[3/n][Adjoint Module] Fix adjoint source weighting on a symmetry plane

[smartalecH]

Stack

Each PR is based on the one above it, so every diff here is just its own delta.

	PR
1	#3277	Fix MaterialGrid design-variable attribution (#1984)
2	#3290	Fix source deposition across chunk boundaries
3	#3292	Fix adjoint source weighting on a symmetry plane (#3291) ← you are here
4	#3280	Enable proper JAX support in the adjoint module
5	#3281	Differentiable angular-spectrum propagation
6	#3283	Adjoint gradients w.r.t. source amplitudes
7	#3284	Launch a mode through a stratified stack
8	#3285	Adjoint gradients w.r.t. geometry (centre and size)
9	#3286	Register a material grid's susceptibilities
10	#3287	Evaluate the dispersive adjoint at the discrete lineshape
11	#3293	Subpixel-smooth dispersive materials and their shape derivative
12	#3294	Scalable Pade extrapolation for DFT monitors (#3217)
13	#3295	3D grating coupler example: fiber, grating and mirror

Fixes #3291.

fourier_sourcedata divides each interpolated adjoint source by the multiplicity of the point it sits at, to undo the replication a reduced symmetric domain applies. In the yee_grid = false branch the amplitude is split over the four Yee corners of a voxel, but the divisor was evaluated once at the voxel centre and reused for all four.

Those disagree exactly on a symmetry plane. A point there is its own image, so its multiplicity is 1, while the centre half a pixel away has 2. The corner on the plane was therefore halved when it should not have been, leaving the adjoint source short.

objective vs. the plane	before	after
on the plane	0.7484	1.0002
one pixel off	0.8725	1.0002
clear of it	1.0002	1.0002
extended, spanning it (res 20 / 30 / 40)	0.9602 / 0.9715 / 0.9819	1.0002 / 0.9975 / 1.0000

(finite difference = 1; no symmetry declared is 1.0002 throughout)

The on-plane number is exactly 3/4 and resolution independent — the source's three Yee rows carry weights 1/4, 1/2, 1/4 and the halved one is the middle row, so exactly a quarter of the source goes missing. An extended monitor merely spanning the plane dilutes that single row over the O(1/dx) rows it covers, which is why it presented as a first-order error rather than a constant one. The last row is the common arrangement for a symmetric device, so most symmetric adjoint runs were carrying a few percent of gradient error.

The fix takes the multiplicity of the site each quarter is actually written to. Off the plane nothing changes, and with no symmetry declared every multiplicity is 1, so this is a no-op for the vast majority of runs.

Tests

Meep had no adjoint test that declared a symmetry at all. The first commit adds one, including the part that looks like a bug and is not: with Mirror(Y) the design gradient puts all of its magnitude in y >= 0, because Meep builds the structure on the reduced grid volume, so weights below the plane are never read and a weight above it drives both halves at once. Finite differences confirm both halves — zero below the plane, and exactly 2.0000x above it.

Those two commits are separated deliberately: the first records the on-plane and plane-crossing failures as expectedFailure, and the second turns them into plain assertions, so the diff shows the fix flipping them.

test_adjoint_solver.py (44 gradient checks) and test_adjoint_cyl.py both pass unchanged.

[smartalecH]

Closing in favour of #3296, which is the same branch and the same content, opened from this repository rather than from a fork.

The reason is purely mechanical: this series is a stack of 13 pull requests, each based on the one below it so that every diff is only its own delta. GitHub's native stacked pull requests cannot include a PR opened from a fork, and four of the thirteen — including this one — were. Rather than leave the series half-stacked, all four have been reopened with their branches hosted here so the whole chain can be linked.

Nothing about the change itself has been revised, and the description is carried over verbatim. The discussion and reviews on this PR stay readable here; please continue on #3296.