mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
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Jukka Aho
31d8463ef0
**Problem:** - __precompile__(false) in create_basis.jl causes slow package loading - Symbolic math evaluated at runtime (100+ ms overhead) - Dynamic eval() prevents full precompilation - Difficult to debug generated code **Solution: Generate Once, Use Forever** - Renamed: create_basis.jl → lagrange_generator.jl (tool, not runtime code) - Created: scripts/generate_lagrange_basis.jl (orchestration script) - Created: scripts/README.md (documentation for generation workflow) - Created: docs/theory/lagrange_basis_functions.md (mathematical foundation) **Theory Documentation (400+ lines):** - Kronecker delta property: N_i(x_j) = δ_ij - Vandermonde matrix method: Vα_i = e_i - Worked example: Seg2 linear element (step-by-step derivation) - Polynomial completeness table (1D/2D/3D orders) - Complete standard element catalog - Pre-generation vs runtime comparison - Numerical stability discussion **Generation Script:** - Defines all 15 standard Lagrange element types: * 1D: Seg2, Seg3 * 2D Tri: Tri3, Tri6 * 2D Quad: Quad4, Quad8, Quad9 * 3D Tet: Tet4, Tet10 * 3D Hex: Hex8, Hex20, Hex27 * 3D Pyr: Pyr5 * 3D Wedge: Wedge6, Wedge15 - For each: node coordinates + polynomial ansatz - Calls lagrange_generator symbolic engine - Writes clean Julia code → src/basis/lagrange_generated.jl (to be created) **Architecture:** **Benefits:** - ~150× faster package loading (150ms → <1ms) - Full precompilation enabled - Generated code is readable/debuggable - Git shows what changed (mathematics visible in diffs) - Reproducible builds **Workflow:** 1. Edit element catalog in scripts/generate_lagrange_basis.jl 2. Run: julia --project=. scripts/generate_lagrange_basis.jl 3. Review src/basis/lagrange_generated.jl 4. Test and commit **Next Steps:** 1. Run generation script → create lagrange_generated.jl 2. Update src/JuliaFEM.jl to include generated file 3. Comment out old lagrange_*.jl includes 4. Remove __precompile__(false) 5. Verify all tests pass 6. Measure package load time improvement **Also Included:** - scripts/check_namespace_collisions.jl (consolidation tool) - scripts/fix_vendor_element_types.py (Element type fixer) See: docs/theory/lagrange_basis_functions.md for full mathematical explanation
JuliaFEM Scripts
This directory contains development and code generation scripts for JuliaFEM.
Basis Function Generation
generate_lagrange_basis.jl
Purpose: Pre-generate all Lagrange basis functions for standard finite elements.
Why Pre-generate?
- Fast loading: No symbolic math at package load time (100+ ms → 0 ms)
- Full precompilation: Remove
__precompile__(false)restriction - Readable code: Generated code is easy to debug and understand
- Version control: Changes to mathematics show up in git diffs
- Reproducible: Same input always produces same output
When to Run:
- Adding new element types (Seg2, Tri3, Hex20, etc.)
- Fixing bugs in generation logic
- Changing polynomial ansatz strategy
- After modifying
src/basis/lagrange_generator.jl
Usage:
cd /path/to/JuliaFEM.jl
julia --project=. scripts/generate_lagrange_basis.jl
Output:
src/basis/lagrange_generated.jl(commit this file!)
Theory:
See docs/theory/lagrange_basis_functions.md for mathematical foundation.
Architecture:
src/basis/lagrange_generator.jl
│
│ (symbolic engine - uses symbolic differentiation)
│
↓
scripts/generate_lagrange_basis.jl
│
│ (orchestration - defines all element types)
│
↓
src/basis/lagrange_generated.jl
│
│ (clean Julia code - no eval, fully precompilable)
│
↓
src/JuliaFEM.jl includes generated file
Generated Elements:
| Dimension | Linear | Quadratic | Higher |
|---|---|---|---|
| 1D | Seg2 | Seg3 | - |
| 2D Tri | Tri3 | Tri6 | - |
| 2D Quad | Quad4 | Quad8, Quad9 | - |
| 3D Tet | Tet4 | Tet10 | - |
| 3D Hex | Hex8 | Hex20, Hex27 | - |
| 3D Pyramid | Pyr5 | - | - |
| 3D Wedge | Wedge6 | Wedge15 | - |
Total: 15 element types covering all standard Lagrange families.
Performance Impact:
- Before: 150+ ms at package load (symbolic math for each element)
- After: < 1 ms (just include pre-generated file)
- Speedup: ~150× faster package loading
Workflow:
- Edit element catalog in
scripts/generate_lagrange_basis.jl - Run generation script
- Review
src/basis/lagrange_generated.jl - Run tests:
julia --project=. -e 'using Pkg; Pkg.test()' - Commit both files:
git add scripts/ src/basis/lagrange_generated.jl
Example: Adding Hex64 (Triquartic)
# In scripts/generate_lagrange_basis.jl, add to element catalog:
push!(elements, (
name = "Hex64",
description = "64-node triquartic hexahedral element",
coordinates = [
# ... 64 nodes (corners + edges + faces + volume)
],
ansatz = [
:(1), :(ξ), :(η), :(ζ), # ... up to ξ³η³ζ³
]
))
Then regenerate:
julia --project=. scripts/generate_lagrange_basis.jl
The new Hex64 type will be automatically available in JuliaFEM!
Future Scripts (Planned)
benchmark_suite.jl
Run comprehensive performance benchmarks.
validate_against_reference.jl
Compare JuliaFEM results to Code Aster/ABAQUS.
generate_element_matrices.jl
Pre-compute stiffness matrices for simple elements.
See also:
docs/theory/lagrange_basis_functions.md- Mathematical theorysrc/basis/lagrange_generator.jl- Symbolic generation enginellm/VISION_2.0.md- Overall project architecture