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.
Special issue:
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
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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
Siavash Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
EGUsphere, https://doi.org/10.5194/egusphere-2023-2683, https://doi.org/10.5194/egusphere-2023-2683, 2023
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We introduce the Geoscientific Adjoint Optimisation Platform (G-ADOPT), designed to improve our understanding 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, as 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
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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
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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.
Michael Rubey, Sascha Brune, Christian Heine, D. Rhodri Davies, Simon E. Williams, and R. Dietmar Müller
Solid Earth, 8, 899–919, https://doi.org/10.5194/se-8-899-2017, https://doi.org/10.5194/se-8-899-2017, 2017
Short summary
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Earth's surface is constantly warped up and down by the convecting mantle. Here we derive geodynamic rules for this so-called
dynamic topographyby employing high-resolution numerical models of global mantle convection. We define four types of dynamic topography history that are primarily controlled by the ever-changing pattern of Earth's subduction zones. Our models provide a predictive quantitative framework linking mantle convection with plate tectonics and sedimentary basin evolution.
Siavash Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
EGUsphere, https://doi.org/10.5194/egusphere-2023-2683, https://doi.org/10.5194/egusphere-2023-2683, 2023
Short summary
Short summary
We introduce the Geoscientific Adjoint Optimisation Platform (G-ADOPT), designed to improve our understanding 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, as 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.
Tuomas Kärnä, Stephan C. Kramer, Lawrence Mitchell, David A. Ham, Matthew D. Piggott, and António M. Baptista
Geosci. Model Dev., 11, 4359–4382, https://doi.org/10.5194/gmd-11-4359-2018, https://doi.org/10.5194/gmd-11-4359-2018, 2018
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Unstructured meshes are attractive for coastal ocean modeling, as they allow more accurate representation of complex coastal topography. Unstructured mesh models are, however, often perceived as slow and inaccurate. We present a novel discontinuous Galerkin ocean model: Thetis. We demonstrate that the model is able to simulate baroclinic ocean flows with high accuracy on a triangular prismatic mesh. This work paves the way for highly accurate and efficient three-dimensional coastal ocean models.
Michael Rubey, Sascha Brune, Christian Heine, D. Rhodri Davies, Simon E. Williams, and R. Dietmar Müller
Solid Earth, 8, 899–919, https://doi.org/10.5194/se-8-899-2017, https://doi.org/10.5194/se-8-899-2017, 2017
Short summary
Short summary
Earth's surface is constantly warped up and down by the convecting mantle. Here we derive geodynamic rules for this so-called
dynamic topographyby employing high-resolution numerical models of global mantle convection. We define four types of dynamic topography history that are primarily controlled by the ever-changing pattern of Earth's subduction zones. Our models provide a predictive quantitative framework linking mantle convection with plate tectonics and sedimentary basin evolution.
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High-precision 1′ × 1′ bathymetric model of Philippine Sea inversed from marine gravity anomalies
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Revised manuscript accepted for GMD
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We present version 2 of the numerical code IMEX-SfloW2D. With this version it is possible to simulate a wide range of volcanic mass flows (pyroclastic avalanches, lahars, pyroclastic surges), and here we present its application to transient dilute pyroclastic density currents (PDCs). A simulation of the 1883 Krakatau eruption demonstrates the capability of the numerical model to face a complex natural case involving the propagation of PDCs over the sea surface and across topographic obstacles.
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The waxing and waning of the Antarctic ice sheet caused the Earth’s surface to deform, which is stabilizing the ice sheet and mainly determined by the spatially variable viscosity of the mantle. Including this feedback in model simulations led to significant differences in ice sheet extent and ice thickness over the last glacial cycle. The results underline and quantify the importance of including this local feedback effect in ice sheet models when simulating the Antarctic ice sheet evolution.
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In this work, we propose a flexible framework to generate and interact with geological models using explicit surface representations. The essence of the work lies in the determination of the flexible control mesh, topologically similar to the main geological structure, watertight and controllable with few control points, to manage the geological structures. We exploited the subdivision surface method in our work, which is commonly used in the animation and gaming industry.
Leonardo Mingari, Antonio Costa, Giovanni Macedonio, and Arnau Folch
Geosci. Model Dev., 16, 3459–3478, https://doi.org/10.5194/gmd-16-3459-2023, https://doi.org/10.5194/gmd-16-3459-2023, 2023
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Two novel techniques for ensemble-based data assimilation, suitable for semi-positive-definite variables with highly skewed uncertainty distributions such as tephra deposit mass loading, are applied to reconstruct the tephra fallout deposit resulting from the 2015 Calbuco eruption in Chile. The deposit spatial distribution and the ashfall volume according to the analyses are in good agreement with estimations based on field measurements and isopach maps reported in previous studies.
