BUG: CellDiameter on extruded meshes no longer works about firedrake

[connorjward]

Fixed in FEniCS/ufl#295 (though we also need to update our UFL fork).

[connorjward]

This is very curious. I have looked at the commits for TSFC and UFL in the last year and none of them seem to touch CellDiameter.

[wence-]

My guess is FEniCS/ufl#197

That probably changed the implemented of cell_diameter in apply_geometry_lowering in UFL to return CellDiameter for extruded hex cells, rather than fall-through to the Q1 case.

[connorjward]

Spot on @wence-, thanks! For an extruded mesh we have domain.ufl_coordinate_element().degree() == (1, 1) which was a previously permissible element. Now though we have domain.ufl_coordinate_element().embedded_superdegree == 2 which is no longer allowed.

This might well be a simple fix. Looking at where embedded_superdegree is defined we should probably be using max instead of sum (we even use min for embedded_subdegree).

[wence-]

Nah, sum is correct, since a Q1 element contains some quadratic polynomials, so it is embedded in the complete polynomial space P2.

[wence-]

That implementation is, however, probably wrong because it should probably say sum(sub.embedded_superdegree() for sub in sub_elements()) (which would handle the case of TPE(TPE(interval, interval), interval) (say)

[connorjward]

OK. Do you have any suggestion for what the right thing is to do here? Should CellDiameter for an extruded mesh not be supported?

[wence-]

I think in apply_geometry_lowering the check for Q1 cells needs to be reinstated. So it does something like:

if all(degree == 1 for degree in self.degree()): 
    # can do affine and/or Q1 lowering

I don't know exactly how to check for Q1, but notice that previously the check was (pseudo-code)

if not (P1 or Q1):
    dont_lower
elif P1:
    lower_simplex
else:
    # must be Q1
    lower_hypercube

But now the check is:

if not P1:
    dont_lower
elif P1:
    lower_simplex
else:
    # unreachable
    lower_hypercube

[connorjward]

I believe that degree() is no longer a UFL finite element property and now only embedded_{super,sub}degree exist so this may be tricky to fix. I have added this to the agenda for the next Firedrake meeting.

[dham]

This looks like a mistake in the UFL changes last year. The test for geometry lowering is using the embedded_superdegree but it should be using the embedded_subdegree. The reason subdegree is right is that you care about whether the edges are straight, not whether there are any quadratic functions on the interior.