Firedrake: automating the finite element method by composing abstractions

File Description SizeFormat 
1501.01809v3.pdfFile embargoed until 01 January 10000599.82 kBAdobe PDF    Request a copy
Title: Firedrake: automating the finite element method by composing abstractions
Author(s): Mitchell, L
Ham, DA
McRae, ATT
Rathgeber, F
Lange, M
Luporini, F
Kelly, PHJ
Bercea, G-T
Markall, G
Item Type: Journal Article
Abstract: 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.
Publication Date: 31-Dec-2015
Date of Acceptance: 16-Sep-2016
URI: http://hdl.handle.net/10044/1/40323
ISSN: 1557-7295
Publisher: Association for Computing Machinery
Journal / Book Title: ACM Transactions on Mathematical Software
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Natural Environment Research Council (NERC)
Engineering & Physical Science Research Council (EPSRC)
Natural Environment Research Council (NERC)
Natural Environment Research Council (NERC)
Engineering & Physical Science Research Council (E
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/I00677X/1
NE/I021098/1
EP/I012036/1
NE/K008951/1
NE/K006789/1
EP/L000407/1
EP/M011054/1
Keywords: cs.MS
cs.MS
cs.NA
math.NA
G.1.8; G.4
Numerical & Computational Mathematics
0802 Computation Theory And Mathematics
0806 Information Systems
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Mathematics
Computing
Centre for Environmental Policy
Faculty of Natural Sciences



Items in Spiral are protected by copyright, with all rights reserved, unless otherwise indicated.

Creative Commons