Restricted Cofunction RHS

[pbrubeck]

Description

This PR enables solve(a == assemble(L), u, bcs, restrict={False|True}) without requiring users to set the boundary nodes to zero when they provide a Cofunction RHS. Here we also solved a few other issues:

1. V and V.dual() do no longer compare to the same thing.
2. assemble(form, bcs, zero_bc_nodes=True) is the new default, and for the False case we throw an error because we will try to apply primal inhomogenous data on a dual Cofunction.

Depends on firedrakeproject/ufl#53

Fixes #3203, #3498, and #3130

Supersedes #3214, #3754

[github-actions]

	Tests	Passed ✅	Skipped ⏭️	Failed ❌
Firedrake complex	8126 ran	6652 passed	1474 skipped	0 failed

[github-actions]

	Tests	Passed ✅	Skipped ⏭️	Failed ❌
Firedrake real	8132 ran	7457 passed	675 skipped	0 failed

[ksagiyam]

I understand why you do this, but I would like to think a bit more to see if there is any better solution.

[ksagiyam]

I hoped something like self.F = interpolate(F, V_res.dual()) would work, but it looks not supported, so maybe this is fine.

[pbrubeck]

I found a way to make self.F = action(replace(F, {u: u_res}), interpolate(v_res, V)) work. It requires fixing some FormSum bugs, and fixing the way assemble optimizes and applies BCs on BaseForms.

[ksagiyam]

Sounds good.

[ksagiyam]

Please fix CI.

[ksagiyam]

I hoped something like self.F = interpolate(F, V_res.dual()) would work, but it looks not supported, so maybe this is fine.

[connorjward]

We do the same for ufl.classes.Zero on line 199 so this should probably be combined. In general I am a bit concerned about this code because we do not tape Assigner. @Ig-dolci knows more I believe.

[pbrubeck]

I see. I copied this from Function.assign, and just noticed that Function.assign is decorated with @FunctionMixin._ad_annotate_assign. This is required for bc.set(Cofunction, float) if we want to set diagonal entries to 1.