Firedrake: automating the finite element method by composing abstractions

Rathgeber, Florian; Ham, David A.; Mitchell, Lawrence; Lange, Michael; Luporini, Fabio; Mcrae, Andrew T.T.; Bercea, Gheorghe-Teodor; Markall, Graham R.; Kelly, Paul H.J.

doi:10.1145/2998441

Firedrake: automating the finite element method by composing abstractions

Rathgeber, Florian; Ham, David A.; Mitchell, Lawrence; Lange, Michael; Luporini, Fabio; Mcrae, Andrew T.T.; Bercea, Gheorghe-Teodor; Markall, Graham R.; Kelly, Paul H.J.

Authors

Florian Rathgeber

David A. Ham

Lawrence Mitchell

Michael Lange

Fabio Luporini

Andrew T.T. Mcrae

Gheorghe-Teodor Bercea

Graham R. Markall

Paul H.J. Kelly

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 centered on the composition of several existing and new abstractions for particular aspects of scientific computing. The result is a more complete separation of concerns that 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 optimizations. This includes factorizing mixed function spaces, transforming and vectorizing 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 of pure variational formulations, such as flux limiters.

Citation

Rathgeber, F., Ham, D. A., Mitchell, L., Lange, M., Luporini, F., Mcrae, A. T., …Kelly, P. H. (2017). Firedrake: automating the finite element method by composing abstractions. ACM Transactions on Mathematical Software, 43(3), Article 24. https://doi.org/10.1145/2998441

Journal Article Type	Article
Acceptance Date	Sep 15, 2016
Online Publication Date	Dec 22, 2016
Publication Date	Jan 16, 2017
Deposit Date	Aug 1, 2018
Publicly Available Date	Aug 2, 2018
Journal	ACM Transactions on Mathematical Software
Print ISSN	0098-3500
Electronic ISSN	1557-7295
Publisher	Association for Computing Machinery (ACM)
Peer Reviewed	Peer Reviewed
Volume	43
Issue	3
Article Number	24
DOI	https://doi.org/10.1145/2998441
Related Public URLs	https://arxiv.org/pdf/1501.01809.pdf

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Copyright Statement
2016 Copyright is held by the owner/author(s). This work is licensed under a Creative Commons Attribution International 4.0 License.