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docs: Remove old blog/ and design/ directories
- Delete docs/blog/ directory (files moved to docs/src/book/blog/) - Delete docs/design/ directory (files moved to docs/src/book/design/) - Cleanup after three-tier documentation reorganization - Old locations no longer needed after migration to docs/src/ structure
This commit is contained in:
Jukka Aho
@@ -1,139 +0,0 @@
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---
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title: "Copying is Faster Than Mutating: A Counterintuitive Performance Win"
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author: "Jukka Aho"
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date: "2025-11-09"
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categories: ["Performance", "Benchmarks"]
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tags: ["immutability", "type-stability", "quick-reference"]
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description: "TL;DR version: How immutable elements are 130x faster with zero allocations"
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---
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## TL;DR
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We made our FEM code **130x faster** by making it immutable. Yes, copying everything is faster than mutating in place. No, we're not crazy. We have benchmarks.
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## The "Stupid" Idea
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**Old code (mutable Dict):**
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```julia
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element.fields[:E] = 210e9 # Mutate in place - "fast"
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```
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**New code (immutable NamedTuple):**
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```julia
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element = update(element, E=210e9) # Copy entire struct - "slow"
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```
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Which do you think is faster?
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## The Shocking Results
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```text
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Field access: 41x faster (immutable)
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Assembly loop: 130x faster (immutable)
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1000 element mesh: 120x faster (immutable)
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Memory allocations: 70,000 → 0 (immutable)
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```
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**Immutable is 100x faster AND uses zero memory.**
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## The Secret: Type Stability
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```julia
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# Dict{Symbol,Any} - Type unstable
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element.fields[:E] # Compiler: "What type is this? 🤷"
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# Cost: hash lookup + pointer chase + runtime dispatch ≈ 45 nanoseconds
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# NamedTuple{(:E,:ν),Tuple{Float64,Float64}} - Type stable
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element.fields.E # Compiler: "Float64 at offset 0. Got it."
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# Cost: inline to CPU register ≈ 1 nanosecond
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```
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**45x slower just to read a field.** Multiply by millions of accesses in FEM assembly.
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## The Compiler Magic
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When you write:
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```julia
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element = ImmutableElement((1,2,3,4), (E=210e9, ν=0.3))
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element = update(element, temperature=293.15)
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```
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The compiler sees:
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- Old element not used → reuse stack space
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- New element same size → copy is one assignment
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- All types known → inline everything
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- Result: **Zero heap allocations, SIMD vectorization, GPU-ready**
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When you write:
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```julia
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element.fields[:temperature] = 293.15
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```
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The Dict must:
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- Compute hash of `:temperature`
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- Check if key exists (pointer chasing)
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- Maybe resize Dict (heap allocation)
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- Store as `Any` → runtime dispatch on next access
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- Result: **Heap allocations, type instability, CPU-only**
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## Real-World Impact
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**Assemble 10,000 element mesh:**
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| Implementation | Time | Memory | GPU |
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|----------------|------|---------|-----|
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| Dict (mutable) | 2.4s | 450 MB, 7M allocs | ✗ |
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| NamedTuple (immutable) | **0.02s** | **0 MB, 0 allocs** | ✓ |
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Interactive vs coffee break. Million-element mesh vs out-of-memory. GPU vs CPU-only.
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## The Lesson
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Your programming intuition is from 1990s C/C++:
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- ✓ Mutation is fast ← **TRUE IN C**
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- ✓ Copying is slow ← **TRUE IN C**
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- ✗ Type doesn't matter ← **FALSE IN MODERN COMPILERS**
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2025 reality:
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- **Type stability is everything**
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- Compiler optimizes away struct copies
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- Mutation breaks type inference
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- Immutability enables GPU acceleration
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## Try It Yourself
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```bash
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git clone https://github.com/JuliaFEM/JuliaFEM.jl
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cd JuliaFEM.jl
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julia benchmarks/element_immutability_benchmark.jl
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```
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Full article: `docs/blog/immutability_performance.md`
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## Bottom Line
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We made the "wrong" choice (copy everything, mutate nothing) and got:
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- 130x faster code
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- Zero allocations
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- GPU compatibility
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- Better parallelization
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**Copying > Mutating. Immutability > Mutation. Type stability > Everything.**
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Measure, don't assume. The evidence is in the benchmarks.
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---
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*JuliaFEM 1.0 architecture, November 2025*
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*Benchmark: Intel i7-12700K, Julia 1.12.1*
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*Full results in repository*
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@@ -1,415 +0,0 @@
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# # Krylov Subspace Iterations Meet Nodal Assembly: A Revolution in Contact Mechanics
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#
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# **Author:** Jukka Aho
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# **Date:** November 2025
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# **Status:** Vision and demonstration of JuliaFEM v1.0 architecture
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# ## The Clever Combination Nobody Talks About
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#
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# Here's something that should be obvious but isn't: **Krylov subspace methods combined
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# with nodal assembly are the natural way to solve contact problems**. Yet almost every
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# FEM code does it the hard way—assembling global matrices element-by-element and then
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# complaining about memory usage.
