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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.

Features:

• 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.