Firedrake is a new tool for automating the numerical solution of partial differential equations. Firedrake
adopts the domain-specific language for the finite element method of the FEniCS project, but with a pure
Python runtime-only implementation centred on the composition of several existing and new abstractions for
particular aspects of scientific computing. The result is a more complete separation of concerns which eases
the incorporation of separate contributions from computer scientists, numerical analysts and application
specialists. These contributions may add functionality, or improve performance.
Firedrake benefits from automatically applying new optimisations. This includes factorising mixed function
spaces, transforming and vectorising inner loops, and intrinsically supporting block matrix operations.
Importantly, Firedrake presents a simple public API for escaping the UFL abstraction. This allows users to
implement common operations that fall outside pure variational formulations, such as flux-limiters.