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 …

We introduce Devito, a new domain-specific language for implementing high-performance
finite-difference partial differential equation solvers. The motivating application is exploration …

The tremendous increase in global industrial activity has resulted in high utilization of
natural energy resources and increase in global warming over the last few decades …

Parallelization of the finite-element method (FEM) has been contemplated by the scientific
and high-performance computing community for over a decade. Most of the computations in …

We describe and implement a symbolic algebra for scalar and vector-valued finite elements,
enabling the computer generation of elements with tensor product structure on quadrilateral …

Exascale computing will feature novel and potentially disruptive hardware architectures.
Exploiting these to their full potential is non-trivial. Numerical modelling frameworks …

A form compiler takes a high-level description of the weak form of partial differential
equations and produces low-level code that carries out the finite element assembly. In this …

Present-day stencil codes are implemented in general-purpose programming languages,
such as Fortran, C, or Java, Python or derivates thereof, and harnesses for parallelism, such …

We present an algorithm for the optimization of a class of finite-element integration loop
nests. This algorithm, which exploits fundamental mathematical properties of finite-element …

The use of composable abstractions allows the application of new and established
algorithms to a wide range of problems, while automatically inheriting the benefits of well …