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Cited by 508

The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.

Firedrake: Automating the Finite Element Method by Composing Abstractions

Open access
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.·2017·ACM Transactions on Mathematical Software
DOI 10.1145/2998441
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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.

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Metadata

Authors
Rathgeber, F., Ham, D. A., Mitchell, L., Lange, M., Luporini, F., Mcrae, A. T. T., Bercea, G.-T., Markall, G. R., & Kelly, P. H. J.
Venue
ACM Transactions on Mathematical Software
Publisher
Association for Computing Machinery (ACM)
Published
2016-12-21
Volume
43
Issue
3
Pages
1-27
ISSN
  • 0098-3500 (ISSN-L)
  • 1557-7295
DOI
10.1145/2998441
OpenAlex
W2168522485
Cited by
508
References
18
FWCI
27.92
Type
journal article
Language
en
Open access
hybrid

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CoChat. (2026). Citation check: Firedrake: Automating the Finite Element Method by Composing Abstractions. https://app.cochat.ai/papers/10.1145/2998441
The paper
Rathgeber, F., Ham, D. A., Mitchell, L., Lange, M., Luporini, F., Mcrae, A. T. T., Bercea, G.-T., Markall, G. R., & Kelly, P. H. J. (2017). Firedrake: Automating the Finite Element Method by Composing Abstractions. ACM Transactions on Mathematical Software. https://doi.org/10.1145/2998441

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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.