BUG: Incorrect entity orientations on non-overlapping quad meshes

[pbrubeck]

Describe the bug
Non-overlapping quad meshes seem to be getting incorrect entity orientations.

Steps to Reproduce
Steps to reproduce the behavior:

from firedrake import *
distribution = {"overlap_type": (DistributedMeshOverlapType.NONE, 0)}
mesh = UnitSquareMesh(2, 1, quadrilateral=True, distribution_parameters=distribution)
x, y = SpatialCoordinate(mesh)
V = FunctionSpace(mesh, "RTCE", 1)
f = Function(V).project(grad(2*x + y))
print(f.dat.data_with_halos)

mpiexec -n 1 script.py

[1. 1. 1. 1. 1. 1. 1.]

mpiexec -n 2 script.py

[1.50000000e+00 1.00000000e+00 1.00000000e+00 2.77555756e-17]
[ 2.77555756e-17  1.00000000e+00 -1.50000000e+00  1.00000000e+00]

Expected behavior
The coefficients of grad(2*x+y) in RTCE(1) on a 2x1 mesh should all be either 1 or -1.

[pbrubeck]

It seems that we are off by the sign of the JacobianDeterminant, at least on this very simple case.

Jdet = JacobianDeterminant(mesh)
s = Jdet / abs(Jdet)
f = Function(V).project(s * grad(2*x + y))
print(f.dat.data_with_halos)

mpiexec -n 2 script.py

[1. 1. 1. 1.]
[ 1. -1.  1. -1.]

[ksagiyam]

temp.py:

from firedrake import *


distribution = {
    "overlap_type": (DistributedMeshOverlapType.NONE, 0),
    "partitioner_type": "simple",
}
mesh = UnitSquareMesh(
    2, 1, quadrilateral=True, distribution_parameters=distribution,
)
plex = mesh.topology_dm
plex.viewFromOptions("-dm_view")
print(mesh.comm.rank)
print(mesh.cell_closure)

Run:

mpiexec -n 2 python temp.py -dm_view ascii::ascii_info_detail

Output:

Cones:
[0] Max cone size: 4
[0]: 0 <---- 5 (0)
[0]: 0 <---- 6 (0)
[0]: 0 <---- 7 (0)
[0]: 0 <---- 8 (0)
[0]: 5 <---- 1 (0)
[0]: 5 <---- 2 (0)
[0]: 6 <---- 2 (0)
[0]: 6 <---- 4 (0)
[0]: 7 <---- 4 (0)
[0]: 7 <---- 3 (0)
[0]: 8 <---- 3 (0)
[0]: 8 <---- 1 (0)
[1] Max cone size: 4
[1]: 0 <---- 5 (-1)
[1]: 0 <---- 6 (0)
[1]: 0 <---- 7 (0)
[1]: 0 <---- 8 (0)
[1]: 5 <---- 2 (0)
[1]: 5 <---- 1 (0)
[1]: 6 <---- 2 (0)
[1]: 6 <---- 4 (0)
[1]: 7 <---- 4 (0)
[1]: 7 <---- 3 (0)
[1]: 8 <---- 3 (0)
[1]: 8 <---- 1 (0)
coordinates with 1 fields
  field 0 with 2 components
Process 0:
  (   1) dof  2 offset   0 0. 0.
  (   2) dof  2 offset   2 0. 1.
  (   3) dof  2 offset   4 0.5 0.
  (   4) dof  2 offset   6 0.5 1.
Process 1:
  (   1) dof  2 offset   0 0.5 0.
  (   2) dof  2 offset   2 0.5 1.
  (   3) dof  2 offset   4 1. 0.
  (   4) dof  2 offset   6 1. 1.

...

0
[[1 2 3 4 5 7 8 6 0]]
1
[[2 1 4 3 5 7 6 8 0]]

This suggests that those two cells look like:

rank0:           rank 1:

2-----6---->4    2-----6---->4
^           ^    |           | 
|           |    5           7
5           7    |           |
|           |    v           v
1-----8---->3    1-----8---->3

, where the numbers are the local plex numbers and the arrows indicate how FIAT reference cell is mapped.

So rank 0 (7) and rank 1 (5) have mismatching orientations, which is not expected.

First place to inspect is probably this block:

firedrake/firedrake/mesh.py

Line 1290 in 237c17e

elif cell.cellname() == "quadrilateral":

.