Hui Gao, Xinming Wu, Jinyu Zhang, Xiaoming Sun, and Zhengfa Bi
Geosci. Model Dev., 16, 2495–2513, https://doi.org/10.5194/gmd-16-2495-2023, https://doi.org/10.5194/gmd-16-2495-2023, 2023
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We propose a workflow to automatically generate synthetic seismic data and corresponding stratigraphic labels (e.g., clinoform facies, relative geologic time, and synchronous horizons) by geological and geophysical forward modeling. Trained with only synthetic datasets, our network works well to accurately and efficiently predict clinoform facies in 2D and 3D field seismic data. Such a workflow can be easily extended for other geological and geophysical scenarios in the future.
Malte Jörn Ziebarth and Sebastian von Specht
EGUsphere, https://doi.org/10.5194/egusphere-2023-222, https://doi.org/10.5194/egusphere-2023-222, 2023
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Thermal energy from the active Earth’s interior constantly dissipates through the Earth’s surface. This heat flow is not spatially uniform and its exact pattern is hard to predict since it depends on crustal and mantle properties, both varying across scales. Our new model “REHEATFUNQ” addresses this difficulty by treating the fluctuations of heat flow within a region statistically. REHEATFUNQ estimates the regional distribution of heat flow and quantifies known structural signals therein.
Ibsen Chivata Cardenas, Terje Aven, and Roger Flage
Geosci. Model Dev., 16, 1601–1615, https://doi.org/10.5194/gmd-16-1601-2023, https://doi.org/10.5194/gmd-16-1601-2023, 2023
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We discuss challenges in uncertainty quantification for geohazard assessments. The challenges arise from limited data and the one-off nature of geohazard features. The challenges include the credibility of predictions, input uncertainty, and assumptions’ impact. Considerations to increase credibility of the quantification are provided. Crucial tasks in the quantification are the exhaustive scrutiny of the background knowledge coupled with the assessment of deviations of assumptions made.
Zhengfa Bi, Xinming Wu, Zhaoliang Li, Dekuan Chang, and Xueshan Yong
Geosci. Model Dev., 15, 6841–6861, https://doi.org/10.5194/gmd-15-6841-2022, https://doi.org/10.5194/gmd-15-6841-2022, 2022
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We present an implicit modeling method based on deep learning to produce a geologically valid and structurally compatible model from unevenly sampled structural data. Trained with automatically generated synthetic data with realistic features, our network can efficiently model geological structures without the need to solve large systems of mathematical equations, opening new opportunities for further leveraging deep learning to improve modeling capacity in many Earth science applications.
Federico Brogi, Simone Colucci, Jacopo Matrone, Chiara Paola Montagna, Mattia De' Michieli Vitturi, and Paolo Papale
Geosci. Model Dev., 15, 3773–3796, https://doi.org/10.5194/gmd-15-3773-2022, https://doi.org/10.5194/gmd-15-3773-2022, 2022
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Computer simulations play a fundamental role in understanding volcanic phenomena. The growing complexity of these simulations requires the development of flexible computational tools that can easily switch between sub-models and solution techniques as well as optimizations. MagmaFOAM is a newly developed library that allows for maximum flexibility for solving multiphase volcanic flows and promotes collaborative work for in-house and community model development, testing, and comparison.
Grace A. Nield, Matt A. King, Rebekka Steffen, and Bas Blank
Geosci. Model Dev., 15, 2489–2503, https://doi.org/10.5194/gmd-15-2489-2022, https://doi.org/10.5194/gmd-15-2489-2022, 2022
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We present a finite-element model of post-seismic solid Earth deformation built in the software package Abaqus for the purpose of calculating post-seismic deformation in the far field of major earthquakes. The model is benchmarked against an existing open-source post-seismic model demonstrating good agreement. The advantage over existing models is the potential for simple modification to include 3-D Earth structure, non-linear rheologies and alternative or multiple sources of stress change.
Alessandro Lechmann, David Mair, Akitaka Ariga, Tomoko Ariga, Antonio Ereditato, Ryuichi Nishiyama, Ciro Pistillo, Paola Scampoli, Mykhailo Vladymyrov, and Fritz Schlunegger
Geosci. Model Dev., 15, 2441–2473, https://doi.org/10.5194/gmd-15-2441-2022, https://doi.org/10.5194/gmd-15-2441-2022, 2022
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Muon tomography is a technology that is used often in geoscientific research. The know-how of data analysis is, however, still possessed by physicists who developed this technology. This article aims at providing geoscientists with the necessary tools to perform their own analyses. We hope that a lower threshold to enter the field of muon tomography will allow more geoscientists to engage with muon tomography. SMAUG is set up in a modular way to allow for its own modules to work in between.
Zuzanna M. Swirad and Adam P. Young
Geosci. Model Dev., 15, 1499–1512, https://doi.org/10.5194/gmd-15-1499-2022, https://doi.org/10.5194/gmd-15-1499-2022, 2022
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Cliff base and top lines that delimit coastal cliff faces are usually manually digitized based on maps, aerial photographs, terrain models, etc. However, manual mapping is time consuming and depends on the mapper's decisions and skills. To increase the objectivity and efficiency of cliff mapping, we developed CliffDelineaTool, an algorithm that identifies cliff base and top positions along cross-shore transects using elevation and slope characteristics.
