김경종
149 lines
5.4 KiB
Markdown
149 lines
5.4 KiB
Markdown
# 정식화 문서 작성 가이드
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이 디렉터리는 Formulation Agent가 작성하거나 제안한 기능별 유한요소 정식화 문서를 보관하는 위치다.
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기본 파일명은 `docs/formulations/<feature-id>-formulation.md` 형식을 사용한다. 각 문서는 Requirement Agent의 요구조건과 Research Agent의 연구 브리프를 입력으로 받아 Implementation Planning Agent와 Implementation Agent가 사용할 수 있는 수학/알고리즘 계약을 제공해야 한다.
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## Formulation Agent 역할
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Formulation Agent는 구현 가능한 FEM 정식화 문서를 작성한다.
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수행한다:
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- strong form, weak form, discretization을 정리한다.
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- shape functions, `B` matrix 또는 kinematic operator를 정의한다.
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- constitutive contract, element residual/internal force, stiffness/tangent matrix를 정리한다.
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- numerical integration, mapping, Jacobian 규칙을 명시한다.
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- output recovery, algorithm pseudocode, edge case, numerical risk를 정리한다.
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- Numerical Review Agent가 검토할 handoff 항목을 남긴다.
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수행하지 않는다:
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- C++ 코드를 구현하지 않는다.
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- C++ API나 파일 구조를 설계하지 않는다.
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- Abaqus, Nastran 또는 레퍼런스 솔버를 직접 실행하지 않는다.
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- reference HDF5 파일이나 deterministic CSV view를 생성하지 않는다.
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- release readiness를 승인하지 않는다.
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- Numerical Review Agent 검토 전 정식화를 최종 승인하지 않는다.
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## 문서 템플릿
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```markdown
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# <feature title> Formulation
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## Metadata
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- feature_id: <feature-id>
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- source_requirement: docs/requirements/<feature-id>.md
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- source_research: docs/research/<feature-id>-research.md
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- status: draft | needs-research | ready-for-numerical-review
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- owner_agent: formulation-agent
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- date: <YYYY-MM-DD>
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## Scope and Assumptions
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- analysis_type: linear static | nonlinear static | modal | dynamic | other
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- element_type: <target element>
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- deformation: small | large | TBD
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- linearity: linear | nonlinear | TBD
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- material_model_boundary: <scope>
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- coordinate_system: <global/local coordinates>
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- units: <unit system>
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## Primary Variables and DOFs
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- nodal_variables: <variables>
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- dof_ordering: <ordering>
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- sign_convention: <convention>
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- constrained_free_dof_assumptions: <assumptions>
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## Strong Form and Boundary Conditions
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- governing_equation: <equation>
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- dirichlet_boundary: <essential BC>
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- neumann_boundary: <natural BC>
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- natural_boundary_terms: <terms>
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## Weak or Variational Form
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- test_functions: <definition>
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- integration_by_parts: <steps>
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- internal_virtual_work: <expression>
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- external_virtual_work: <expression>
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## Discretization
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- interpolation: <field interpolation>
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- shape_functions: <shape functions>
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- partition_of_unity_check: <expected check>
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- kronecker_delta_check: <expected check>
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- nodal_layout: <layout>
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## Kinematics
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- strain_displacement_relation: <relation>
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- B_matrix_or_kinematic_operator: <definition>
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- deformation_gradient: <definition or N/A>
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- strain_measure: <definition or N/A>
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## Constitutive Contract
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- elasticity_matrix_or_stress_update: <contract>
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- material_state_variables: <variables or N/A>
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- assumptions_and_constraints: <assumptions>
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## Element Equations
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- internal_force_or_residual: <expression>
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- external_force: <expression>
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- stiffness_or_tangent_matrix: <expression>
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- mass_or_damping: <required expression or N/A>
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- vector_matrix_dimensions: <dimensions>
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## Mapping and Numerical Integration
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- reference_coordinates: <coordinates>
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- isoparametric_mapping: <mapping>
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- jacobian: <definition>
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- determinant_checks: <validity checks>
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- gauss_points_and_weights: <rule>
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- integration_policy: full | reduced | selective | analytical | TBD
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## Output Recovery
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- displacement: <location and convention>
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- reaction: <calculation>
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- element_force: <calculation>
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- strain: <location and recovery>
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- stress: <location and recovery>
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- nodal_extrapolation: <policy or N/A>
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## Algorithm Pseudocode
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```text
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math-level element routine and assembly flow only
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no C++ signatures, class names, or file paths
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```
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## Numerical Risks
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- rigid_body_modes: <risk/check>
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- patch_test: <expected test>
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- symmetry: <expected property>
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- positive_definiteness: <expected property>
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- hourglass: <risk or N/A>
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- shear_locking: <risk or N/A>
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- volumetric_locking: <risk or N/A>
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- distortion: <risk/check>
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- singular_jacobian: <risk/check>
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## Open Issues and Downstream Handoff
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### Numerical Review Agent
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- <derivations, assumptions, numerical risks, open issues>
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### I/O Definition Agent
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- <required inputs, outputs, units, coordinate conventions, output locations>
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### Reference Model Agent
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- <benchmarkable quantities, patch test needs, expected invariants, edge cases>
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### Implementation Planning Agent
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- <math-level pseudocode, acceptance-relevant quantities, tests to write first>
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```
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## 품질 기준
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- 요구조건과 연구 브리프에 없는 값을 임의로 확정하지 않는다.
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- strong form, weak form, discretization, kinematics, constitutive contract, element equations를 구분한다.
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- shape functions는 가능한 경우 partition of unity와 Kronecker delta 검사를 포함한다.
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- numerical integration은 integration point, weight, 적분 대상, full/reduced/selective 정책을 포함한다.
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- mapping은 reference coordinates, Jacobian, determinant validity check를 포함한다.
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- output recovery는 nodal, element-level, integration-point 위치를 구분한다.
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- numerical risk는 rigid body modes, patch test, hourglass, locking, Jacobian 문제를 명시한다.
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