RESEARCH QUESTION: Should JuliaFEM use hand-calculated derivatives or AD?
Created comprehensive benchmark comparing:
- Manual: Hand-calculated derivatives (traditional FEM)
- AD: Tensors.jl gradient() (automatic differentiation)
RESULTS (AMD Ryzen 9, Julia 1.12.1):
- Manual: 8.7 ns, 0 allocations
- AD: 268.1 ns, 0 allocations
- AD is 30× SLOWER than manual
KEY FINDINGS:
✅ Both achieve zero allocations (Tensors.jl is well-optimized)
❌ AD has 30× compute overhead from dual number arithmetic
⚠️ In assembly loops: millions of calls = 10+ seconds extra per solve
RECOMMENDATION:
- Keep manual derivatives for common elements (Tet10, Hex8, Quad4, etc.)
- Use AD for prototyping and rare elements
- Unit test manual vs AD to catch errors
- Future: Generate derivatives symbolically (Symbolics.jl)
WHY NOT AD EVERYWHERE?
Assembly is hottest path in FEM. 30× overhead = unacceptable for
production code. Users will notice the performance difference.
WHY NOT ABANDON AD?
- Excellent for prototyping
- Required for exotic bases (NURBS)
- Perfect for unit testing manual derivatives
- Zero allocations impressive
Files:
- benchmarks/tet10_derivatives_benchmark.jl (runnable benchmark)
- docs/benchmarks/shape_function_derivatives_ad_vs_manual.md (analysis)
Dependencies added: BenchmarkTools
This answers the research question definitively with data.
Jukka Aho