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#
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# Why is nodal assembly + Krylov so brilliant for contact mechanics?
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#
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# 1. **Contact is inherently nodal**: When you write down the weak form of contact,
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# the constraints appear at nodes, not elements. Contact forces, gaps, friction—all
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# defined node-to-node.
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#
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# 2. **Krylov methods don't need the matrix**: They only need the matrix-vector product
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# operator. You never have to form the global matrix. Just give me `y = A*x` and I'm
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# happy.
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#
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# 3. **Nodal assembly gives you the rows**: Building matrix rows node-by-node is the
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# most natural way to incorporate nodal contact constraints. No scatter/gather
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# gymnastics needed.
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#
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# The result? **O(N) memory instead of O(N²), and contact constraints that fall out
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# naturally from the formulation.**
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#
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# Traditional FEM codes can't do this because they're locked into element assembly
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# paradigms from the 1970s. We're not.
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# ## A Broader Vision: Nodal Material Modeling
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#
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# Here's where it gets controversial. Today, everyone computes material state
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# (stress, plastic strain, damage) at **integration points**. This feels natural
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# because that's where we evaluate integrals, right?
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#
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# **Wrong. It's backwards.**
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#
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# Think about it: Why should the material state depend on the numerical integration
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# scheme? You can't get analytical solutions at the element level because you've
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# *assumed* you'll use Gaussian quadrature. The physics is now **constrained by the
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# numerical method**. That's insane!
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#
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# ### The Nodal Material State Hypothesis
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#
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# **I claim that material modeling should also be nodal**, for the same reasons contact
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# is nodal:
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#
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# 1. **Variational consistency**: The weak form naturally places material response at
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# nodes when you do it properly. Integration points are an implementation detail.
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#
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# 2. **Physical meaning**: Nodes represent physical points in space. Integration points?
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# They're mathematical constructs that change when you pick a different quadrature rule.
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#
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# 3. **Scalability**: Nodal material state scales linearly with problem size.
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# Integration point state scales with elements × points per element.
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#
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# 4. **Contact-material coupling**: When contact happens, material state at the contact
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# node matters. Why store it somewhere else and interpolate?
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#
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# ### Why Nobody Believes This (Yet)
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#
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# Every material scientist will tell you I'm crazy. "You need integration points for
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# plasticity!" "What about locking?" "This violates the patch test!"
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#
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# **I will show them they're wrong.** Not today, but it's coming. The math works out
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# when you do the variational formulation correctly. It just requires thinking beyond
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# 1970s element technology.
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#
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# For now, we focus on contact (where nodal is already accepted), and we build the
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# infrastructure that will eventually support nodal materials too.
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# ## The Krylov Advantage: Solving Unsymmetric Systems
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#
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# Here's another key insight: **Real problems are unsymmetric**.
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#
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# - **Material nonlinearity**: Tangent stiffness from plasticity is usually unsymmetric
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# - **Contact**: Contact contributions are inherently unsymmetric (one-sided constraints)
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# - **Large deformations**: Geometric nonlinearity introduces unsymmetry
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#
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# Traditional FEM codes use direct solvers (LU decomposition) which don't care about
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# symmetry but scale as O(N³). Iterative solvers designed for symmetric problems
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# (Conjugate Gradient) fail on unsymmetric systems.
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#
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# **Enter GMRES**: Generalized Minimal Residual method. It solves unsymmetric systems
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# as long as they're invertible (positive definite is enough). Combined with nodal
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# assembly, you get:
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#
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# - O(N·iter) time complexity (vs O(N³) for direct)
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# - O(N) memory (vs O(N²) for storing full matrix)
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# - Handles unsymmetry naturally
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# - Works with contact, plasticity, large deformation—everything
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# ## Demonstration: GMRES on Unsymmetric System
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#
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# Let's prove this works with a simple example: 10×10 positive definite but
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# unsymmetric system, solved with GMRES using nodal assembly pattern.
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using LinearAlgebra
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using Random
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using Printf
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println("="^70)
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println("GMRES + Nodal Assembly: Unsymmetric System Demo")
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println("="^70)
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println()
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# ### Problem Setup
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#
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# Create a positive definite but unsymmetric matrix. This mimics what you get from
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# contact mechanics or material nonlinearity.
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Random.seed!(42)
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N = 10
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# Start with symmetric positive definite
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A_sym = rand(N, N)
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A_sym = A_sym' * A_sym + 10.0 * I(N)
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# Add small unsymmetric part (mimics contact or material nonlinearity)
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# Keep it small to maintain positive definiteness
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A_unsym = rand(N, N) * 0.1
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A = A_sym + A_unsym
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# Check if positive definite (all eigenvalues positive and real)
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evals = eigvals(A)
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evals_real = real.(evals)
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all_real = all(abs.(imag.(evals)) .< 1e-10)
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all_positive = all(evals_real .> 0)
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println("Matrix properties:")
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println(" Size: $(N)×$(N)")
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println(" Symmetric: ", issymmetric(A))
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if all_real
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println(" Eigenvalues (real): ", evals_real)
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println(" All positive: ", all_positive)
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else
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println(" Eigenvalues: ", evals)
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println(" All positive: ", all_positive)
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end
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println(" Condition number: ", cond(A))
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println()
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# ### Exact Solution
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#
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# We know the answer—this lets us verify convergence.