Holly Kyeore Han, Natalya Gomez, and Jeannette Xiu Wen Wan
Geosci. Model Dev., 15, 1355–1373, https://doi.org/10.5194/gmd-15-1355-2022, https://doi.org/10.5194/gmd-15-1355-2022, 2022
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Interactions between ice sheets, sea level and the solid Earth occur over a range of timescales from years to tens of thousands of years. This requires coupled ice-sheet–sea-level models to exchange information frequently, leading to a quadratic increase in computation time with the number of model timesteps. We present a new sea-level model algorithm that allows coupled models to improve the computational feasibility and precisely capture short-term interactions within longer simulations.
Jérémie Giraud, Vitaliy Ogarko, Roland Martin, Mark Jessell, and Mark Lindsay
Geosci. Model Dev., 14, 6681–6709, https://doi.org/10.5194/gmd-14-6681-2021, https://doi.org/10.5194/gmd-14-6681-2021, 2021
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We review different techniques to model the Earth's subsurface from geophysical data (gravity field anomaly, magnetic field anomaly) using geological models and measurements of the rocks' properties. We show examples of application using idealised examples reproducing realistic features and provide theoretical details of the open-source algorithm we use.
Eric A. de Kemp
Geosci. Model Dev., 14, 6661–6680, https://doi.org/10.5194/gmd-14-6661-2021, https://doi.org/10.5194/gmd-14-6661-2021, 2021
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This is a proof of concept and review paper of spatial agents, with initial research focusing on geomodelling. The results may be of interest to others working on complex regional geological modelling with sparse data. Structural agent-based swarming behaviour is key to advancing this field. The study provides groundwork for research in structural geology 3D modelling with spatial agents. This work was done with NetLogo, a free agent modelling platform used mostly for teaching complex systems.
José M. Bastías Espejo, Andy Wilkins, Gabriel C. Rau, and Philipp Blum
Geosci. Model Dev., 14, 6257–6272, https://doi.org/10.5194/gmd-14-6257-2021, https://doi.org/10.5194/gmd-14-6257-2021, 2021
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The hydraulic and mechanical properties of the subsurface are inherently heterogeneous. RHEA is a simulator that can perform couple hydro-geomechanical processes in heterogeneous porous media with steep gradients. RHEA is able to fully integrate spatial heterogeneity, allowing allocation of distributed hydraulic and geomechanical properties at mesh element level. RHEA is a valuable tool that can simulate problems considering realistic heterogeneity inherent to geologic formations.
Lachlan Grose, Laurent Ailleres, Gautier Laurent, Guillaume Caumon, Mark Jessell, and Robin Armit
Geosci. Model Dev., 14, 6197–6213, https://doi.org/10.5194/gmd-14-6197-2021, https://doi.org/10.5194/gmd-14-6197-2021, 2021
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Fault discontinuities in rock packages represent the plane where two blocks of rock have moved. They are challenging to incorporate into geological models because the geometry of the faulted rock units are defined by not only the location of the discontinuity but also the kinematics of the fault. In this paper, we outline a structural geology framework for incorporating faults into geological models by directly incorporating kinematics into the mathematical framework of the model.
Florence Colleoni, Laura De Santis, Enrico Pochini, Edy Forlin, Riccardo Geletti, Giuseppe Brancatelli, Magdala Tesauro, Martina Busetti, and Carla Braitenberg
Geosci. Model Dev., 14, 5285–5305, https://doi.org/10.5194/gmd-14-5285-2021, https://doi.org/10.5194/gmd-14-5285-2021, 2021
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PALEOSTRIP has been developed in the framework of past Antarctic ice sheet reconstructions for periods when bathymetry around Antarctica differed substantially from today. It has been designed for users with no knowledge of numerical modelling and allows users to switch on and off the processes involved in backtracking and backstripping. Applications are broad, and it can be used to restore any continental margin bathymetry or sediment thickness and to perform basin analysis.
Lachlan Grose, Laurent Ailleres, Gautier Laurent, and Mark Jessell
Geosci. Model Dev., 14, 3915–3937, https://doi.org/10.5194/gmd-14-3915-2021, https://doi.org/10.5194/gmd-14-3915-2021, 2021
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LoopStructural is an open-source 3D geological modelling library with a model design allowing for multiple different algorithms to be used for comparison for the same geology. Geological structures are modelled using structural geology concepts and techniques, allowing for complex structures such as overprinted folds and faults to be modelled. In the paper, we demonstrate automatically generating a 3-D model from map2loop-processed geological survey data of the Flinders Ranges, South Australia.
Zhenjiao Jiang, Dirk Mallants, Lei Gao, Tim Munday, Gregoire Mariethoz, and Luk Peeters
Geosci. Model Dev., 14, 3421–3435, https://doi.org/10.5194/gmd-14-3421-2021, https://doi.org/10.5194/gmd-14-3421-2021, 2021
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Fast and reliable tools are required to extract hidden information from big geophysical and remote sensing data. A deep-learning model in 3D image construction from 2D image(s) is here developed for paleovalley mapping from globally available digital elevation data. The outstanding performance for 3D subsurface imaging gives confidence that this generic novel tool will make better use of existing geophysical and remote sensing data for improved management of limited earth resources.
