Firedrake is an automated system for the solution of partial differential equations using the finite element method (FEM). Firedrake uses sophisticated code generation to provide mathematicians, scientists, and engineers with a very high productivity way to create sophisticated high performance simulations.


  • Expressive specification of any PDE using the Unified Form Language from the FEniCS Project.

  • Sophisticated, programmable solvers through seamless coupling with PETSc.

  • Triangular, quadrilateral, and tetrahedral unstructured meshes.

  • Layered meshes of triangular wedges or hexahedra.

  • Vast range of finite element spaces.

  • Sophisticated automatic optimisation, including sum factorisation for high order elements, and vectorisation.

  • Geometric multigrid.

  • Customisable operator preconditioners.

  • Support for static condensation, hybridisation, and HDG methods.

River plume simulated with the Firedrake-based Thetis ocean model.