er6s4FhLRrwVo7aVdS4BgUE7eMN4pq3YHjZRId_sQT8Cq0dx6sHl6$ )

4. You can always get my orientation for things by calling DMPlexOrient().

5. Orientations are representors for elements of the dihedral group of the
k-cell. I am almost done with a description of this for every geometric
cell supported (of course you can define any cell you want in Plex). I can
show you this if you want, although it is unfinished.

  Thanks,

     Matt


> Best
>
>     Matteo
>
> --
> Prof. Matteo Semplice
> Università degli Studi dell’Insubria
> Dipartimento di Scienza e Alta Tecnologia – DiSAT
> Professore Associato
> Via Valleggio, 11 – 22100 Como (CO) – Italia
> tel.: +39 031 2386316
>
>

-- 
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

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