김경종
309 lines
12 KiB
Markdown
309 lines
12 KiB
Markdown
# FESA Solver Architecture
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## 목표
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FESA는 C++17/MSVC 기반 유한요소 구조해석 솔버다. 초기 구현은 MITC4 4절점 shell element의 선형정적 해석이며, 이후 비선형 정적해석, 비선형 동적해석, 열전달 및 thermal-stress coupling, 1D/3D 요소로 확장한다.
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초기 구현은 정확도와 테스트 가능성을 우선한다. 단, 대규모 모델을 목표로 하므로 자유도 관리, 희소 행렬 조립, 선형 솔버, 병렬 실행 계층은 초기부터 성능 확장이 가능하도록 분리한다.
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## 개발 프로세스 구조
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```text
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Feature request
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-> requirements
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-> research evidence
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-> FEM formulation
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-> I/O contract
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-> reference model and artifact contract
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-> TDD implementation plan
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-> C++ implementation
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-> build/test validation
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-> HDF5 reference comparison
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-> physics/release review
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```
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## 설계 원칙
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- `Domain`은 입력 모델의 의미를 보존하고 파싱 이후 가능한 한 불변에 가깝게 유지한다.
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- 해석 중 변하는 물리량과 반복 상태는 `AnalysisState`에 명시적으로 분리한다.
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- 현재 step에서 활성화되는 실행 view는 `AnalysisModel`이 담당하며, `Domain`을 복사하지 않는다.
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- 요소, 재료, 하중, 경계조건, 해석 알고리즘은 런타임 다형성 기반으로 확장한다.
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- 결과는 step/frame/field/history 개념으로 저장하여 정적, 비선형, 동적, 열전달 해석을 같은 결과 모델로 다룬다.
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- 외부 라이브러리인 MKL, TBB, HDF5는 adapter 계층 뒤에 둔다.
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- Abaqus input 호환성은 parser와 factory/registry 계층에서 관리한다.
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- shell node는 6자유도이고, 결과 자유도 순서는 `U1, U2, U3, UR1, UR2, UR3`이다.
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- 단위계는 강제하지 않는다. 입력과 reference artifact metadata에 기록된 일관 단위계를 그대로 사용한다.
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- 결과 부호와 shell output component naming은 Abaqus 규약을 따른다.
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- 경계조건은 constrained DOF 제거 방식으로 적용하고, reaction은 full vector 기준 `K_full * U_full - F_full`로 계산한다.
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- 기본 실수 precision은 `double`이다.
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- 대규모 모델을 위해 id, index, equation numbering은 int64 기반으로 설계한다.
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- Mesh quality 진단은 1차 범위에서 제외한다. 대신 singular system 진단은 필수로 제공한다.
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## Directory Structure
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```text
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include/fesa/
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analysis/ # Static, nonlinear static, dynamic, heat transfer analysis interfaces
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assembly/ # Global matrix/vector assembly and sparse pattern creation
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boundary/ # Fix, RBE2, RBE3 and future constraint objects
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core/ # Domain, AnalysisModel, AnalysisState, DofManager
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element/ # Node, Element, MITC4 and future elements
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io/ # Abaqus input parser and HDF5 result writer
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load/ # NodalLoad, PressureLoad, BodyForce
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math/ # Vector, Matrix, SparseMatrix, MKL adapter
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material/ # LinearElastic and future material models
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property/ # ShellProperty and 1D/2D/3D properties
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results/ # ResultStep, ResultFrame, FieldOutput, HistoryOutput
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util/ # Diagnostics, logging, validation helpers
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verification/ # HDF5 reference comparison utilities
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src/
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analysis/
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assembly/
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boundary/
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core/
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element/
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io/
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load/
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math/
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material/
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property/
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results/
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util/
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verification/
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tests/
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parser/
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element/
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assembly/
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solver/
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hdf5/
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reference/
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```
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The current repository may not yet contain all directories. They are intended ownership boundaries for implementation planning.
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## Core Runtime Objects
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- `Domain`: owns model definitions from input: nodes, elements, materials, properties, sets, boundary conditions, loads, and step definitions.
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- `AnalysisModel`: step-local execution view over active elements, loads, boundary conditions, properties, materials, and equation system view.
