[BUG]: Interpolation into symmetric rank-2 tensors broken

[michalhabera]

Summarize the issue

Recent changes altered the value shape of symmetric rank-2 tensors, being rank-1 with shape (dim * (dim + 1)/2, ). This means that interpolation of objects with shape (dim, dim) into symmetric rank-2 tensors does not work anymore.

See https://github.com/FEniCS/dolfinx/blob/main/cpp/dolfinx/fem/FiniteElement.cpp#L118

How to reproduce the bug

Interpolate into symmetric rank-2 tensors.

Minimal Example (Python)

import dolfinx
from mpi4py import MPI

mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 1, 1)

REG = dolfinx.fem.functionspace(mesh, ("Regge", 1))
Psymm = dolfinx.fem.functionspace(mesh, ("P", 1, (2, 2), True))

print(f"Regge value shape: {REG.element.value_shape}")
print(f"Psymm value shape: {Psymm.element.value_shape}")

f0 = dolfinx.fem.Function(REG)
f1 = dolfinx.fem.Function(Psymm)

f0.interpolate(f1)

Output (Python)

Regge value shape: [2 2]
Psymm value shape: [3]
Traceback (most recent call last):
  File "/home/UNILU/symm_interp.py", line 15, in <module>
    f0.interpolate(f1)
  File "/home/UNILU/dolfinx/python/dolfinx/fem/function.py", line 459, in interpolate
    _interpolate(u0)
  File "/usr/lib/python3.12/functools.py", line 909, in wrapper
    return dispatch(args[0].__class__)(*args, **kw)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/UNILU/dolfinx/python/dolfinx/fem/function.py", line 445, in _
    self._cpp_object.interpolate(u0._cpp_object, cells0, cells1)  # type: ignore
    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
RuntimeError: Interpolation: elements have different value dimensions

Version

main branch

DOLFINx git commit

No response

Installation

No response

Additional information

No response

[garth-wells]

I'd say the underlying issue here is that for 3x3 symmetric tensors UFL (or is it now Basix?) reports a value shape of (6,) rather than (3, 3) plus a 'block size' of 6. I left a comment at

dolfinx/cpp/dolfinx/fem/FiniteElement.cpp

Line 118 in a547191

// TODO: symmetric rank-2 symmetric tensors are presently constructed

. Before we had a hack where function spaces and elements sometimes reported the same value shape, and sometimes different, and sometimes did some implicit mutations behind the scenes.

The value shape is (3, 3) because they're rank-2 tensors, Symmetry just implies a constraint. We could try a UFL-level fix, or we could try a temporary hack in DOLFINx to address the isssue.