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
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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.
Bastian van den Bout, Theo van Asch, Wei Hu, Chenxiao X. Tang, Olga Mavrouli, Victor G. Jetten, and Cees J. van Westen
Geosci. Model Dev., 14, 1841–1864, https://doi.org/10.5194/gmd-14-1841-2021, https://doi.org/10.5194/gmd-14-1841-2021, 2021
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Landslides, debris flows and other types of dense gravity-driven flows threaten livelihoods around the globe. Understanding the mechanics of these flows can be crucial for predicting their behaviour and reducing disaster risk. Numerical models assume that the solids and fluids of the flow are unstructured. The newly presented model captures the internal structure during movement. This important step can lead to more accurate predictions of landslide movement.
Andrzej Górszczyk and Stéphane Operto
Geosci. Model Dev., 14, 1773–1799, https://doi.org/10.5194/gmd-14-1773-2021, https://doi.org/10.5194/gmd-14-1773-2021, 2021
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We present the 3D multi-parameter synthetic geomodel of the subduction zone, as well as the workflow designed to implement all of its components. The model contains different geological structures of various scales and complexities. It is intended to serve as a tool for the geophysical community to validate imaging approaches, design acquisition techniques, estimate uncertainties, benchmark computing approaches, etc.
Mattia de' Michieli Vitturi and Federica Pardini
Geosci. Model Dev., 14, 1345–1377, https://doi.org/10.5194/gmd-14-1345-2021, https://doi.org/10.5194/gmd-14-1345-2021, 2021
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Here, we present PLUME-MoM-TSM, a volcanic plume model that allows us to quantify the formation of aggregates during the rise of the plume, model the phase change of water, and include the possibility to simulate the initial spreading of the tephra umbrella cloud intruding from the volcanic column into the atmosphere. The model is first applied to the 2015 Calbuco eruption (Chile) and provides an analytical relationship between the upwind spreading and some characteristic of the volcanic column.
Zhikui Guo, Lars Rüpke, and Chunhui Tao
Geosci. Model Dev., 13, 6547–6565, https://doi.org/10.5194/gmd-13-6547-2020, https://doi.org/10.5194/gmd-13-6547-2020, 2020
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We present the 3-D hydro-thermo-transport model HydrothermalFoam v1.0, which we designed to provide the marine geosciences community with an easy-to-use and state-of-the-art tool for simulating mass and energy transport in submarine hydrothermal systems. HydrothermalFoam is based on the popular open-source platform OpenFOAM, comes with a number of tutorials, and is published under the GNU General Public License v3.0.
Marisol Monterrubio-Velasco, F. Ramón Zúñiga, Quetzalcoatl Rodríguez-Pérez, Otilio Rojas, Armando Aguilar-Meléndez, and Josep de la Puente
Geosci. Model Dev., 13, 6361–6381, https://doi.org/10.5194/gmd-13-6361-2020, https://doi.org/10.5194/gmd-13-6361-2020, 2020
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The Mexican subduction zone along the Pacific coast is one of the most active seismic zones in the world, where every year larger-magnitude earthquakes shake huge inland cities such as Mexico City. In this work, we use TREMOL (sThochastic Rupture Earthquake ModeL) to simulate the seismicity observed in this zone. Our numerical results reinforce the hypothesis that in some subduction regions single asperities are responsible for producing the observed seismicity.
Thomas Zwinger, Grace A. Nield, Juha Ruokolainen, and Matt A. King
Geosci. Model Dev., 13, 1155–1164, https://doi.org/10.5194/gmd-13-1155-2020, https://doi.org/10.5194/gmd-13-1155-2020, 2020
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We present a newly developed flat-earth model, Elmer/Earth, for viscoelastic treatment of solid earth deformation under ice loads. Unlike many previous approaches with proprietary software, this model is based on the open-source FEM code Elmer, with the advantage for scientists to apply and alter the model without license constraints. The new-generation full-stress ice-sheet model Elmer/Ice shares the same code base, enabling future coupled ice-sheet–glacial-isostatic-adjustment simulations.
Swarup Chauhan, Kathleen Sell, Wolfram Rühaak, Thorsten Wille, and Ingo Sass
Geosci. Model Dev., 13, 315–334, https://doi.org/10.5194/gmd-13-315-2020, https://doi.org/10.5194/gmd-13-315-2020, 2020
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We present CobWeb 1.0, a graphical user interface for analysing tomographic images of geomaterials. CobWeb offers different machine learning techniques for accurate multiphase image segmentation and visualizing material specific parameters such as pore size distribution, relative porosity and volume fraction. We demonstrate a novel approach of dual filtration and dual segmentation to eliminate edge enhancement artefact in synchrotron-tomographic datasets and provide the computational code.