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x_exact = Float64[i for i in 1:N]
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b = A * x_exact
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println("Exact solution: x = [1, 2, 3, ..., $N]")
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println()
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# ### Nodal Assembly Pattern
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#
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# Define the row-by-row assembly interface. In real FEM, `get_row(i)` would
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# assemble contributions from all elements connected to node `i`.
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"""
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get_row(A, i) -> Vector{Float64}
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Nodal assembly: return the i-th row of the system matrix.
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In real FEM, this would sum contributions from all elements touching node i.
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"""
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function get_row(A::Matrix{Float64}, i::Int)
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return A[i, :]
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end
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"""
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matvec_nodal(A, x) -> Vector{Float64}
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Matrix-vector product using nodal assembly.
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Computes y = A*x by assembling and using one row at a time.
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"""
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function matvec_nodal(A::Matrix{Float64}, x::Vector{Float64})
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n = length(x)
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y = zeros(Float64, n)
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for i in 1:n
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row = get_row(A, i)
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y[i] = dot(row, x)
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end
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return y
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end
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# Test the nodal matvec
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x_test = ones(N)
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y_test = matvec_nodal(A, x_test)
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y_direct = A * x_test
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println("Nodal matvec test:")
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println(" Error vs direct: ", norm(y_test - y_direct))
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println(" ✓ Nodal assembly working correctly")
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println()
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# ### GMRES Implementation
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#
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# Simplified GMRES for demonstration. Production code would use Krylov.jl,
|
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# but this shows the core algorithm clearly.
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|
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"""
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gmres_simple(A, b, x0; maxiter=100, tol=1e-10)
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Simplified GMRES using nodal assembly pattern.
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Only needs matrix-vector product—never forms full matrix.
|
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"""
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function gmres_simple(A::Matrix{Float64}, b::Vector{Float64}, x0::Vector{Float64};
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maxiter::Int=100, tol::Float64=1e-10)
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n = length(b)
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x = copy(x0)
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|
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# Arnoldi iteration vectors
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V = zeros(Float64, n, maxiter + 1)
|
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H = zeros(Float64, maxiter + 1, maxiter)
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|
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# Initial residual
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r = b - matvec_nodal(A, x)
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β = norm(r)
|
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V[:, 1] = r / β
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|
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# Store residual history
|
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residuals = Float64[β]
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|
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println("GMRES iteration:")
|
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@printf(" Initial residual: %.6e\n", β)
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println()
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|
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for j in 1:maxiter
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# Arnoldi: build orthonormal basis for Krylov subspace
|
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w = matvec_nodal(A, V[:, j])
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|
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# Modified Gram-Schmidt orthogonalization
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for i in 1:j
|
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H[i, j] = dot(w, V[:, i])
|
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w -= H[i, j] * V[:, i]
|
||||
end
|
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|
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H[j+1, j] = norm(w)
|
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|
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if H[j+1, j] > 1e-14
|
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V[:, j+1] = w / H[j+1, j]
|
||||
end
|
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|
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# Solve least squares problem: min ||β*e₁ - H*y||
|
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e1 = zeros(j + 1)
|
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e1[1] = β
|
||||
|
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# Use QR factorization (simple, stable)
|
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Hj = H[1:j+1, 1:j]
|
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y = Hj \ e1
|
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|
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# Update solution
|
||||
x_new = x0 + V[:, 1:j] * y
|
||||
|
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# Compute residual
|
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r = b - matvec_nodal(A, x_new)
|
||||
res_norm = norm(r)
|
||||
push!(residuals, res_norm)
|
||||
|
||||
reduction = 100.0 * (1.0 - res_norm / β)
|
||||
@printf(" Iteration %3d: residual = %.6e (reduction: %.2f%%)\n",
|
||||
j, res_norm, reduction)
|
||||
|
||||
if res_norm < tol
|
||||
println()
|
||||
println(" ✓ Converged in $j iterations")
|
||||
return x_new, j, res_norm, residuals
|
||||
end
|
||||
|
||||
x = x_new
|
||||
end
|
||||
|
||||
println()
|
||||
println(" ⚠ Did not converge in $maxiter iterations")
|
||||
return x, maxiter, norm(b - matvec_nodal(A, x)), residuals
|
||||
end
|
||||
|
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# ### Solve with GMRES
|
||||
|
||||
x0 = zeros(N)
|
||||
x_solution, iters, final_res, res_history = gmres_simple(A, b, x0, maxiter=50, tol=1e-10)
|
||||
|
||||
println()
|
||||
|
||||
# ### Verification
|
||||
|
||||
error_abs = norm(x_solution - x_exact)
|
||||
error_rel = error_abs / norm(x_exact)
|
||||
|
||||
println("="^70)
|
||||
println("Verification Results")
|
||||
println("="^70)
|
||||
println()
|
||||
println("Solution comparison:")
|
||||
println(" Exact: ", join([@sprintf("%.3f", x) for x in x_exact], ", "))
|
||||
println(" Computed: ", join([@sprintf("%.3f", x) for x in x_solution], ", "))
|
||||
println()
|
||||
println("Error metrics:")
|
||||
@printf(" Absolute error: %.6e\n", error_abs)
|
||||
@printf(" Relative error: %.6e\n", error_rel)
|
||||
@printf(" Final residual: %.6e\n", final_res)
|
||||
println(" Iterations: $iters")
|
||||
println()
|
||||
|
||||
if error_rel < 1e-6
|
||||
println("✅ VERIFICATION PASSED")
|
||||
else
|
||||
println("❌ VERIFICATION FAILED")
|
||||
end
|
||||
println()
|
||||
|
||||
# ## Key Insights from This Demonstration
|
||||
|
||||
println("="^70)
|
||||
println("Why This Matters for JuliaFEM v1.0")
|
||||
println("="^70)
|
||||
println()
|
||||
|
||||
println("""
|
||||
1. **Unsymmetric systems are solved naturally**
|
||||
- Matrix is positive definite but unsymmetric ✓
|
||||
- GMRES converges in $iters iterations ✓
|
||||
- Solution accurate to 1e-$(Int(round(-log10(error_rel)))) relative error ✓
|
||||
- This is what real contact/plasticity problems look like
|
||||
|
||||
2. **Nodal assembly works perfectly**
|
||||
- Never formed global matrix explicitly
|
||||
- Only used get_row(i) interface—one row at a time
|
||||
- Memory: O(N) instead of O(N²)
|
||||
- In real FEM: get_row(i) assembles from elements touching node i
|
||||
|
||||
3. **Krylov methods scale**
|
||||
- This demo: $N×$N system, $iters iterations
|
||||
- Scales to millions: 1M×1M system, ~100 iterations typical
|
||||
- Time: O(N·iter) vs O(N³) for direct solvers
|
||||
- Memory: O(N) vs O(N²) for storing full matrix
|
||||
|
||||
4. **Contact mechanics fits naturally**
|
||||
- Contact constraints modify rows for contact nodes
|
||||
- No special treatment needed—just part of get_row(i)
|
||||
- Nodal formulation, nodal assembly, nodal constraints
|
||||
- Everything at the same level—beautiful!
|
||||
|
||||
5. **Foundation for future: Nodal materials**
|
||||
- Same infrastructure supports nodal material state
|
||||
- Material history at nodes, not integration points
|
||||
- Physically meaningful, numerically efficient
|
||||
- Controversial today, obvious tomorrow
|
||||
""")
|
||||
|
||||
println("="^70)
|
||||
println()
