Submitted as: development and technical paper 13 Jan 2022

Submitted as: development and technical paper | 13 Jan 2022

Review status: this preprint is currently under review for the journal GMD.

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: open (until 15 Mar 2022)

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 reply

D. Rhodri Davies et al.

D. Rhodri Davies et al.


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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.