mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-10-02 14:23:58 +00:00
Jukka Aho
bf6bfc2c7b
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
75 lines
1.8 KiB
Markdown
75 lines
1.8 KiB
Markdown
# Heat Equation Example: From Gmsh to Physics
|
|
# Addresses Issue #183: Academic usage without built-in physics
|
|
|
|
This example demonstrates the complete workflow:
|
|
1. Generate mesh using Gmsh
|
|
2. Load mesh into JuliaFEM
|
|
3. Assemble stiffness matrix and mass matrix
|
|
4. Extract matrices for external solvers (e.g., DifferentialEquations.jl)
|
|
5. 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
|
|
|
|
```bash
|
|
gmsh -2 unit_square.geo -o unit_square.msh
|
|
```
|
|
|
|
This creates a triangular mesh of the unit square.
|
|
|
|
### 2. Run the example
|
|
|
|
```bash
|
|
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):
|
|
|
|
```julia
|
|
# 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
|
|
|
|
## See Also
|
|
|
|
- Tutorial: `docs/book/gmsh_tutorial.md` (comprehensive step-by-step)
|
|
- Issue #183: https://github.com/JuliaFEM/JuliaFEM.jl/issues/183
|