|
||||
|
||||
# ## The Path Forward
|
||||
#
|
||||
# This demonstration proves the concept works. For JuliaFEM v1.0:
|
||||
#
|
||||
# ### Immediate (Months 1-3)
|
||||
# - Implement `get_row(node_id, elements)` for real element assembly
|
||||
# - Integrate Krylov.jl for production-quality GMRES
|
||||
# - Add preconditioning (Jacobi, ILU) for faster convergence
|
||||
# - Handle contact constraints in row modification
|
||||
#
|
||||
# ### Near-term (Months 4-6)
|
||||
# - Matrix-free operators with GPU acceleration
|
||||
# - Distributed assembly across MPI ranks
|
||||
# - Strong scaling studies (speedup vs number of processes)
|
||||
# - Contact mechanics validation (Hertz, patch tests)
|
||||
#
|
||||
# ### Long-term (Months 7-12)
|
||||
# - Nodal material state experiments (plasticity at nodes)
|
||||
# - Compare integration-point vs nodal material models
|
||||
# - Publish results showing nodal materials work
|
||||
# - Prove the material scientists wrong 😎
|
||||
#
|
||||
# ### Vision (Beyond v1.0)
|
||||
# - Complete nodal formulation: geometry, contact, materials
|
||||
# - Demonstrate 10M DOF contact problems on multi-GPU clusters
|
||||
# - Show that element-centric thinking was 20th century
|
||||
# - Lead the field into 21st century FEM
|
||||
|
||||
# ## Conclusion
|
||||
#
|
||||
# **Krylov subspace iterations + nodal assembly is not just a technical choice—it's
|
||||
# the philosophically correct approach to contact mechanics.**
|
||||
#
|
||||
# Contact is nodal. Constraints are nodal. Solution method should be nodal.
|
||||
#
|
||||
# Traditional FEM uses element assembly because that's how it was done in 1970
|
||||
# (before iterative solvers were practical). We're not constrained by history.
|
||||
#
|
||||
# **And soon we'll show that materials should be nodal too.** The math works.
|
||||
# The numerics work (as shown in this demo). The physics makes sense.
|
||||
#
|
||||
# It just requires thinking clearly about what the weak form actually says,
|
||||
# rather than cargo-culting element assembly from outdated textbooks.
|
||||
#
|
||||
# *Welcome to JuliaFEM v1.0. Where we assemble by nodes, solve with Krylov,
|
||||
# and refuse to be constrained by integration point theology.*
|
||||
#
|
||||
# ---
|
||||
#
|
||||
# **References:**
|
||||
# - Saad, Y. (2003). *Iterative Methods for Sparse Linear Systems*. SIAM.
|
||||
# - Wriggers, P. (2006). *Computational Contact Mechanics*. Springer.
|
||||
# - Aho, J. (2025). "Why Material Scientists Are Wrong About Integration Points"
|
||||
# (forthcoming, controversy expected 😉)
|
||||
|
||||
println("Demo complete. For production code, see:")
|
||||
println(" - demos/krylov_mpi_gpu_demo.jl (distributed multi-GPU solver)")
|
||||
println(" - docs/book/nodal_assembly_multigpu.md (strategic document)")
|
||||
println()
|
||||
@@ -1,491 +0,0 @@
|
||||
---
|
||||
title: "Element Immutability: Design Decision and Rationale"
|
||||
author: "Jukka Aho"
|
||||
date: "2025-11-09"
|
||||
status: "IMPLEMENTED"
|
||||
phase: "Phase 1B"
|
||||
categories: ["Design", "Architecture"]
|
||||
tags: ["immutability", "performance", "design-decision"]
|
||||
benchmark: "benchmarks/element_immutability_benchmark.jl"
|
||||
---
|
||||
|
||||
## Executive Summary
|
||||
|
||||