Loïc Huder, Nicolas Gillet, and Franck Thollard
Geosci. Model Dev., 12, 3795–3803, https://doi.org/10.5194/gmd-12-3795-2019, https://doi.org/10.5194/gmd-12-3795-2019, 2019
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The pygeodyn package is a geomagnetic data assimilation tool written in Python. It gives access to the Earth's core flow dynamics, controlled by geomagnetic observations, by means of a reduced numerical model anchored to geodynamo simulation statistics. It aims to provide the community with a user-friendly and tunable data assimilation algorithm. It can be used for education, geomagnetic model production or tests in conjunction with webgeodyn, a set of visualization tools for geomagnetic models.
Mattia de' Michieli Vitturi, Tomaso Esposti Ongaro, Giacomo Lari, and Alvaro Aravena
Geosci. Model Dev., 12, 581–595, https://doi.org/10.5194/gmd-12-581-2019, https://doi.org/10.5194/gmd-12-581-2019, 2019
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Pyroclastic avalanches are a type of granular flow generated at active volcanoes by different mechanisms, including the collapse of steep pyroclastic deposits (e.g., scoria and ash cones) and fountaining during moderately explosive eruptions. We present IMEX_SfloW2D, a depth-averaged flow model describing the granular mixture as a single-phase granular fluid. Benchmark cases and preliminary application to the simulation of the 11 February pyroclastic avalanche at Mt. Etna (Italy) are shown.
Yihao Wu, Zhicai Luo, Bo Zhong, and Chuang Xu
Geosci. Model Dev., 11, 4797–4815, https://doi.org/10.5194/gmd-11-4797-2018, https://doi.org/10.5194/gmd-11-4797-2018, 2018
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A multilayer approach is parameterized for model development, and the multiple layers are located at different depths beneath the Earth’s surface. This method may be beneficial for gravity/manget field modeling, which may outperform the traditional single-layer approach.
Andres Payo, Bismarck Jigena Antelo, Martin Hurst, Monica Palaseanu-Lovejoy, Chris Williams, Gareth Jenkins, Kathryn Lee, David Favis-Mortlock, Andrew Barkwith, and Michael A. Ellis
Geosci. Model Dev., 11, 4317–4337, https://doi.org/10.5194/gmd-11-4317-2018, https://doi.org/10.5194/gmd-11-4317-2018, 2018
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We describe a new algorithm that automatically delineates the cliff top and toe of a cliffed coastline from a digital elevation model (DEM). The algorithm builds upon existing methods but is specifically designed to resolve very irregular planform coastlines with many bays and capes, such as parts of the coastline of Great Britain.
Hugo Cruz-Jiménez, Guotu Li, Paul Martin Mai, Ibrahim Hoteit, and Omar M. Knio
Geosci. Model Dev., 11, 3071–3088, https://doi.org/10.5194/gmd-11-3071-2018, https://doi.org/10.5194/gmd-11-3071-2018, 2018
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One of the most important challenges seismologists and earthquake engineers face is reliably estimating ground motion in an area prone to large damaging earthquakes. This study aimed at better understanding the relationship between characteristics of geological faults (e.g., hypocenter location, rupture size/location, etc.) and resulting ground motion, via statistical analysis of a rupture simulation model. This study provides important insight on ground-motion responses to geological faults.
Fabio Crameri
Geosci. Model Dev., 11, 2541–2562, https://doi.org/10.5194/gmd-11-2541-2018, https://doi.org/10.5194/gmd-11-2541-2018, 2018
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Firstly, this study acts as a compilation of key geodynamic diagnostics and describes how to automatise them for a more efficient scientific procedure. Secondly, it outlines today's key pitfalls of scientific visualisation and provides means to circumvent them with, for example, a novel set of fully scientific colour maps. Thirdly, it introduces StagLab 3.0, a software that applies such fully automated diagnostics and state-of-the-art visualisation in the blink of an eye.
Michael Bock, Olaf Conrad, Andreas Günther, Ernst Gehrt, Rainer Baritz, and Jürgen Böhner
Geosci. Model Dev., 11, 1641–1652, https://doi.org/10.5194/gmd-11-1641-2018, https://doi.org/10.5194/gmd-11-1641-2018, 2018
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We introduce the Soil and
Landscape Evolution Model (SaLEM) for the prediction of soil parent material evolution following a lithologically differentiated approach. The GIS tool is working within the software framework SAGA GIS. Weathering, erosion and transport functions are calibrated using extrinsic and intrinsic parameter data. First results indicate that our approach shows evidence for the spatiotemporal prediction of soil parental material properties.
Karthik Iyer, Henrik Svensen, and Daniel W. Schmid
Geosci. Model Dev., 11, 43–60, https://doi.org/10.5194/gmd-11-43-2018, https://doi.org/10.5194/gmd-11-43-2018, 2018
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Igneous intrusions in sedimentary basins have a profound effect on the thermal structure of the hosting sedimentary rocks. In this paper, we present a user-friendly 1-D FEM-based tool, SILLi, that calculates the thermal effects of sill intrusions on the enclosing sedimentary stratigraphy. The motivation is to make a standardized numerical toolkit openly available that can be widely used by scientists with different backgrounds to test the effects of magmatic bodies in a wide variety of settings.
