[rogeriojorge]

Summary

• add an optional collision/diffusion diagonal preconditioner factory for implicit midpoint
• pass optional preconditioner factories through to SOLVAX Newton–Krylov
• test the exact midpoint diagonal and the preconditioned Diffrax integration path

The inverse action is local and matrix-free:

(I + dt / 2 * (nu C + D k²))⁻¹

The electromagnetic residual is left unchanged. Users opt in with
ImplicitMidpoint(preconditioner=collision_diffusion_preconditioner).

Depends on #27.

Why

Collisions are diagonal in Hermite space and diffusion is diagonal in Fourier
space, so their exact midpoint contribution is the cheapest physics-based
approximation to the full kinetic Jacobian. It requires no assembled matrix,
factorization, or communication and is compatible with local Hermite shards.

Validation

• pytest -q: 7 passed
• repository fatal flake8 checks and Ruff lint pass
• 65² / (28,4,4), dt=1e-3, 20 midpoint steps, D=1:
  • no preconditioner: 92.61 s
  • collision/diffusion preconditioner: 15.97 s (5.8x faster)
  • relative endpoint difference: 1.96e-11 in Ck, 1.55e-13 in Fk
  • energy drift improves from 4.85e-16 to 1.21e-16
• nonstiff D=0 control:
  • 10.88 s without versus 11.03 s with preconditioning (+1.4%)
  • relative Ck difference 2.48e-15; energy agrees to roundoff

Distributed nonlinear/Krylov inner products are intentionally left to a
separate PR after the midpoint and parallel stacks share a common base.

[rogeriojorge]

Superseded by the x-streaming line preconditioner in #21, which includes collision and diffusion and needs ~25x fewer GMRES iterations than this diagonal (133 vs 3527 on the stiff Landau case).