Articles | Volume 15, issue 13
https://doi.org/10.5194/gmd-15-5127-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
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https://doi.org/10.5194/gmd-15-5127-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| Highlight paper
| 
05 Jul 2022
Development and technical paper | Highlight paper |
| 05 Jul 2022
| 05 Jul 2022
Towards automatic finite-element methods for geodynamics via Firedrake
D. Rhodri Davies
CORRESPONDING AUTHOR
Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia
Stephan C. Kramer
Department of Earth Science and Engineering, Imperial College London, London, UK
Sia Ghelichkhan
Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia
Angus Gibson
Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia
Related authors
William Scott, Mark Hoggard, Thomas Duvernay, Sia Ghelichkhan, Angus Gibson, Dale Roberts, Stephan C. Kramer, and D. Rhodri Davies
EGUsphere, https://doi.org/10.5194/egusphere-2025-4168, https://doi.org/10.5194/egusphere-2025-4168, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
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Melting ice sheets drive solid Earth deformation and sea-level change on timescales of decades to thousands of years. Here, we present G-ADOPT, which models movement of the solid Earth in response to surface loads. It has flexibility in domain geometry, deformation mechanism parameterisation, and is scalable on high performance computers. Automatic derivation of adjoint sensitivity kernels also provides a means to assimilate historical and modern observations into future sea-level forecasts.
Sia Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
Geosci. Model Dev., 17, 5057–5086, https://doi.org/10.5194/gmd-17-5057-2024, https://doi.org/10.5194/gmd-17-5057-2024, 2024
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We introduce the Geoscientific ADjoint Optimisation PlaTform (G-ADOPT), designed for inverse modelling of Earth system processes, with an initial focus on mantle dynamics. G-ADOPT is built upon Firedrake, Dolfin-Adjoint and the Rapid Optimisation Library, which work together to optimise models using an adjoint method, aligning them with seismic and geologic datasets. We demonstrate G-ADOPT's ability to reconstruct mantle evolution and thus be a powerful tool in geosciences.
Stephan C. Kramer, D. Rhodri Davies, and Cian R. Wilson
Geosci. Model Dev., 14, 1899–1919, https://doi.org/10.5194/gmd-14-1899-2021, https://doi.org/10.5194/gmd-14-1899-2021, 2021
Short summary
Short summary
Computational models of Earth's mantle require rigorous verification and validation. Analytical solutions of the underlying Stokes equations provide a method to verify that these equations are accurately solved for. However, their derivation in spherical and cylindrical shell domains with physically relevant boundary conditions is involved. This paper provides a number of solutions. They are provided in a Python package (Assess) and their use is demonstrated in a convergence study with Fluidity.
Lior Suchoy, Saskia Goes, Benjamin Maunder, Fanny Garel, and Rhodri Davies
Solid Earth, 12, 79–93, https://doi.org/10.5194/se-12-79-2021, https://doi.org/10.5194/se-12-79-2021, 2021
Short summary
Short summary
We use 2D numerical models to highlight the role of basal drag in subduction force balance. We show that basal drag can significantly affect velocities and evolution in our simulations and suggest an explanation as to why there are no trends in plate velocities with age in the Cenozoic subduction record (which we extracted from recent reconstruction using GPlates). The insights into the role of basal drag will help set up global models of plate dynamics or specific regional subduction models.
William Scott, Mark Hoggard, Thomas Duvernay, Sia Ghelichkhan, Angus Gibson, Dale Roberts, Stephan C. Kramer, and D. Rhodri Davies
EGUsphere, https://doi.org/10.5194/egusphere-2025-4168, https://doi.org/10.5194/egusphere-2025-4168, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
Melting ice sheets drive solid Earth deformation and sea-level change on timescales of decades to thousands of years. Here, we present G-ADOPT, which models movement of the solid Earth in response to surface loads. It has flexibility in domain geometry, deformation mechanism parameterisation, and is scalable on high performance computers. Automatic derivation of adjoint sensitivity kernels also provides a means to assimilate historical and modern observations into future sea-level forecasts.