Charles M. Shobe, Gregory E. Tucker, and Katherine R. Barnhart
Geosci. Model Dev., 10, 4577–4604, https://doi.org/10.5194/gmd-10-4577-2017, https://doi.org/10.5194/gmd-10-4577-2017, 2017
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Rivers control the movement of sediment and nutrients across Earth's surface. Understanding how rivers change through time is important for mitigating natural hazards and predicting Earth's response to climate change. We develop a new computer model for predicting how rivers cut through sediment and rock. Our model is designed to be joined with models of flooding, landslides, vegetation change, and other factors to provide a comprehensive toolbox for predicting changes to the landscape.
Diego Takahashi and Vanderlei C. Oliveira Jr.
Geosci. Model Dev., 10, 3591–3608, https://doi.org/10.5194/gmd-10-3591-2017, https://doi.org/10.5194/gmd-10-3591-2017, 2017
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Ellipsoids are the only bodies for which the self-demagnetization can be treated analytically. This property is useful for modelling compact orebodies having high susceptibility. We present a review of the magnetic modelling of ellipsoids, propose a way of determining the isotropic susceptibility above which the self-demagnetization must be considered, and discuss the ambiguity between confocal ellipsoids, as well as provide a set of routines to model the magnetic field produced by ellipsoids.
Hein J. van Heck, J. Huw Davies, Tim Elliott, and Don Porcelli
Geosci. Model Dev., 9, 1399–1411, https://doi.org/10.5194/gmd-9-1399-2016, https://doi.org/10.5194/gmd-9-1399-2016, 2016
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Currently, extensive geochemical databases of surface observations exist, but satisfying explanations of underlying mantle processes are lacking. We have implemented a new way to track both bulk compositions and concentrations of trace elements in a mantle convection code. In our model, chemical fractionation happens at evolving melting zones. We compare our results to a semi-analytical theory relating observed arrays of correlated Pb isotope compositions to melting age distributions.
J. Florian Wellmann, Sam T. Thiele, Mark D. Lindsay, and Mark W. Jessell
Geosci. Model Dev., 9, 1019–1035, https://doi.org/10.5194/gmd-9-1019-2016, https://doi.org/10.5194/gmd-9-1019-2016, 2016
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We often obtain knowledge about the subsurface in the form of structural geological models, as a basis for subsurface usage or resource extraction. Here, we provide a modelling code to construct such models on the basis of significant deformational events in geological history, encapsulated in kinematic equations. Our methods simplify complex dynamic processes, but enable us to evaluate how events interact, and finally how certain we are about predictions of structures in the subsurface.
A. D. Wickert
Geosci. Model Dev., 9, 997–1017, https://doi.org/10.5194/gmd-9-997-2016, https://doi.org/10.5194/gmd-9-997-2016, 2016
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Earth's lithosphere bends beneath surface loads, such as ice, sediments, and mountain belts. The pattern of this bending, or flexural isostatic response, is a function of both the loads and the spatially variable strength of the lithosphere. gFlex is an easy-to-use program to calculate flexural isostastic response, and may be used to better understand how ice sheets, glaciers, large lakes, sedimentary basins, volcanoes, and other surface loads interact with the solid Earth.
A. Folch, A. Costa, and G. Macedonio
Geosci. Model Dev., 9, 431–450, https://doi.org/10.5194/gmd-9-431-2016, https://doi.org/10.5194/gmd-9-431-2016, 2016
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We present FPLUME-1.0, a steady-state 1-D cross-section-averaged eruption column model based on the buoyant plume theory (BPT). The model accounts for plume bending by wind, entrainment of ambient moisture, effects of water phase changes, particle fallout and re-entrainment, a new parameterization for the air entrainment coefficients and a model for wet aggregation of ash particles in presence of liquid water or ice.
M. Dumon and E. Van Ranst
Geosci. Model Dev., 9, 41–57, https://doi.org/10.5194/gmd-9-41-2016, https://doi.org/10.5194/gmd-9-41-2016, 2016
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This paper presents a FOSS model called PyXRD used to improve the quantification of complex mixed-layer phyllosilicate assemblages using X-ray diffraction. The novelty of this model is the ab initio incorporation of the multi-specimen method, making it possible to share phases and their parameters across multiple specimens. We present results from a comparison of PyXRD with Sybilla v2.2.2 and a number of theoretical experiments illustrating the use of the multi-specimen set-up.
M. Mergili, J. Krenn, and H.-J. Chu
Geosci. Model Dev., 8, 4027–4043, https://doi.org/10.5194/gmd-8-4027-2015, https://doi.org/10.5194/gmd-8-4027-2015, 2015
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r.randomwalk is a flexible and multi-functional open-source GIS tool for simulating the propagation of mass movements. Mass points are routed from given release pixels through a digital elevation model until a defined break criterion is reached. In contrast to existing tools, r.randomwalk includes functionalities to account for parameter uncertainties, and it offers built-in functions for validation and visualization. We show the key functionalities of r.randomwalk for three test areas.
