---
name: fesa-numerical-review
description: Use when independently reviewing FESA FEM numerical review evidence, formulation correctness, stability risks, patch tests, locking, Jacobian handling, and implementation planning readiness.
---

# FESA Numerical Review

Use this skill to review a formulation as a numerical algorithm contract before implementation planning.

## Inputs

Read these first:

- `AGENTS.md`
- `docs/SOLVER_AGENT_DESIGN.md`
- `docs/numerical-reviews/README.md`
- `docs/formulations/<feature-id>-formulation.md`
- Related requirements and research documents when needed

## Workflow

1. Lead with findings and required revisions.
2. Check dimensional consistency, signs, DOF ordering, constrained/free assumptions, and coordinate transforms.
3. Review B matrix or kinematic operator consistency.
4. Review constitutive matrix or stress update contract.
5. Review Jacobian rules, determinant checks, derivative transforms, and distortion handling.
6. Review integration rule, Gauss points, weights, and full/reduced/selective integration policy.
7. Check element residual, internal force, external force, stiffness, tangent, symmetry, and positive definiteness expectations.
8. Assess rigid body modes, patch test readiness, hourglass, shear locking, volumetric locking, singular Jacobian, conditioning, and convergence risk.
9. Decide status: `pass-for-implementation-planning`, `needs-formulation-revision`, `needs-research`, `needs-reference-model`, or `blocked`.

## Output Contract

Produce or revise `docs/numerical-reviews/<feature-id>-review.md` with:

- Metadata and source formulation
- Review Verdict
- Critical Findings
- Numerical Risk Assessment
- Consistency Checks
- Verification Readiness
- Required Revisions
- Downstream Handoff

## Boundaries

- Do not implement code.
- Do not edit formulations directly.
- Do not design C++ APIs or file ownership.
- Do not run Abaqus, Nastran, or any reference solver.
- Do not generate reference HDF5 files or deterministic CSV views.
- Do not approve release readiness.
- Do not decide reference comparison success.

## Quality Gate

- `pass-for-implementation-planning` means implementation planning may begin, not that the feature is complete.
- Confirmed defects, risks, open questions, and test recommendations are separated.
- Missing derivations are returned to Formulation Agent instead of being silently fixed.
- Evidence gaps are routed to Research Agent or Reference Model Agent.

## Handoff

Send pass results to Implementation Planning Agent and Reference Model Agent. Send math defects to Formulation Agent, source gaps to Research Agent, and blocked decisions to Coordinator Agent.