Firedrake: automating the finite element method by composing abstractions

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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: 16-Jan-2017
Date of Acceptance: 16-Sep-2016
URI: http://hdl.handle.net/10044/1/40323
DOI: https://dx.doi.org/10.1145/2998441
ISSN: 1557-7295
Publisher: Association for Computing Machinery
Journal / Book Title: ACM Transactions on Mathematical Software
Volume: 43
Issue: 3
Copyright Statement: This work is licensed under a Creative Commons Attribution International 4.0 License.
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 (EPSRC)
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: Science & Technology
Technology
Physical Sciences
Computer Science, Software Engineering
Mathematics, Applied
Computer Science
Mathematics
Abstraction
code generation
UFL
PARALLEL
cs.MS
cs.MS
cs.NA
math.NA
G.1.8; G.4
0802 Computation Theory And Mathematics
0806 Information Systems
Numerical & Computational Mathematics
Publication Status: Published
Article Number: 24
Appears in Collections:Faculty of Engineering
Mathematics
Computing
Earth Science and Engineering
Centre for Environmental Policy
Faculty of Natural Sciences



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