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Firedrake: Automating the Finite Element Method by Composing Abstractions

Authors:

Florian Rathgeber,

Lawrence Mitchell,

Fabio Luporini,

Andrew T. T. Mcrae,

Gheorghe-Teodor Bercea,

Graham R. Markall,

Paul H. J. KellyAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 43, Issue 3

Article No.: 24, Pages 1 - 27

https://doi.org/10.1145/2998441

Published: 21 December 2016 Publication History

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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Index Terms

Firedrake: Automating the Finite Element Method by Composing Abstractions
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
  2. Mathematical software

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 43, Issue 3

September 2017

232 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2988516

Editor:
Michael A. Heroux
Sandia National Laboratories, USA

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Copyright © 2016 Owner/Author.

This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 21 December 2016

Accepted: 01 September 2016

Revised: 01 July 2016

Received: 01 January 2015

Published in TOMS Volume 43, Issue 3

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https://doi.org/10.5194/tc-18-2583-2024
Rasheed SWarder SPlancherel YPiggott M(2024)Nearshore tsunami amplitudes across the Maldives archipelago due to worst-case seismic scenarios in the Indian OceanNatural Hazards and Earth System Sciences10.5194/nhess-24-737-202424:3(737-755)Online publication date: 5-Mar-2024
https://doi.org/10.5194/nhess-24-737-2024
Ghelichkhan SGibson ADavies DKramer SHam D(2024)Automatic adjoint-based inversion schemes for geodynamics: reconstructing the evolution of Earth's mantle in space and timeGeoscientific Model Development10.5194/gmd-17-5057-202417:13(5057-5086)Online publication date: 3-Jul-2024
https://doi.org/10.5194/gmd-17-5057-2024
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