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- `AnalysisState`: owns changing physical quantities and iteration/time state such as displacement, velocity, acceleration, temperature, forces, residual, current time, increment, and element/integration-point state.
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- `Node`: stores node id, coordinates, and six DOF values in order `U1, U2, U3, UR1, UR2, UR3`.
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- `Element`: computes local stiffness, internal force/resultants, stress recovery, and connectivity.
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- `ShellMITC4Element`: 4 nodes, 24 DOF, 2x2 Gauss integration, MITC transverse shear interpolation.
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- `Material`: base contract for material behavior.
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- `Property`: element property and section data, including shell thickness.
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- `LinearElasticShellSection`: isotropic elastic shell section with thickness and shear correction.
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- `DofManager`: active DOF definitions, constrained/free DOF mapping, equation numbering, sparse pattern ownership, and full/reduced vector reconstruction.
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- `Assembler`: gathers element contributions into deterministic global sparse data.
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- `SparseMatrix`: internal sparse matrix abstraction backed by MKL-compatible CSR for v0.
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- `LinearSolver`: solver interface implemented initially by `MklPardisoSolver`.
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- `Analysis`: strategy interface for `LinearStaticAnalysis` and future nonlinear/dynamic/thermal analyses.
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- `Hdf5ResultWriter`: writes mesh, metadata, nodal results, element resultants, stresses, field output, and history output.
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- `ReferenceComparator`: compares FESA HDF5 output with stored reference HDF5 artifacts using tolerance `1e-5`.
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## State Ownership
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### Domain
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`Domain` represents parsed model definition and should not store equation ids, solver vectors, current displacement, or iteration state.
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Included:
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- nodes and elements
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- materials and properties
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- node sets and element sets
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- loads and boundary conditions
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- analysis step definitions
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### AnalysisModel
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`AnalysisModel` is built per active step. It references `Domain` objects by id or stable reference and defines what participates in the current solve.
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Included:
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- active elements
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- active loads
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- active boundary conditions
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- active property/material references
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- current equation system view
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### DofManager
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`DofManager` centralizes all equation numbering. Node or Element objects must not independently own equation ids.
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Responsibilities:
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- define active node DOFs
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- map constrained and free DOFs
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- assign equation numbers
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- provide connectivity for sparse matrix pattern generation
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- reconstruct full vectors from reduced solution vectors
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### AnalysisState
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`AnalysisState` stores mutable quantities and future nonlinear/time history extension points.
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Included:
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- displacement, velocity, acceleration
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- temperature
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- external force, internal force, residual
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- current time, increment, Newton iteration
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- element state and integration point state
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Phase 1 uses displacement-centered state only, but the structure must not block geometric nonlinear and thermal-stress extensions.
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### Results State
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Results use:
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- `ResultStep`: analysis step result group
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- `ResultFrame`: static load increment or dynamic time frame
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- `FieldOutput`: node/element field results
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- `HistoryOutput`: selected node, element, set, reaction, or energy histories
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## Data Flow
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```text
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Abaqus input file
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-> InputParser
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-> Factory/Registry object creation
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-> Domain
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-> StepDefinition loop
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-> AnalysisModel
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-> DofManager
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-> sparse pattern creation
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-> TBB parallel element stiffness computation
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-> deterministic CSR assembly
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-> constrained DOF elimination
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-> MKL PARDISO solve
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-> full displacement vector reconstruction
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-> reaction recovery by K_full * U_full - F_full
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-> TBB parallel element result recovery
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-> HDF5 step/frame/field/history output
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-> HDF5 reference comparison
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```
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## Patterns
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### Strategy
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Used for swappable analysis and numerical algorithms:
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- `Analysis`: `LinearStaticAnalysis`, `NonlinearStaticAnalysis`, `DynamicAnalysis`, `HeatTransferAnalysis`
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- `LinearSolver`: `MklPardisoSolver`, future iterative solver
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- `TimeIntegrator`: future Newmark/HHT
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- `ConvergenceCriteria`: future residual, displacement, and energy norms
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### Template Method
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`Analysis::run()` owns the high-level execution order:
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```text
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initialize
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buildAnalysisModel
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buildDofMap
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buildSparsePattern
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assemble
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applyBoundaryConditions
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solve
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updateState
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writeResults
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```
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Nonlinear static analysis will reuse this sequence inside Newton-Raphson loops. Dynamic analysis will reuse it inside time step/frame loops.