Davor Dundovic, Joseph G. Wallwork, Stephan C. Kramer, Fabien Gillet-Chaulet, Regine Hock, and Matthew D. Piggott
Geosci. Model Dev., 18, 4023–4044, https://doi.org/10.5194/gmd-18-4023-2025, https://doi.org/10.5194/gmd-18-4023-2025, 2025
Short summary
Short summary
Accurate numerical studies of glaciers often require high-resolution simulations, which often prove too demanding even for modern computers. In this paper we develop a method that identifies whether different parts of a glacier require high or low resolution based on its physical features, such as its thickness and velocity. We show that by doing so we can achieve a more optimal simulation accuracy for the available computing resources compared to uniform-resolution simulations.
Conor P. B. O'Malley, Gareth G. Roberts, James Panton, Fred D. Richards, J. Huw Davies, Victoria M. Fernandes, and Sia Ghelichkhan
Geosci. Model Dev., 17, 9023–9049, https://doi.org/10.5194/gmd-17-9023-2024, https://doi.org/10.5194/gmd-17-9023-2024, 2024
Short summary
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We wish to understand how the history of flowing rock within Earth's interior impacts deflection of its surface. Observations exist to address this problem, and mathematics and different computing tools can be used to predict histories of flow. We explore how modeling choices impact calculated vertical deflections. The sensitivity of vertical motions at Earth's surface to deep flow is assessed, demonstrating how surface observations can enlighten flow histories.
Sia Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
Geosci. Model Dev., 17, 5057–5086, https://doi.org/10.5194/gmd-17-5057-2024, https://doi.org/10.5194/gmd-17-5057-2024, 2024
Short summary
Short summary
We introduce the Geoscientific ADjoint Optimisation PlaTform (G-ADOPT), designed for inverse modelling of Earth system processes, with an initial focus on mantle dynamics. G-ADOPT is built upon Firedrake, Dolfin-Adjoint and the Rapid Optimisation Library, which work together to optimise models using an adjoint method, aligning them with seismic and geologic datasets. We demonstrate G-ADOPT's ability to reconstruct mantle evolution and thus be a powerful tool in geosciences.
Stephan C. Kramer, D. Rhodri Davies, and Cian R. Wilson
Geosci. Model Dev., 14, 1899–1919, https://doi.org/10.5194/gmd-14-1899-2021, https://doi.org/10.5194/gmd-14-1899-2021, 2021
Short summary
Short summary
Computational models of Earth's mantle require rigorous verification and validation. Analytical solutions of the underlying Stokes equations provide a method to verify that these equations are accurately solved for. However, their derivation in spherical and cylindrical shell domains with physically relevant boundary conditions is involved. This paper provides a number of solutions. They are provided in a Python package (Assess) and their use is demonstrated in a convergence study with Fluidity.
Lior Suchoy, Saskia Goes, Benjamin Maunder, Fanny Garel, and Rhodri Davies
Solid Earth, 12, 79–93, https://doi.org/10.5194/se-12-79-2021, https://doi.org/10.5194/se-12-79-2021, 2021
Short summary
Short summary
We use 2D numerical models to highlight the role of basal drag in subduction force balance. We show that basal drag can significantly affect velocities and evolution in our simulations and suggest an explanation as to why there are no trends in plate velocities with age in the Cenozoic subduction record (which we extracted from recent reconstruction using GPlates). The insights into the role of basal drag will help set up global models of plate dynamics or specific regional subduction models.
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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.
This paper introduces Firedrake, a new automatic system to generate code and solve partial...
Short summary
Firedrake is a state-of-the-art system that automatically generates highly optimised code for simulating finite-element (FE) problems in geophysical fluid dynamics. It creates a separation of concerns between employing the FE method and implementing it. Here, we demonstrate the applicability and benefits 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.
Firedrake is a state-of-the-art system that automatically generates highly optimised code for...
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