A modern Fortran finite element library designed for ease of use, inspired by FreeFEM and FEniCS.

Features

• FEniCS-style API: Natural mathematical notation inspired by FEniCS/FreeFEM
• Simple Forms Syntax: Define weak forms using inner(grad(u), grad(v))*dx
• One-line plotting: call plot(uh, title="Solution", colormap="viridis")
• Support for various element types:
  • P1 Lagrange: Linear elements with optimal convergence
  • Nédélec edge elements: H(curl) conforming for electromagnetic problems
• Vector problems: Curl-curl equations with GMRES iterative solver
• Built-in visualization: Automatic plotting with fortplotlib integration
• Minimal code: Solve PDEs in ~10 lines of meaningful code
• Test-driven development with comprehensive test suite

Quick Start

# Build the library
fpm build

# Run tests
fpm test

# Run examples
fpm run --example simple_poisson

Usage Example

FortFEM provides a clean, FEniCS-inspired API for defining finite element problems:

program poisson_example
    use fortfem_api
    
    ! Create mesh and function space
    mesh = unit_square_mesh(20)
    Vh = function_space(mesh, "Lagrange", 1)
    
    ! Define trial and test functions
    u = trial_function(Vh)
    v = test_function(Vh)
    f = constant(1.0_dp)
    
    ! Define weak form using natural mathematical notation
    a = inner(grad(u), grad(v))*dx  ! Bilinear form: ∫ ∇u·∇v dx
    L = f*v*dx                      ! Linear form:   ∫ f v dx
    
    ! Solve and plot in one line
    uh = function(Vh)
    bc = dirichlet_bc(Vh, 0.0_dp)
    call solve(a == L, uh, bc)
    call plot(uh, title="Poisson Solution", colormap="viridis")
end program

Examples

Explore the examples/ directory for complete working examples:

• Simple Poisson solver - FEniCS-style API demonstration with plotting
• Curl-curl electromagnetic - Vector problems with Nédélec elements and GMRES solver
• Plotting demonstration - Comprehensive plotting API showcase
• Mesh plotting - Mesh visualization examples

Project Structure

• src/ - Core library modules
• test/ - Comprehensive test suite
• example/ - Example programs
• doc/ - Documentation
• app/ - Main applications

Navigation

• API Documentation - Detailed module and procedure documentation
• Source Files - Browse the source code
• Program Structure - Main programs and procedures
• Design Documentation - Architecture and design decisions

Quick Links

• Getting Started - Build and run your first FE simulation
• Examples - Complete working examples
• Module Reference - Complete API reference

Contributing

1. Check the GitHub Issues for current development priorities
2. Follow strict TDD: write tests first
3. See CLAUDE.md for development guidelines

License

See LICENSE for details.