JuliaFEM 1.0 adopts **immutable elements with type-stable fields** as a core architectural decision. While this appears counterintuitive (requiring element copies instead of in-place mutation), benchmarks demonstrate **40-130x performance improvement** over the mutable Dict-based approach.
|
||||
|
||||
**Key Results:**
|
||||
|
||||
- Field access: **40x faster** (1ns vs 45ns per read)
|
||||
- Assembly loop: **130x faster** (9ns vs 1,124ns per element)
|
||||
- Large mesh: **120x faster** (0.01ms vs 1.2ms for 1000 elements)
|
||||
- Memory: **Zero allocations** in hot path (vs 70,000 allocations)
|
||||
- GPU/HPC: **Compatible** (all bits types vs pointers)
|
||||
|
||||
---
|
||||
|
||||
## The Counterintuitive API Change
|
||||
|
||||
### Old API (Mutable, Dict-based)
|
||||
|
||||
```julia
|
||||
# Create element with mutable fields
|
||||
element = Element(Tet10, [1,2,3,4,5,6,7,8,9,10])
|
||||
|
||||
# Add fields dynamically
|
||||
update!(element, "E", 210e9)
|
||||
update!(element, "ν", 0.3)
|
||||
update!(element, "temperature", 293.15)
|
||||
|
||||
# Fields stored in Dict{Symbol,Any} - type unstable!
|
||||
element.fields # → Dict(:E => 210e9, :ν => 0.3, :temperature => 293.15)
|
||||
```
|
||||
|
||||
**Pros:** Familiar, flexible, feels efficient (no copies)
|
||||
**Cons:** Type-unstable, 100ns Dict lookup overhead, no GPU support
|
||||
|
||||
### New API (Immutable, Type-stable)
|
||||
|
||||
```julia
|
||||
# Create element with type-stable fields
|
||||
element = Element(Lagrange{Tetrahedron,2}, (1,2,3,4,5,6,7,8,9,10),
|
||||
fields=(E=210e9, ν=0.3))
|
||||
|
||||
# Update returns NEW element (immutable)
|
||||
element = update(element, temperature=293.15)
|
||||
|
||||
# Fields stored in NamedTuple - type stable!
|
||||
element.fields # → (E=210e9, ν=0.3, temperature=293.15)
|
||||
typeof(element.fields) # → NamedTuple{(:E,:ν,:temperature), Tuple{Float64,Float64,Float64}}
|
||||
```
|
||||
|
||||
**Pros:** Type-stable, 1ns access, GPU-compatible, zero allocations
|
||||
**Cons:** Requires element copy (but compiler optimizes away!)
|
||||
|
||||
---
|
||||
|
||||
## Why Immutability Wins
|
||||
|
||||
### 1. Type Stability is Everything
|
||||
|
||||
In FEM assembly, field access happens **millions of times**:
|
||||
|
||||
```julia
|
||||
# Assembly loop: 10 integration points × 1000 elements = 10,000 field accesses
|
||||
for element in mesh
|
||||
for ip in integration_points
|
||||
E = element.fields[:E] # Dict lookup: 45ns EACH TIME
|
||||
ν = element.fields[:ν] # Another 45ns
|
||||
# ... compute stiffness
|
||||
end
|
||||
end
|
||||
```
|
||||
|
||||
**Mutable (Dict):** `45ns × 20,000 = 900µs` (Dict lookups)
|
||||
**Immutable (Tuple):** `1ns × 20,000 = 20µs` (direct access)
|
||||
|
||||
**Result:** 45x speedup just from field access!
|
||||
|
||||
### 2. Compiler Optimizations
|
||||
|
||||
Type-stable code enables:
|
||||
|
||||
- **Inlining:** Field access becomes single instruction
|
||||
- **SIMD:** Vectorization across multiple elements
|
||||
- **Constant propagation:** Compiler knows exact types
|
||||
- **Stack allocation:** No heap allocations for small structs
|
||||
|
||||
Example: Assembly loop with immutable elements **completely inlines**:
|
||||
|
||||
```julia
|
||||
# Before optimization (conceptual):
|
||||
E = element.fields.E # Field access
|
||||
λ = E * ν / ... # Material computation
|
||||
|
||||
# After optimization (actual machine code):
|
||||
λ = 210e9 * 0.3 / ... # Constants folded, direct computation!
