Fix FourierFields adjoint for D and B fields in isotropic media

[mawc2019]

This PR fixes #2090. FourierFields adjoint gradients for D and B fields in isotropic media now become consistent with finite-difference gradients.

[oskooi]

It would be useful to add a unit test in this PR which should fail using the current master branch since this is a bug fix.

[mawc2019]

However, the current version of this PR does not yield correct adjoint gradients if the monitor is placed inside the design region. Should we deal with this case?

[smartalecH]

However, the current version of this PR does not yield correct adjoint gradients if the monitor is placed inside the design region. Should we deal with this case?

That piece of code would need to go here:

meep/src/meepgeom.cpp

Lines 3003 to 3006 in 91d36ba

	/********* compute λᵀbᵤ ***************/
	/* not yet implemented/needed */
	/**************************************/
	}

Actually.... I think we want the $g_\rho$ term... which should be easy to add?

[stevengj]

Looks fine, albeit missing a test.

I agree that it would be good to add support for D fields in the design region, but this is nontrivial, and meanwhile this PR is a strict improvement over what we have now.

[mawc2019]

It would be useful to add a unit test in this PR which should fail using the current master branch since this is a bug fix.

I changed an existing test in test_adjoint_solver.py to the new test. To be specific, in the functions forward_simulation_complex_fields and adjoint_solver_complex_fields, Ez has been changed to Dz and default_material=silicon has been added. I think the new test (for Dz) can substitute for the old test (for Ez). Besides, in test_adjoint_solver.py, another test for Ez has already existed.

[oskooi]

Looks like this assert statement is failing for the single-precision build. You can try increasing the tolerance for single precision using e.g.:

self.assertClose(adjsol_obj,Dz2_unperturbed,epsilon=1e-4 if mp.is_single_precision() else 1e-6)

[mawc2019]

In my place, this line does not cause error even with single precision. I guess the error message in my place is different from that given by the online check. But I cannot see the detailed error message in the online-check logs. Can I ask where I should find the detailed error message?

[oskooi]

To find the log of the failing CI run, click on the "Details" button below next to "CI / Test Python 3.10 with MPI (true)" or the "Actions" tab above (next to "Discussions" and "Projects"). From there, for the failing run locate the "Artifacts" section and then download the log file. In this case, this would be py3.10-tests-mpi-true.log which shows:

Ran 7 tests in 307.004s

FAILED (failures=1)
FAIL: test_complex_fields (__main__.TestAdjointSolver)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/home/runner/work/meep/meep/build/meep-1.24.0-beta/_build/sub/python/../../../python/tests/test_adjoint_solver.py", line 525, in test_complex_fields
    self.assertClose(adj_scale,fd_grad,epsilon=tol)
  File "/home/runner/work/meep/meep/build/meep-1.24.0-beta/python/tests/utils.py", line 28, in assertClose
    self.assertLessEqual(diff_norm, epsilon * np.maximum(x_norm, y_norm), msg)
AssertionError: 0.001776412917294544 not less than or equal to 0.0005871758943843297 : 

[mawc2019]

Thanks! The tolerance for single precision is adjusted further.