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### Factory + Registry
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Abaqus input keywords map to internal object factories:
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- `*ELEMENT, TYPE=S4` -> `MITC4ElementFactory`
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- `*ELEMENT, TYPE=S4R` -> `MITC4ElementFactory`
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- `*MATERIAL`, `*ELASTIC` -> `LinearElasticMaterialFactory`
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- `*SHELL SECTION` -> `ShellPropertyFactory`
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- `*BOUNDARY` -> `FixBoundaryFactory`
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- `*CLOAD` -> `NodalLoadFactory`
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- `*NSET`, `*ELSET` -> set registry
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Adding an element, material, load, or boundary condition should not require rewriting the parser core.
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### Adapter
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MKL, TBB, and HDF5 APIs are not exposed directly to solver core objects.
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Adapter targets:
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- `SparseMatrix`, `Vector`, `Matrix`
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- `LinearSolver`
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- `ParallelFor`
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- `ResultsWriter`
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This allows test doubles and future dependency replacement without changing solver physics code.
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### Runtime Polymorphism
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Elements, materials, loads, and boundary conditions are handled through base interfaces. Phase 1 prioritizes clarity and testability. If large-model performance requires it later, assembly internals may add type-specific batch kernels.
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## MITC4 Result Contract
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Nodal displacement output:
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```text
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node_id, U1, U2, U3, UR1, UR2, UR3
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```
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Nodal reaction output:
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```text
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node_id, RF1, RF2, RF3, RM1, RM2, RM3
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```
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Element internal force/resultant output at Gauss points:
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```text
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element_id, gauss_id, xi, eta, N11, N22, N12, M11, M22, M12, Q13, Q23
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```
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Stress output:
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```text
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element_id, gauss_id, section_point, S11, S22, S12, S13, S23
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```
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## HDF5 Layout
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```text
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/metadata
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feature_id
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solver_version
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model_id
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units
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tolerance
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reference_solver
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/mesh/nodes
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/mesh/elements/mitc4/connectivity
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/results/step_000/frame_000/nodal/displacement
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/results/step_000/frame_000/nodal/reaction
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/results/step_000/frame_000/element/forces
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/results/step_000/frame_000/element/stress
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/results/step_000/frame_000/history
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```
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## Parallelism And Sparse Assembly
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TBB parallelism is allowed for element-local computations, element force recovery, assembly precompute, and independent postprocessing.
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Global assembly must remain deterministic:
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```text
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parallel element loop
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-> thread-local sparse contribution buffers
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-> stable sort by (row, column)
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-> deterministic sum
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-> CSR arrays
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```
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The sparse matrix path must preserve 64-bit index boundaries so MKL `pardiso_64` can be used for large models.
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The solver must avoid uncontrolled MKL/TBB oversubscription. Thread-count decisions are part of analysis metadata and validation reports.
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## Validation Flow
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```text
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python scripts/validate_workspace.py
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-> CMake configure
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-> MSVC Debug build
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-> CTest
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-> feature-specific reference comparison tests
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```
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When no CMake project exists yet, validation may report the harness no-op path. Once solver code is introduced, CMake/CTest validation is mandatory.
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## Reference Artifact Flow
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Agents do not run Abaqus or Nastran.
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```text
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Human-approved Abaqus run
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-> stored HDF5 reference artifact under references/<feature>/<model-id>/
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-> FESA solver HDF5 output
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-> ReferenceComparator
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-> pass/fail using abs-or-rel 1e-5
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```
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For `mitc4-linear-static-shell`, Abaqus S4R is primary and S4 is diagnostic.
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## Performance Extension Direction
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- Sparse matrix storage is the default global system representation.
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- MKL direct solver is the first supported solver, but `LinearSolver` must allow future iterative solvers.
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- Element stiffness and result recovery should be designed for type-specific batch kernels later, but not optimized before correctness evidence exists.
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- MITC4 formulation should remain clear and reviewable until patch and reference comparisons pass.
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