|
||||
```
|
||||
|
||||
### 3. Zero Allocations
|
||||
|
||||
**Mutable elements:** Every field update allocates
|
||||
|
||||
```julia
|
||||
julia> @benchmark update!(element, "temperature", 293.15)
|
||||
Allocs: 100 # One allocation per update!
|
||||
Memory: 1600 bytes
|
||||
```
|
||||
|
||||
**Immutable elements:** Stack allocation only
|
||||
|
||||
```julia
|
||||
julia> @benchmark element = update(element, temperature=293.15)
|
||||
Allocs: 0 # Compiler optimizes to stack!
|
||||
Memory: 0 bytes
|
||||
```
|
||||
|
||||
**Why?** Modern Julia compiler recognizes stack-only pattern and eliminates heap allocations entirely.
|
||||
|
||||
### 4. GPU/HPC Compatibility
|
||||
|
||||
**Mutable elements with Dict:**
|
||||
|
||||
```julia
|
||||
struct MutableElement
|
||||
fields::Dict{Symbol,Any} # POINTER → cannot transfer to GPU
|
||||
end
|
||||
```
|
||||
|
||||
**Immutable elements with NamedTuple:**
|
||||
|
||||
```julia
|
||||
struct ImmutableElement{F}
|
||||
fields::F # All bits types → can transfer to GPU!
|
||||
end
|
||||
```
|
||||
|
||||
GPU kernels require:
|
||||
|
||||
- No pointers (CPU memory → GPU memory not allowed)
|
||||
- No dynamic dispatch (GPU can't call CPU functions)
|
||||
- All data as bits types (can be copied to GPU)
|
||||
|
||||
Only immutable, type-stable elements satisfy these requirements.
|
||||
|
||||
---
|
||||
|
||||
## Benchmark Results
|
||||
|
||||
Run: `julia --project=. benchmarks/element_immutability_benchmark.jl`
|
||||
|
||||
### Field Access (1000 reads)
|
||||
|
||||
| Implementation | Time/read | Speedup |
|
||||
|---------------|-----------|---------|
|
||||
| Mutable (Dict) | 45ns | 1x (baseline) |
|
||||
| Immutable (Tuple) | 1ns | **40x** |
|
||||
|
||||
### Field Update (100 writes)
|
||||
|
||||
| Implementation | Time/update | Allocations |
|
||||
|---------------|-------------|-------------|
|
||||
| Mutable (mutate) | 12ns | 100 |
|
||||
| Immutable (copy) | 0.03ns | 0 |
|
||||
|
||||
**Surprise:** Creating new structs is **400x faster** than mutating Dict!
|
||||
|
||||
### Assembly Loop (single element)
|
||||
|
||||
| Implementation | Time | Allocations |
|
||||
|---------------|------|-------------|
|
||||
| Mutable | 1,124ns | 69 |
|
||||
| Immutable | 9ns | 0 |
|
||||
|
||||
**Speedup:** **130x faster**
|
||||
|
||||
### Large Mesh (1000 elements)
|
||||
|
||||
| Implementation | Time | Memory |
|
||||
|----------------|--------|--------|
|
||||
| Mutable | 1.2ms | 1.1 MB |
|
||||
| Immutable | 0.01ms | 0 KB |
|
||||
|
||||
**Speedup:** **120x faster**, zero allocations
|
||||
|
||||
---
|
||||
|
||||
## Common Misconceptions
|
||||
|
||||
### "Copying structs is expensive"
|
||||
|
||||
**False.** Small structs (< 128 bytes) are stack-allocated:
|
||||
|
||||
```julia
|
||||
# This looks like it copies:
|
||||
new_element = update(old_element, temperature=300.0)
|
||||
|
||||
# But actually compiles to:
|
||||
# mov rax, [old_fields] # Load old fields
|
||||
# mov [new_fields], rax # Store to new location (STACK!)
|
||||
# mov [new_fields+24], 300.0 # Update temperature field
|
||||
```
|
||||
|
||||
No heap allocation, no GC pressure, just register/stack operations.
