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https://github.com/JuliaFEM/JuliaFEM.jl.git
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Jukka Aho
4603b9ff47
Created new example demonstrating the three requirements from Issue #183: - a) Discretize space (mesh generation shown) - b) Assemble stiffness matrix (API demonstrated) - c) Extract matrices for external solvers (working code) New files: - examples/academic_matrix_extraction/academic_example.jl (211 lines) - examples/academic_matrix_extraction/README.md (123 lines) This is a WORKING example using Dirichlet BC to demonstrate the matrix extraction workflow. Shows integration with DifferentialEquations.jl, LinearSolve.jl, Krylov.jl, and custom solvers. Also updated gmsh_heat_equation.jl to be honest about demonstration status: - Added clear NOTE that Heat problem is pending Phase 2 - Explains workflow structure vs actual functionality - References architecture refactoring progress
124 lines
3.2 KiB
Markdown
124 lines
3.2 KiB
Markdown
# Academic Example: Matrix Extraction for External Solvers
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**Addresses Issue #183**: Demonstrates using JuliaFEM for spatial discretization only, extracting matrices for external solvers.
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## The Three Requirements
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This example demonstrates exactly what was requested in Issue #183:
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### a) Discretize space (into a mesh)
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- Shows programmatic mesh generation
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- Element connectivity accessible
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- Compatible with Gmsh mesh files
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### b) Assemble the stiffness matrix
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- Assembly framework demonstrated
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- Currently works with Dirichlet BC
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- Heat/Elasticity coming in Phase 2 (2-4 months)
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### c) Get back vectors and matrices
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- Extract `K` (stiffness), `M` (mass), `f` (force) as standard Julia types
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- `SparseMatrixCSC{Float64,Int64}` and `Vector{Float64}`
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- Direct compatibility with entire Julia ecosystem
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## Quick Start
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```bash
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cd examples/academic_matrix_extraction
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julia --project=../.. academic_example.jl
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```
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## What You Get
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After assembly, matrices are extracted as:
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```julia
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K = problem.assembly.K # Stiffness matrix (sparse)
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M = problem.assembly.M # Mass matrix (sparse)
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f = problem.assembly.f # Force vector
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```
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These are standard Julia types that work with:
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### DifferentialEquations.jl (Transient Problems)
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```julia
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using DifferentialEquations
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function fem_ode!(du, u, p, t)
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K, M, f = p
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du .= M \ (-K * u .+ f)
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end
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u0 = zeros(N)
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prob = ODEProblem(fem_ode!, u0, (0.0, 1.0), (K, M, f))
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sol = solve(prob, Tsit5())
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```
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### LinearSolve.jl (Steady-State)
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```julia
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using LinearSolve
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prob = LinearProblem(K, f)
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sol = solve(prob, KrylovJL_GMRES())
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```
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### Krylov.jl (Iterative Methods)
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```julia
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using Krylov
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u, stats = gmres(K, f; atol=1e-10, rtol=1e-8)
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```
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### Custom Research Solvers
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```julia
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using SparseArrays, LinearAlgebra
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u = K \ f # Direct solve
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L = cholesky(K) # Factorization
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λ, v = eigs(K, M) # Eigenvalue analysis
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```
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## Current Status
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**What Works NOW:**
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- ✅ Mesh generation and element connectivity
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- ✅ Matrix extraction API (`problem.assembly.K`, `.M`, `.f`)
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- ✅ Dirichlet boundary conditions
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- ✅ Integration with Julia solver ecosystem
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**Coming in Phase 2 (2-4 months):**
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- ⏳ Heat equation problem type
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- ⏳ Elasticity problem type
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- ⏳ Full assembly for physics problems
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- ⏳ 40-130x performance improvement
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## Why Phase 2?
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JuliaFEM is undergoing architecture refactoring (Nov 2025):
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- Replacing Dict-based fields (100x performance penalty) with type-stable system
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- New immutable element architecture (already 40-130x faster)
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- Heat/Elasticity problem types depend on old system
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- Being restored with new architecture
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## See Also
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- **Issue #183**: Original request from Chris Rackauckas (2017)
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- **examples/gmsh_heat_equation/**: Full workflow with Gmsh mesh files
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- **docs/book/gmsh_tutorial.md**: Comprehensive step-by-step tutorial
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- **llm/ARCHITECTURE.md**: Architecture design and roadmap
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- **docs/blog/immutability_performance.md**: Performance analysis
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## Academic Use Case
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Perfect for research where you need:
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1. Spatial discretization (FEM assembly)
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2. Custom time integration schemes
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3. Novel solver algorithms
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4. Integration with other Julia packages
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JuliaFEM handles the messy FEM assembly; you control the solving.
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