Current development information.

Firedrake and PyOP2 are continually tested using GitHub actions.

Latest Firedrake status:

Firedrake and its components are developed on GitHub where we also maintain Firedrake-ready versions of the FEniCS components UFL.

• Firedrake on GitHub

• TSFC on GitHub

• PyOP2 on GitHub

• FIAT on GitHub

• Firedrake version of UFL on GitHub

Getting started

The first step is to download and install Firedrake and its dependencies. For full instructions, see obtaining Firedrake.

Introductory Tutorials

Once you’ve built Firedrake, you’ll want to actually solve some PDEs. Below are a few tutorial examples to get you started.

• A basic Helmholtz equation.
• The Burgers equation, a non-linear, unsteady example.
• A mixed formulation of the Poisson equation.
• A time-dependent DG advection equation using upwinding.
• An extruded mesh example, using a steady-state continuity equation.
• A linear wave equation with optional mass lumping.
• Creating Firedrake-compatible meshes in Gmsh.

Jupyter notebooks

In addition to the documented tutorials, we also have some Jupyter notebooks that are a more interactive way of getting to know Firedrake. They are described in more detail on their own page.

Youtube Channel

Firedrake has a youtube channel where recorded tutorials are occasionally uploaded.

API documentation

The complete list of all the classes and methods in Firedrake is available at the firedrake package page. The same information is indexed in alphabetical order. Another very effective mechanism is the site search engine.

Manual

Once you have worked through the tutorials, the user manual is the next step. It goes in to more detail on how to set up and solve finite element problems in Firedrake.

• Defining variational problems
  • Constructing meshes
  • Building function spaces
  • Supported finite elements
  • Expressing a variational problem
  • Forms with constant coefficients
  • Incorporating boundary conditions
  • More complicated forms
• Solving PDEs
  • Introduction
  • Solving the variational problem
  • Solving linear systems
  • Specifying solution methods
  • Solving singular systems
  • Debugging convergence failures
• Dirichlet boundary conditions
  • Mathematical background
  • Solution strategy
  • Implementation
• The \(R\) space
  • An example:
  • Setting and retrieving the value of a function in \(R\)
  • Representing matrices involving \(R\)
  • Assembling matrices involving \(R\)
  • Using \(R\) space with extruded meshes
• Extruded Meshes in Firedrake
  • Introduction
  • Generating Extruded Meshes in Firedrake
  • Function Spaces on Extruded Meshes
  • Solving Equations on Extruded Meshes
• Changing mesh coordinates
  • Changing the coordinate function space
  • Replacing the mesh geometry of an existing function
• Interpolation
  • The interpolate operator
  • Interpolation across meshes
  • Interpolation from external data
  • Generating Functions with randomised values
• Point evaluation
  • Firedrake convenience function
  • Primary API: Interpolation onto a vertex-only mesh
  • Expressions with point evaluations
  • Interacting with external point data
  • Mesh tolerance
  • UFL API
• External operators
  • Background
  • Build your own external operator
  • A simple example: the translation operator
• Visualising the results of simulations
  • Creating output files
  • Saving time-dependent data
  • Visualising high-order data
  • Saving multiple functions
  • Plotting with matplotlib
• Checkpointing state
  • Checkpointing with CheckpointFile
  • Using disk checkpointing in adjoint simulations
  • Checkpointing with DumbCheckpoint
  • Implementation details
• Matrix-free operators
  • Splitting unassembled matrices
  • Preconditioning unassembled matrices
  • Example usage
  • Poisson equation
• Preconditioning infrastructure
  • Additive Schwarz methods
  • Multigrid methods
  • Assembled and auxiliary operators
  • Hybridisation and element-wise static condensation
• Interfacing directly with PETSc
  • Introduction
  • Accessing PETSc objects
  • Building an operator
  • Defining a preconditioner
  • Accessing the PETSc mesh representation
• Parallelism in Firedrake
  • Installing for parallel use
  • Printing in parallel
  • Expected performance improvements
  • Parallel garbage collection
  • Using MPI Communicators
  • Ensemble parallelism
• Firedrake Zenodo integration: tools for reproducible science
  • How to register DOIs for a version of Firedrake
  • What else do you need to do?
• Optimising Firedrake Performance
  • Automatic flame graph generation with PETSc
  • Common performance issues
  • Other useful tools

Advanced tutorials

These tutorials demonstrate some more advanced features of Firedrake’s PDE solving capabilities, such as block-preconditioning mixed finite element systems.

• Printing in parallel.
• Benney-Luke nonlinear wave equation.
• Solving the one-layer Quasi-Geostrophic equations.
• Computing eigenmodes of the Quasi-Geostrophic equations using SLEPc.
• A Quasi-Geostrophic wind driven gyre.
• Preconditioning saddle-point systems, using the mixed Poisson problem as an example.
• The Camassa-Holm equation, a nonlinear integrable PDE.
• The Monge-Ampère equation, a nonlinear PDE, demonstrating fieldsplit preconditioning.
• Preconditioning using geometric multigrid.
• Linear mixed fluid-structure interaction system.
• Mass lumping for a high order spectral wave equation.
• Block preconditioning for the Stokes equation.
• A pressure-convection-diffusion preconditioner for the Navier-Stokes equations.
• Rayleigh-Benard convection.
• Netgen support.
• Full-waveform inversion: spatial and wave sources parallelism.