Harminv adjoint methods

[smartalecH]

The LDOS is a good way to design around the Q of a resonator. As discussed in the meep tutorial, however, the LDOS can take a long time to simulate for highly resonant structures (since the DFT needs to converge).

Is there a clever way to incorporate Harminv results into our adjoint solver? I realize Harminv isn't an explicit frequency method and consequently probably won't be able to leverage our current machinery... but maybe we can get creative with our hybrid time-domain frequency-domain adjoint?

[stevengj]

Basically you would treat harminv as computing an approximate eigenvalue, and use adjoint methods for eigenvalues. But to do that you need the eigenvector too, so a harminv solves.

[stevengj]

Alternatively, we could try to apply the time-domain adjoint method to Harminv's analysis… it's not necessarily impractical because Harminv only uses one field component at one point, so it only needs to store that value as a function of time.

[stevengj]

It will still be challenging to do optimization with harminv because of the difficulty in consistently tracking the eigenvalue that it returns (out of the several resonances it typically finds).