JuliaFEM.jl/scripts

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:

1. Edit element catalog in scripts/generate_lagrange_basis.jl
2. Run generation script
3. Review src/basis/lagrange_generated.jl
4. Run tests: julia --project=. -e 'using Pkg; Pkg.test()'
5. 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 theory
• src/basis/lagrange_generator.jl - Symbolic generation engine
• llm/VISION_2.0.md - Overall project architecture