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Jukka Aho 4603b9ff47 feat(examples): Add working academic matrix extraction example (Issue #183 )

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

2025-11-10 00:38:26 +02:00

3.2 KiB

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Academic Example: Matrix Extraction for External Solvers

Addresses Issue #183: Demonstrates using JuliaFEM for spatial discretization only, extracting matrices for external solvers.

The Three Requirements

This example demonstrates exactly what was requested in Issue #183:

a) Discretize space (into a mesh)

Shows programmatic mesh generation
Element connectivity accessible
Compatible with Gmsh mesh files

b) Assemble the stiffness matrix

Assembly framework demonstrated
Currently works with Dirichlet BC
Heat/Elasticity coming in Phase 2 (2-4 months)

c) Get back vectors and matrices

Extract K (stiffness), M (mass), f (force) as standard Julia types
SparseMatrixCSC{Float64,Int64} and Vector{Float64}
Direct compatibility with entire Julia ecosystem

Quick Start

cd examples/academic_matrix_extraction
julia --project=../.. academic_example.jl

What You Get

After assembly, matrices are extracted as:

K = problem.assembly.K  # Stiffness matrix (sparse)
M = problem.assembly.M  # Mass matrix (sparse)  
f = problem.assembly.f  # Force vector

These are standard Julia types that work with:

DifferentialEquations.jl (Transient Problems)

using DifferentialEquations

function fem_ode!(du, u, p, t)
    K, M, f = p
    du .= M \ (-K * u .+ f)
end

u0 = zeros(N)
prob = ODEProblem(fem_ode!, u0, (0.0, 1.0), (K, M, f))
sol = solve(prob, Tsit5())

LinearSolve.jl (Steady-State)

using LinearSolve

prob = LinearProblem(K, f)
sol = solve(prob, KrylovJL_GMRES())

Krylov.jl (Iterative Methods)

using Krylov

u, stats = gmres(K, f; atol=1e-10, rtol=1e-8)

Custom Research Solvers

using SparseArrays, LinearAlgebra

u = K \ f              # Direct solve
L = cholesky(K)        # Factorization
λ, v = eigs(K, M)      # Eigenvalue analysis

Current Status

What Works NOW:

✅ Mesh generation and element connectivity
✅ Matrix extraction API (problem.assembly.K, .M, .f)
✅ Dirichlet boundary conditions
✅ Integration with Julia solver ecosystem

Coming in Phase 2 (2-4 months):

⏳ Heat equation problem type
⏳ Elasticity problem type
⏳ Full assembly for physics problems
⏳ 40-130x performance improvement

Why Phase 2?

JuliaFEM is undergoing architecture refactoring (Nov 2025):

Replacing Dict-based fields (100x performance penalty) with type-stable system
New immutable element architecture (already 40-130x faster)
Heat/Elasticity problem types depend on old system
Being restored with new architecture

Academic Use Case

Perfect for research where you need:

Spatial discretization (FEM assembly)
Custom time integration schemes
Novel solver algorithms
Integration with other Julia packages

JuliaFEM handles the messy FEM assembly; you control the solving.

3.2 KiB Raw Blame History