|
||||
|
||||
### "I need mutable fields for time integration"
|
||||
|
||||
**False.** Time-varying fields should be stored separately:
|
||||
|
||||
```julia
|
||||
# Bad: Time history in element (mutable)
|
||||
element.fields[:temperature] = [293.15, 300.0, 310.0] # Vector → allocates
|
||||
|
||||
# Good: Time history separate (immutable element)
|
||||
struct TimeHistory
|
||||
times::Vector{Float64}
|
||||
temperatures::Vector{Float64}
|
||||
end
|
||||
|
||||
element = Element(..., fields=(E=210e9, ν=0.3)) # Constant
|
||||
history = TimeHistory([0.0, 1.0, 2.0], [293.15, 300.0, 310.0]) # Mutable separately
|
||||
```
|
||||
|
||||
Element stays immutable (fast), history is mutable (when needed).
|
||||
|
||||
### "Functional programming is slow"
|
||||
|
||||
**False in Julia.** Persistent data structures (like Clojure) are slow because they allocate on heap. Julia's immutable structs are stack-allocated and get optimized away by compiler.
|
||||
|
||||
```julia
|
||||
# This code:
|
||||
e1 = Element(..., fields=(E=210e9,))
|
||||
e2 = update(e1, ν=0.3)
|
||||
e3 = update(e2, ρ=7850.0)
|
||||
|
||||
# Compiles to:
|
||||
# Stack allocation:
|
||||
# [E] [ν] [ρ]
|
||||
# 210e9 0.3 7850.0 ← Single struct on stack!
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Design Patterns
|
||||
|
||||
### Pattern 1: Initialization with Fields
|
||||
|
||||
```julia
|
||||
# Create element with all known fields upfront
|
||||
element = Element(Lagrange{Triangle,1}, (1,2,3),
|
||||
fields=(E=210e9, ν=0.3, thickness=0.01))
|
||||
```
|
||||
|
||||
### Pattern 2: Progressive Updates
|
||||
|
||||
```julia
|
||||
# Start with minimal fields
|
||||
element = Element(Lagrange{Triangle,1}, (1,2,3), fields=(E=210e9,))
|
||||
|
||||
# Add fields as computed (returns new element)
|
||||
element = update(element, ν=0.3)
|
||||
element = update(element, temperature=compute_temperature(element))
|
||||
```
|
||||
|
||||
### Pattern 3: Batch Updates
|
||||
|
||||
```julia
|
||||
# Update multiple fields at once (efficient!)
|
||||
element = update(element,
|
||||
temperature=300.0,
|
||||
stress=(σ_xx=100e6, σ_yy=50e6, σ_xy=0.0),
|
||||
plastic_strain=0.001)
|
||||
```
|
||||
|
||||
### Pattern 4: Field Inheritance
|
||||
|
||||
```julia
|
||||
# Reuse fields from another element
|
||||
base_fields = (E=210e9, ν=0.3, ρ=7850.0)
|
||||
|
||||
elem1 = Element(Lagrange{Triangle,1}, (1,2,3), fields=base_fields)
|
||||
elem2 = Element(Lagrange{Triangle,1}, (4,5,6), fields=base_fields)
|
||||
# Both share same type → compiler can optimize across elements!
|
||||
```
|
||||
|
||||
### Pattern 5: Conditional Fields
|
||||
|
||||
```julia
|
||||
# Different elements can have different field sets
|
||||
function create_element(topology, conn, use_plasticity)
|
||||
if use_plasticity
|
||||
fields = (E=210e9, ν=0.3, yield_stress=250e6)
|
||||
else
|
||||
fields = (E=210e9, ν=0.3)
|
||||
end
|
||||
return Element(topology, conn, fields=fields)
|
||||
end
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Migration Guide (Old → New)
|
||||
|
||||
### Old Code (Mutable)
|
||||
|
||||
```julia
|
||||
# Create element
|
||||
element = Element(Tet10, [1,2,3,4,5,6,7,8,9,10])
|
||||
|
||||
# Add fields
|
||||
update!(element, "E", 210e9)
|
||||
update!(element, "ν", 0.3)
|
||||
|
||||
# Access fields
|
||||
E = element.fields[:E]
|
||||
```
|
||||
|
||||
### New Code (Immutable)
|
||||
|
||||
```julia
|
||||
# Create element with fields
|
||||
element = Element(Lagrange{Tetrahedron,2}, (1,2,3,4,5,6,7,8,9,10),
|
||||
fields=(E=210e9, ν=0.3))
|
||||
|
||||
# Update returns new element
|
||||
element = update(element, temperature=293.15)
|
||||
|
||||
# Access fields (type-stable!)
|
||||
E = element.fields.E
|
||||
```
|
||||
|
||||
### Key Changes
|
||||
|
||||
1. **Creation:** Include fields at construction time
|
||||
2. **Update:** Assign result: `element = update(element, ...)`
|
||||
3. **Access:** Use dot syntax: `element.fields.E` not `element.fields[:E]`
|
||||
4. **Types:** Prefer NamedTuple over Dict: `(E=210e9,)` not `Dict(:E => 210e9)`
|
||||
|
||||
---
|
||||
|
||||
## Implementation Details
|
||||
|
||||
### Element Definition
|
||||
|
||||
```julia
|
||||
struct Element{N,NIP,F,B} <: AbstractElement{F,B}
|
||||
id::UInt
|
||||
connectivity::NTuple{N,UInt} # Immutable tuple
|
||||
integration_points::NTuple{NIP,IP} # Immutable tuple
|
||||
fields::F # Type-stable! (NamedTuple or struct)
|
||||
basis::B # Type-stable!
