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Jukka Aho bf6bfc2c7b docs(examples): Add README for gmsh heat equation example

New file: examples/gmsh_heat_equation/README.md (74 lines)

Quick-start documentation covering:
- Problem statement (heat equation with BCs)
- Quick start commands (mesh generation, run example)
- What you get (assembly workflow, matrix extraction)
- Academic usage section directly addressing Issue #183
- Code snippet showing K, M, f extraction for external solvers
- File listing and links to comprehensive tutorial

Provides immediate context for users discovering this example

2025-11-09 23:23:18 +02:00

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Heat Equation Example: From Gmsh to Physics

Addresses Issue #183: Academic usage without built-in physics

This example demonstrates the complete workflow:

Generate mesh using Gmsh
Load mesh into JuliaFEM
Assemble stiffness matrix and mass matrix
Extract matrices for external solvers (e.g., DifferentialEquations.jl)
Solve the heat equation

Problem Statement

Solve the transient heat equation on a unit square:

∂u/∂t = α∇²u + f(x,y,t)

with boundary conditions:

u = 0 on left edge (Dirichlet)
∂u/∂n = 0 on other edges (Neumann, natural BC)

Initial condition: u(x,y,0) = sin(πx)sin(πy)

Quick Start

1. Generate mesh

gmsh -2 unit_square.geo -o unit_square.msh

This creates a triangular mesh of the unit square.

2. Run the example

julia --project gmsh_heat_equation.jl

What You Get

The example shows how to:

Load Gmsh mesh files
Create FEM elements with material properties
Assemble global stiffness matrix K and mass matrix M
Apply Dirichlet boundary conditions
Extract the resulting ODE system: M du/dt = -K u + f
Solve using your own time integrator

For Academic Users (Issue #183)

If you want to use JuliaFEM just for discretization (not the built-in physics):

# After assembly, extract the matrices:
K = problem.assembly.K  # Stiffness matrix (SparseMatrixCSC)
M = problem.assembly.M  # Mass matrix (SparseMatrixCSC)
f = problem.assembly.f  # Force vector

# Now use these with DifferentialEquations.jl, Krylov.jl, etc.
# The ODE system is: M * du/dt = -K * u + f

Files

unit_square.geo - Gmsh geometry definition
gmsh_heat_equation.jl - Complete working example
README.md - This file

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