Laplace

[unalmis]

(see PlasmaControl#1360)

• All the solvers are thoroughly tested. See the shared paper to explain this PR. Significantly improved adjoint solve from earlier. It seems like this is still the only differentiable 3d laplace solver on the internet that works on multiply connected geometry.
• Tested and confirmed agreement with BIE3D package. plotter.py
• This PR includes my FFT improvements significantly improve free surface optimization (both old and new) and anything that involves singular integrals. Even the flaky GitHub ci benchmarks detect this.
• Non-invasive, backward compatible, new magnetic field api implemented. Without the new api, the code would be unreadable.
• There are other applications besides free surface.
• The linear solve to compute the objective function only takes around 2 gmres iterations. Gradient based optimization is very fast. Using a fast multipole technique would greatly improve performance. There are jax libraries that do this, but that can be a later pull request to merge after this.

iterative plots

stop tolerance denotes typical stop tol in most applications. gmres is expected to always invert the linear system in a few iterations. after stateful opt, my guess is it will be reduced to 1 iteration.