V. Naipal, C. Reick, J. Pongratz, and K. Van Oost
Geosci. Model Dev., 8, 2893–2913, https://doi.org/10.5194/gmd-8-2893-2015, https://doi.org/10.5194/gmd-8-2893-2015, 2015
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We adjusted the topographical and rainfall erosivity factors that are the triggers of erosion in the Revised Universal Soil Loss Equation (RUSLE) model to make the model better applicable at coarse resolution on a global scale. The adjusted RUSLE model compares much better to current high resolution estimates of soil erosion in the USA and Europe. It therefore provides a basis for estimating past and future global impacts of soil erosion on climate with the use of Earth system models.
Cited articles
Ahrens, J., Geveci, B., and Law, C.: Paraview: An End-User Tool for Large Data Visualization, The Visualization Handbook, Elsevier, 717–731,
https://doi.org/10.1016/B978-012387582-2/50038-1, 2005. a
Alisic, L., Gurnis, M., Stadler, G., Burstedde, C., Wilcox, L. C., and Ghattas, O.: Slab stress and strain rate as constraints on global mantle flow, Geophys. Res. Lett., 37, L22308, https://doi.org/10.1029/2010GL045312, 2010. a
Amestoy, P., Duff, I. S., Koster, J., and L'Excellent, J.-Y.: A Fully
Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling, SIAM
J. Matrix Anal. A., 23, 15–41, 2001. a
Amestoy, P., Buttari, A., L'Excellent, J.-Y., and Mary, T.: Performance and
Scalability of the Block Low-Rank Multifrontal Factorization on Multicore
Architectures, ACM T. Math. Softw. 45, 2:1–2:26,
2019. a
Austermann, J., Kaye, B., Mitrovica, J., and Huybers, P.: A statistical
analysis of the correlation between large igneous provinces and lower mantle
seismic structure, Geophys. J. Int., 197, 1–9, https://doi.org/10.1093/gji/ggt500,
2014. a
Balay, S., Abhyankar, S., Adams, M. F., Brown, J., Brune, P., Buschelman, K.,
Dalcin, L., Dener, A., Eijkhout, V., Gropp, W. D., Karpeyev, D., Kaushik, D.,
Knepley, M. G., May, D. A., McInnes, L. C., Mills, R. T., Munson, T., Rupp,
K., Sanan, P., Smith, B. F., Zampini, S., Zhang, H., and Zhang, H.: PETSc
Users Manual, Tech. Rep. ANL-95/11 – Revision 3.15, Argonne National
Laboratory, https://www.mcs.anl.gov/petsc (last access: 1 May 2022),
2021a. a, b, c, d, e, f, g
Balay, S., Abhyankar, S., Adams, M. F., Brown, J., Brune, P., Buschelman, K.,
Dalcin, L., Dener, A., Eijkhout, V., Gropp, W. D., Karpeyev, D., Kaushik, D.,
Knepley, M. G., May, D. A., McInnes, L. C., Mills, R. T., Munson, T., Rupp,
K., Sanan, P., Smith, B. F., Zampini, S., Zhang, H., and Zhang, H.: PETSc
Web page, https://www.mcs.anl.gov/petsc (last access: 1 May 2022),,
2021b. a, b, c, d, e, f
Bangerth, W., Hartmann, R., and Kanschat, G.: deal.II – A general-purpose
object-oriented finite element library, ACM T. Math. Software, 33, 42-es,
https://doi.org/10.1145/1268776.1268779, 2007. a
Bangerth, W., Dannberg, J., Gassmoeller, R., and Heister, T.: ASPECT v2.2.0,
Zenodo [code], https://doi.org/10.5281/zenodo.3924604, 2020. a, b
Baumgardner, J. R.: Three-dimensional treatment of convective flow in the
Earth's mantle, J. Stat. Phys., 39, 501–511, https://doi.org/10.1007/BF01008348,
1985. a, b
Bercovici, D., Schubert, G., and Glatzmaier, G. A.: Three-dimensional
convection of an infinite-Prandtl-number compressible fluid in a basally
heated spherical shell, J. Fluid Mech., 239, 683–719, 1992. a
Beucher, R., Moresi, L., Giordani, J., Mansour, J., Sandiford, D., Farrington,
R., Mondy, L., Mallard, C., Rey, P., Duclaux, G., Kaluza, O., Laik, A., and
Morón, S.: UWGeodynamics: A teaching and research tool for numerical
geodynamic modelling, J. Open Source Softw., 4, 1136,
https://doi.org/10.21105/joss.01136, 2019. a
Birch, F.: Elasticity and constitution of the Earth's interior, J. Geophys.
Res., 57, 227–286, 1952. a
Blankenbach, B., Busse, F., Christensen, U., Cserepes, L., Gunkel, D., Hansen,
U., Harder, H., Jarvis, G., Koch, M., Marquart, G., Moore, D., Olson, P.,
Schmeling, H., and Schnaubelt, T.: A benchmark comparison for mantle
convection codes, Geophys. J. Int., 98, 23–38,
https://doi.org/10.1111/j.1365-246X.1989.tb05511.x, 1989. a, b, c, d, e, f, g, h, i, j, k
Bower, D. J., Gurnis, M., and Seton, M.: Lower mantle structure from
paleogeographically constrained dynamic Earth models, Geochem. Geophy.
