p-multigrid: remove custom interpolation code

[pbrubeck]

Stack

Merge in this order, each PR retargets to main once the one above it lands:

#	PR	what
1	firedrakeproject/fiat#269	gem: sum factorise independent contractions
2	firedrakeproject/fiat#271	FInAT: select H(div)/H(curl) components with a Delta
3	firedrakeproject/fiat#268	FInAT: dual evaluate on each sub-element's own points
4	#5295	tsfc: dual evaluation against a Cofunction
5	#5289	p-multigrid: remove custom interpolation
6	#5297	tsfc: contract each block after unconcatenating

2 and 6 are a pair: neither is worth anything alone, though 2 is harmless on its
own — it changes how a component is selected, not what is selected.
5 and 6 are siblings on 4, in either order.

Only 4 carries a DROP BEFORE MERGE commit, pinning FIAT to
pbrubeck/fix/dual-enriched, which is now the top of the FIAT stack; 5 and 6
inherit it. Drop it once the FIAT side has landed.

Removes ~1050 lines of hand-written interpolation machinery from
firedrake/preconditioners/pmg.py — StandaloneInterpolationMatrix,
MixedInterpolationMatrix, kronmxv, get_permutation_to_nodal_elements,
evaluate_dual and friends — and replaces the p-multigrid transfer operators with
the generic assemble(interpolate(TrialFunction(cV), fV)). The helpers that are still
needed move to firedrake/preconditioners/fdm.py.

Stacked on #5295, which fixes the matrix-free adjoint interpolation this now relies on.
Also needs firedrakeproject/fiat#268 — see the DROP BEFORE MERGE commit, which
applies to both PRs in the stack.

Bugs this exposed

Routing the transfers through the generic interpolation path uncovered three defects
that the bespoke code had been bypassing. Two are fixed in the PRs below this one; the
Firedrake-side ones are in the second commit here:

• Rectangular matrices got the wrong bcs. Assembling a two-form Interpolate
  matrix-free passed the same bcs as both the row and the column bcs of the
  ImplicitMatrixContext, and left on_diag at its default of True. Neither holds
  when interpolating between two different spaces: applying the target space's bcs to
  the source side raised Cofunction defined on incompatible FunctionSpace, and
  on_diag made multTranspose write the row values into the column vector. The bcs
  are now split by the space they are defined on, as the assembled path already does,
  and on_diag is set from whether the two spaces coincide. A bc on a component of a
  mixed space is defined on an IndexedProxyFunctionSpace rather than on the space
  itself, so the comparison walks up to the top-level parent — without that, bcs on a
  mixed space were silently dropped from both lists and the preconditioner degraded
  (test_p_multigrid_mixed needed 8 iterations instead of 7).

• Nullspace coarsening used a deleted API. coarsen_nullspace called
  interpolate.getNestSubMatrix(i, i), which only MixedInterpolationMatrix provided.
  It now recurses over the sub-spaces and builds the interpolation matrix locally.

Testing

suite	result
tests/firedrake/regression/test_fdm.py	16 passed
tests/firedrake/multigrid/test_p_multigrid.py	23 passed
tests/firedrake/multigrid	338 passed, 22 skipped
interpolation regression suites	175 passed
make srclint	clean

Matrix-free mult/multTranspose were also compared against the assembled matrix
across 47 element/mesh combinations, all agreeing to machine precision.

🤖 Generated with Claude Code

[leo-collins]

interpolation seems like a strange place to have this. Maybe put it as a method on BCBase?

[pbrubeck]

Suggested change

	if is_dual(Vrow):
	Vrow = Vrow.dual()
	if is_dual(Vcol):
	Vcol = Vcol.dual()
	Vcol = Vcol.dual()