[#647] Phase 4 — 3-way head-to-head: GEODE freeform vs FDTD-density vs low-DOF parametric

[rjwalters]

Problem

Epic #647 is a result paper: the freeform GEODE optimum (Phase 3, #650-class) only becomes a contribution when shown to beat what the celebrated structured-grid diff-EM world and classical parametric antenna optimization can reach on the same curved conformal problem. This phase builds the 3-way head-to-head that carries the paper.

Proposed solution

• FDTD-density baseline: stand up an FDTD-density adjoint optimizer (Meep-adjoint / ceviche-style) on the identical curved conformal spec; quantify staircasing / boundary error and its effect on the achievable match. This is the "structured grid can't represent curved metal" evidence.
• Low-DOF parametric baseline: a few-parameter sweep (the Ghassemi / HFSS-optimetrics regime) showing it cannot reach the freeform optimum.
• Report all three on one axis (achieved spec, DOF count, honest cost) with a crisp figure.

Acceptance criteria

• FDTD-density baseline runs the same problem; staircasing/boundary-error and best-achievable match quantified.
• Parametric baseline quantified; freeform-vs-parametric performance gap reported.
• A single head-to-head figure/table: GEODE freeform vs FDTD-density vs parametric — GEODE wins on solution quality, with honest cost accounting (or an honest-negative writeup if it doesn't).

Dependencies

Part of #647. Blocked on Phase 3 (#650-class) — needs the GEODE freeform result to compare against. The external-tool baselines may need operator setup (Meep/ceviche env); flag if so.