Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Professor of Computational Mathematics



+44 (0)20 7594 3468colin.cotter




755Huxley BuildingSouth Kensington Campus






BibTex format

author = {McRae, ATT and Mitchell, L and Bercea and Ham, DA and Cotter and McRae and Bercea and Mitchell and Ham and Cotter},
doi = {10.1137/15M1021167},
journal = {SIAM Journal on Scientific Computing},
pages = {S25--S47},
title = {Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements},
url = {},
volume = {38},
year = {2016}

RIS format (EndNote, RefMan)

AB - 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 implemented as an extension to the domain-specific language UFL, the Unified Form Language. This allows users to construct many finite element spaces beyond those supported by existing software packages. We have made corresponding extensions to FIAT, the FInite element Automatic Tabulator, to enable numerical tabulation of such spaces. This tabulation is consequently used during the automatic generation of low-level code that carries out local assembly operations, within the wider context of solving finite element problems posed over such function spaces. We have done this work within the code-generation pipeline of the software package Firedrake; we make use of the full Firedrake package to present numerical examples.
AU - McRae,ATT
AU - Mitchell,L
AU - Bercea
AU - Ham,DA
AU - Cotter
AU - McRae
AU - Bercea
AU - Mitchell
AU - Ham
AU - Cotter
DO - 10.1137/15M1021167
EP - 47
PY - 2016///
SN - 1095-7197
SP - 25
TI - Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements
T2 - SIAM Journal on Scientific Computing
UR -
UR -
UR -
VL - 38
ER -