The Inversive-Distance solver built its Hessian inline by full finite
differences: n perturbations × a full O(F) gradient eval = O(n·F) per Newton
iteration (quadratic in mesh size), with no fast path at all (api-performance
audit B1, second half).
Port the per-face block-FD scheme already used by HyperIdeal (Phase 9b):
the gradient decomposes by face (G_v = Θ_v − Σ_{f∋v} α_v, and each face's
angles depend only on its 3 vertex DOFs), so the Hessian decomposes into
per-face 3×3 blocks. Cost drops to O(F) face evaluations, a ≈ n/6 speed-up.
- inversive_distance_functional.hpp: add the pure 3→3 kernel
inversive_distance_face_grad_contribs (returns the per-face contribution
−α to G; mirrors the gradient's face-skip on ℓ²≤0 exactly).
- inversive_distance_hessian.hpp (new): full-FD baseline + block-FD + sym
variants, mirroring hyper_ideal_hessian.hpp.
- newton_solver.hpp: drop the inline full-FD lambda; call
inversive_distance_hessian_block_fd_sym.
- test: InversiveDistance_BlockFDHessianMatchesFullFD cross-validates the
two Hessians entry-wise on a perturbed (off-equilibrium) config.
291/291 CGAL tests pass; all Inversive-Distance convergence tests unchanged.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
