Preprints
https://doi.org/10.5194/gmd-2021-367
https://doi.org/10.5194/gmd-2021-367
Submitted as: development and technical paper
 | Highlight paper
13 Jan 2022
Submitted as: development and technical paper  | Highlight paper | 13 Jan 2022
Status: a revised version of this preprint was accepted for the journal GMD and is expected to appear here in due course.

Automating Finite Element Methods for Geodynamics via Firedrake

D. Rhodri Davies1, Stephan C. Kramer2, Siavash Ghelichkhan1, and Angus Gibson1 D. Rhodri Davies et al.
  • 1Research School of Earth Sciences, The Australian National University, Canberra, ACT, Australia
  • 2Department of Earth Science and Engineering, Imperial College London, London, UK

Abstract. Firedrake is an automated system for solving partial differential equations using the finite element method. By applying sophisticated performance optimisations through automatic code-generation techniques, it provides a means to create accurate, efficient, flexible, easily extensible, scalable, transparent and reproducible research software, that is ideally suited to simulating a wide-range of problems in geophysical fluid dynamics. Here, we demonstrate the applicability of Firedrake for geodynamical simulation, with a focus on mantle dynamics. The accuracy and efficiency of the approach is confirmed via comparisons against a suite of analytical and benchmark cases of systematically increasing complexity, whilst parallel scalability is demonstrated up to 12288 compute cores, where the problem size and the number of processing cores are simultaneously increased. In addition, Firedrake's flexibility is highlighted via straightforward application to different physical (e.g. complex nonlinear rheologies, compressibility) and geometrical (2-D and 3-D Cartesian and spherical domains) scenarios. Finally, a representative simulation of global mantle convection is examined, which incorporates 230 Myr of plate motion history as a kinematic surface boundary condition, confirming its suitability for addressing research problems at the frontiers of global mantle dynamics research.

D. Rhodri Davies et al.

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC2: 'Reply on CC1', D. Rhodri Davies, 26 Jan 2022
  • RC1: 'Comment on gmd-2021-367', Anonymous Referee #1, 05 Feb 2022
  • RC2: 'Comment on gmd-2021-367', Cedric THIEULOT, 10 Feb 2022
  • RC3: 'Comment on gmd-2021-367', Marcus Mohr, 15 Feb 2022
  • RC4: 'Comment on gmd-2021-367', Wolfgang Bangerth, 25 Feb 2022
  • RC5: 'Comment on gmd-2021-367', Anonymous Referee #5, 16 Mar 2022
  • RC6: 'Comment on gmd-2021-367', Anonymous Referee #6, 16 Mar 2022
  • RC7: 'Comment on gmd-2021-367', Carsten Burstedde, 18 Mar 2022
  • AC1: 'Response to all reviewer comments.', D. Rhodri Davies, 09 May 2022

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC2: 'Reply on CC1', D. Rhodri Davies, 26 Jan 2022
  • RC1: 'Comment on gmd-2021-367', Anonymous Referee #1, 05 Feb 2022
  • RC2: 'Comment on gmd-2021-367', Cedric THIEULOT, 10 Feb 2022
  • RC3: 'Comment on gmd-2021-367', Marcus Mohr, 15 Feb 2022
  • RC4: 'Comment on gmd-2021-367', Wolfgang Bangerth, 25 Feb 2022
  • RC5: 'Comment on gmd-2021-367', Anonymous Referee #5, 16 Mar 2022
  • RC6: 'Comment on gmd-2021-367', Anonymous Referee #6, 16 Mar 2022
  • RC7: 'Comment on gmd-2021-367', Carsten Burstedde, 18 Mar 2022
  • AC1: 'Response to all reviewer comments.', D. Rhodri Davies, 09 May 2022

D. Rhodri Davies et al.

D. Rhodri Davies et al.

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Executive editor
This paper introduces Firedrake, a new automatic system to generate code and solve partial differential equations using finite element methods. This capability is a core need of many models, and consequently a source of significant redundant software development effort. Because it does not prescribe a particular set of equations, the Firedrake software is applicable to a wide range of geoscientific models. Firedrake demonstrates remarkable computational efficiency, scaling beyond 12,000 computing cores. It is also free-libre open source software, contributing to improvements in scientific computational replicability and reproducibility.
Short summary
Firedrake is a unique computational modelling framework that automatically generates code to simulate a wide-range of geoscientific processes, including global ocean circulation, weather systems and glacial flow. In this paper, we demonstrate the benefits and applicability of Firedrake for simulating geodynamical flows, with a focus on the slow creeping motion of Earth's mantle over geological timescales, which is ultimately the engine driving our dynamic Earth.