Fix: half-cell DFN with surface form + lumped thermal fails to build (#5414)

[gaoflow]

Problem

In half-cell mode ({"working electrode": "positive"}) the planar Li-metal negative electrode causes two submodels to be skipped, both of which previously registered key boundary conditions:

• The negative branch of BaseSurfaceFormConductivity.set_boundary_conditions was the only place that registered the inter-domain BCs on phi_e (the concatenated electrolyte potential). With no BC key on the concatenation, Discretisation.set_internal_boundary_conditions cannot split it into per-orphan BCs, so grad(phi_e_s) / grad(phi_e_p) end up internal-edge-only at discretisation time.
• base_ohm.BaseModel.set_boundary_conditions returned the moment the negative electrode was planar, silently dropping the BCs on the porous positive electrode potential phi_s_p too.

In the surface form, phi_s_p is built as -IndefiniteIntegral(i_s / sigma, x_p) + boundary_value(...), so the solid Ohmic-heating term -inner(i_s_p, grad(phi_s_p)) and the electrolyte Ohmic-heating term -inner(i_e_X, grad(phi_e_X)) in base_thermal.BaseThermal._get_standard_coupled_variables both ended up multiplying an IndefiniteIntegral matrix of shape (n, n+1) by an internal-edge integrand of shape (n-1, 1). Building any DFN with this combination then crashed:

pybamm.expression_tree.exceptions.ShapeError: Cannot find shape
(original error: matmul: dimension mismatch with signature
(n,k=21),(k=19,m)->(n,m))

The bug fires whenever all three of these are on:

working electrode	surface form	thermal
positive	algebraic / differential	lumped (or any non-isothermal option that triggers the Ohmic heating path)

Originally reported in #5414 with the standard Xu2019 parameter set and a DFN + "thermal": "lumped".

Root cause

Two independent BC-registration sites silently no-op in the half-cell path:

1. src/pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/full_surface_form_conductivity.py — phi_e BC is registered inside if self.domain == "negative": (lines 206–215 before this PR). Half-cell DFN skips the negative submodel via if self.options.electrode_types.get(domain) == "planar": continue, so the BC is never added.
2. src/pybamm/models/submodels/electrode/ohm/base_ohm.py — set_boundary_conditions bails out as soon as the negative electrode is planar (if self.options.electrode_types["negative"] == "planar": return), instead of checking the current submodel's domain. So the positive instance — which is porous in a positive half-cell — also returns without registering its phi_s_p BC.

Fix

1. full_surface_form_conductivity.py: register the phi_e BC from the separator submodel's set_boundary_conditions instead. The separator submodel is the one that is always instantiated for both full-cell and half-cell models. The BC values mirror the half-cell convention used by BaseElectrolyteConductivity.set_boundary_conditions: Dirichlet(phi_e_ref) on the left when the negative is planar, Neumann(0) otherwise; Neumann(0) on the right. Use update() rather than assignment to preserve the c_e_s Neumann BCs that get_coupled_variables set earlier in the same submodel's lifecycle.

2. base_ohm.py: gate the early-return on self.options.electrode_types[self.domain] == "planar" instead of on the negative electrode globally. Now the planar submodel still skips (correctly — Li metal has no porous phi_s BC to set), and the porous positive submodel in a half-cell can register its phi_s_p BCs the same way it does in a full-cell.

Together these make the half-cell set_internal_boundary_conditions split work the same way the full-cell one already does, and grad(phi_s_p) / grad(phi_e_p) / grad(phi_e_s) all discretise to full edges.

Verification

The reproducer from #5414 (DFN + Xu2019 + missing thermal parameters + half-cell + surface form + lumped thermal) now builds and solves cleanly:

>>> import pybamm
>>> params = pybamm.ParameterValues("Xu2019")
>>> params.update(missing_keys, check_already_exists=False)
>>> model = pybamm.lithium_ion.DFN({
...     "working electrode": "positive",
...     "surface form": "differential",
...     "thermal": "lumped",
... })
>>> sim = pybamm.Simulation(model, parameter_values=params, C_rate=1.0)
>>> sim.solve([0, 3600])  # finishes cleanly

A 12-entry triage matrix over {DFN} × {full-cell, half-cell} × {surface form: false/algebraic/differential} × {thermal: isothermal/lumped} all build and solve. Full-cell numerics on Chen2020 are unchanged (V_end ≈ 3.51–3.53 V across the matrix, identical to main).

Targeted regression tests live in tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_half_cell_surface_form_5414.py and assert:

• phi_e is a BC key on the half-cell DFN (covers the surface-form fix).
• phi_s_p is a BC key on the half-cell DFN even with "surface form": "false" (covers the base_ohm fix).
• The full half-cell × surface form × thermal matrix builds and solves with finite, physically-plausible voltages.
• Full-cell + lumped + surface-form numerics stay within physical bounds (non-regression sanity).

Test impact

$ python -m pytest tests/unit/test_models/test_submodels/test_electrolyte_conductivity test/unit/test_models/test_submodels/test_electrode -q
2 passed in 2.83s

$ python -m pytest tests/unit/test_models/test_full_battery_models/test_lithium_ion -q
634 passed, 12 skipped in 8.16s

$ python -m pytest tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_dfn.py -q
58 passed, 1 failed in 203.65s   # the one failure is `skfem` optional-dep,
                                 # also fails on `main`

$ python -m pytest tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_half_cell_surface_form_5414.py -v
4 passed in 4.25s

Scope

Three production files plus a new regression test:

• src/pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/full_surface_form_conductivity.py — move the phi_e BC into the separator branch and unify the half-cell vs full-cell BC values with the base-class convention.
• src/pybamm/models/submodels/electrode/ohm/base_ohm.py — make the planar-skip per-domain instead of per-model.
• CHANGELOG.md — unreleased bug-fix entry.
• tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_half_cell_surface_form_5414.py — new regression suite.

No public API changes.