김경종
70 lines
2.8 KiB
Markdown
70 lines
2.8 KiB
Markdown
---
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name: fesa-formulation-spec
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description: Use when drafting FESA FEM formulation specifications, strong or weak forms, shape functions, element equations, numerical integration, Jacobian rules, and output recovery contracts.
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---
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# FESA Formulation Spec
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Use this skill to turn approved requirements and research evidence into an implementable math-level FEM contract.
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## Inputs
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Read these first:
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- `AGENTS.md`
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- `docs/SOLVER_AGENT_DESIGN.md`
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- `docs/formulations/README.md`
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- `docs/requirements/<feature-id>.md`
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- `docs/research/<feature-id>-research.md`
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## Workflow
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1. Confirm scope, assumptions, primary variables, DOFs, sign convention, units, and coordinate system.
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2. Write the Strong Form and boundary conditions.
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3. Write the Weak or Variational Form and natural boundary terms.
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4. Define Discretization: interpolation, shape functions, partition of unity, Kronecker delta checks, and nodal layout.
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5. Define Kinematics: strain-displacement relation, B matrix or kinematic operator, strain measure, and deformation assumptions.
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6. Define Constitutive Contract without creating C++ APIs.
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7. Define Element Equations: residual or internal force, external force, stiffness or tangent, mass or damping when applicable, and dimensions.
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8. Define Mapping and Numerical Integration: reference coordinates, isoparametric mapping, Jacobian, derivative transform, determinant checks, Gauss points, and weights.
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9. Define Output Recovery for displacement, reaction, element force, strain, stress, and nodal extrapolation.
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10. List Numerical Risks and downstream tests.
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## Output Contract
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Produce or revise `docs/formulations/<feature-id>-formulation.md` with:
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- Scope and Assumptions
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- Primary Variables and DOFs
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- Strong Form
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- Weak or Variational Form
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- Discretization
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- Kinematics
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- Constitutive Contract
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- Element Equations
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- Mapping and Numerical Integration
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- Output Recovery
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- Algorithm Pseudocode
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- Numerical Risks
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- Open Issues and Downstream Handoff
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## Boundaries
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- Do not implement C++ code.
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- Do not design C++ APIs.
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- Do not implement parsers.
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- Do not run Abaqus, Nastran, or any reference solver.
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- Do not generate reference CSVs.
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- Do not approve release readiness.
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## Quality Gate
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- Strong form, weak form, discretization, kinematics, constitutive contract, and element equations are distinct.
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- Shape functions include partition of unity and Kronecker delta checks when applicable.
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- Jacobian, determinant validity, derivative transform, integration rule, and output location are explicit.
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- Missing research or requirements become open issues, not assumptions.
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## Handoff
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Send the formulation to Numerical Review Agent first. After review, pass implementation-relevant pseudocode and acceptance quantities to Implementation Planning Agent, I/O needs to I/O Definition Agent, and benchmarkable checks to Reference Model Agent.
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