|
||||
end
|
||||
```
|
||||
|
||||
### Update Implementation
|
||||
|
||||
```julia
|
||||
function update(element::Element, new_fields::NamedTuple)
|
||||
# Merge old and new fields
|
||||
updated_fields = merge(element.fields, new_fields)
|
||||
|
||||
# Create new element (same connectivity, new fields)
|
||||
return Element{N,NIP,typeof(updated_fields),B}(
|
||||
element.id,
|
||||
element.connectivity,
|
||||
element.integration_points,
|
||||
updated_fields,
|
||||
element.basis
|
||||
)
|
||||
end
|
||||
|
||||
# Convenience syntax
|
||||
update(element; kwargs...) = update(element, values(kwargs))
|
||||
```
|
||||
|
||||
### Memory Layout
|
||||
|
||||
```julia
|
||||
# Old mutable element (heap):
|
||||
MutableElement
|
||||
├── id: UInt64 (8 bytes on stack)
|
||||
├── connectivity: Vector (24 bytes pointer → heap)
|
||||
└── fields: Dict (24 bytes pointer → heap)
|
||||
↓
|
||||
[Heap allocations]
|
||||
|
||||
# New immutable element (stack):
|
||||
ImmutableElement
|
||||
├── id: UInt64 (8 bytes)
|
||||
├── connectivity: Tuple (40 bytes, inline)
|
||||
└── fields: NamedTuple (24 bytes, inline)
|
||||
├── E: Float64 (8 bytes)
|
||||
├── ν: Float64 (8 bytes)
|
||||
└── ρ: Float64 (8 bytes)
|
||||
|
||||
Total: 72 bytes, all on stack, cache-friendly!
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Future Work
|
||||
|
||||
### Phase 2: Time-Varying Fields
|
||||
|
||||
Currently, fields are static. For time integration:
|
||||
|
||||
```julia
|
||||
# Option 1: External time history (current approach)
|
||||
struct TimeVaryingField{T}
|
||||
times::Vector{Float64}
|
||||
values::Vector{T}
|
||||
end
|
||||
|
||||
# Element stays immutable
|
||||
element = Element(..., fields=(E=210e9,))
|
||||
temperature_history = TimeVaryingField([0.0, 1.0], [293.15, 300.0])
|
||||
|
||||
# Option 2: Functional fields (future)
|
||||
element = Element(..., fields=(
|
||||
E=210e9,
|
||||
temperature=t -> 293.15 + 10.0*t # Function of time
|
||||
))
|
||||
```
|
||||
|
||||
### Phase 3: GPU Kernels
|
||||
|
||||
With immutable elements, GPU assembly becomes possible:
|
||||
|
||||
```julia
|
||||
using CUDA
|
||||
|
||||
# Transfer elements to GPU (all bits types!)
|
||||
d_elements = CuArray(elements)
|
||||
d_nodes = CuArray(nodes)
|
||||
|
||||
# GPU kernel (parallel over elements)
|
||||
@cuda threads=256 blocks=ceil(Int, n_elements/256) assemble_kernel!(
|
||||
d_K, d_elements, d_nodes
|
||||
)
|
||||
|
||||
# No CPU synchronization needed - immutable = no race conditions!
|
||||
```
|
||||
|
||||
### Phase 4: SIMD Vectorization
|
||||
|
||||
Type-stable elements enable SIMD:
|
||||
|
||||
```julia
|
||||
# Process 4 elements simultaneously (AVX2)
|
||||
function assemble_batch(elements::NTuple{4,Element})
|
||||
@simd for i in 1:4
|
||||
E = elements[i].fields.E # Vectorized load!
|
||||
# ... assembly computation
|
||||
end
|
||||
end
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Conclusion
|
||||
|
||||
**Immutability is not a compromise - it's an optimization.**
|
||||
|
||||
Key takeaways:
|
||||
|
||||
1. **Type stability dominates performance** in tight loops
|
||||
2. **Compiler optimizations** make immutability free
|
||||
3. **Zero allocations** eliminate GC pressure
|
||||
4. **GPU/HPC compatibility** requires immutability
|
||||
5. **Functional patterns** are fast in Julia
|
||||
|
||||
The 40-130x speedup speaks for itself. Immutable elements are the foundation for high-performance, GPU-ready FEM in JuliaFEM 1.0.
|
||||
|
||||
---
|
||||
|
||||
## References
|
||||
|
||||
- Benchmark: `benchmarks/element_immutability_benchmark.jl`
|
||||
- Implementation: `src/elements/elements.jl`
|
||||
- Discussion: GitHub Issue #XXX (TBD)
|
||||
- Related: `docs/design/FIELDS_DESIGN.md` (Phase 3)
|
||||
|
||||
**Last Updated:** November 9, 2025
|
||||
Reference in New Issue
Block a user