Outputs (5)

Firedrake: automating the finite element method by composing abstractions (2016)
Journal Article

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 cen... Read More about Firedrake: automating the finite element method by composing abstractions.

Efficient Mesh Management in Firedrake Using PETSc DMPlex (2016)
Journal Article

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-known performance optimizations. This work highlights the composition of the... Read More about Efficient Mesh Management in Firedrake Using PETSc DMPlex.

A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake (2016)
Journal Article

We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of prismatic cells.... Read More about A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake.

Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements (2016)
Journal Article

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, hexahedral, and triangular prismatic cells. The algebra is impleme... Read More about Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements.

High level implementation of geometric multigrid solvers for finite element problems: Applications in atmospheric modelling (2016)
Journal Article

The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated (mixed) finite element di... Read More about High level implementation of geometric multigrid solvers for finite element problems: Applications in atmospheric modelling.