Geosy., 14, 44–63, https://doi.org/10.1029/2012GC004267, 2013. a, b, c
Bunge, H., Richards, M. A., and Baumgardner, J. R.: Mantle circulation models
with sequential data-assimilation: inferring present-day mantle structure
from plate motion histories, Philos. T. R. Soc. Lond. A, 360,
2545–2567, https://doi.org/10.1098/rsta.2002.1080, 2002. a, b
Bunge, H.-P., Richards, M. A., and Baumgardner, J. R.: The effect of
depth–dependent viscosity on the planform of mantle convection, Nature, 279,
436–438, https://doi.org/10.1038/379436a0, 1996. a
Bunge, H.-P., Richards, M. A., and Baumgardner, J. R.: A sensitivity study of
3-D-spherical mantle convection at 108 Rayleigh number: effects of
depth-dependent viscosity, heating mode and an endothermic phase change, J.
Geophys. Res., 102, 11991–12007, https://doi.org/10.1029/96JB03806, 1997. a, b
Bunge, H.-P., Hagelberg, C. R., and Travis, B. J.: Mantle circulation models
with variational data assimilation: inferring past mantle flow and structure
from plate motion histories and seismic tomography, Geophys. J. Int., 152,
280–301, https://doi.org/10.1046/j.1365-246X.2003.01823.x, 2003. a
Burstedde, C., Wilcox, L. C., and Ghattas, O.:
p4est: Scalable
Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees, SIAM
J. Sci. Comput., 33, 1103–1133, https://doi.org/10.1137/100791634,
2011. a
Burstedde, C., Stadler, G., Alisic, L., Wilcox, L. C., Tan, E., Gurnis, M., and
Ghattas, O.: Large-scale adaptive mantle convection simulation, Geophys. J.
Int., 192, 889–906, https://doi.org/10.1093/gji/ggs070, 2013. a, b
Busse, F. H., Christensen, U., Clever, R., Cserepes, L., Gable, C.,
Giannandrea, E., Guillou, L., Houseman, G., Nataf, H. C., Ogawa, M.,
Parmentier, M., Sotin, C., and Travis, B.: 3D convection at infinite
Prandtl number in Cartesian geometry - a benchmark comparison, Geophys.
Astro. Fluid, 75, 39–59, https://doi.org/10.1080/03091929408203646, 1994. a, b, c, d, e, f, g, h, i, j
Choblet, G., Cadek, O., Couturier, F., and Dumoulin, C.: OEDIPUS: a new tool
to study the dynamics of planetary interiors, Geophys. J. Int., 170, 9–30,
https://doi.org/10.1111/j.1365-246X.2007.03419.x, 2007. a, b
Cockburn, B. and Shi, K.: Devising HDG methods for Stokes flow: An overview,
Comput. Fluids, 98, 221–229, https://doi.org/10.1016/j.compfluid.2013.11.017,
2014. a
Colli, L., Ghelichkhan, S., Bunge, H., and Oeser, J.: Retrodictions of Mid
Paleogene mantle flow and dynamic topography in the Atlantic region from
compressible high resolution adjoint mantle convection models: Sensitivity to
deep mantle viscosity and tomographic input model, Gondwana Res., 53,
252–272, https://doi.org/10.1029/2018GL077338, 2018. a
Dalcin, L., Kler, P. A., Paz, R. R., and Cosimo, A.: Parallel Distributed
Computing using Python, Adv. Water Res., 34, 10.1016/j.advwatres.2011.04.013,
2011. a
Davies, D. R. and Davies, J. H.: Thermally–driven mantle plumes reconcile
multiple hotspot observations, Earth Planet. Sc. Lett., 278, 50–54,
https://doi.org/10.1016/j.epsl.2008.11.027, 2009. a
Davies, D. R., Wilson, C. R., and Kramer, S. C.: Fluidity: a fully unstructured
anisotropic adaptive mesh computational modeling framework for geodynamics,
Geochem. Geophy. Geosy., 120, Q06001, https://doi.org/10.1029/2011GC003551, 2011. a, b, c
Davies, D. R., Goes, S., Davies, J. H., Schuberth, B. S. A., Bunge, H., and
Ritsema, J.: Reconciling dynamic and seismic models of Earth's lower
mantle: the dominant role of thermal heterogeneity, Earth Planet. Sc. Lett.,
353–354, 253–269, https://doi.org/10.1016/j.epsl.2012.08.016, 2012. a, b, c, d
Davies, D. R., Davies, J. H., Bollada, P. C., Hassan, O., Morgan, K., and Nithiarasu, P.: A hierarchical mesh refinement technique for global 3-D spherical mantle convection modelling, Geosci. Model Dev., 6, 1095–1107, https://doi.org/10.5194/gmd-6-1095-2013, 2013. a, b, c, d
Davies, D. R., Goes, S., and Lau, H. C. P.: Thermally Dominated Deep Mantle
LLSVPs: A Review, in: The Earth's Heterogeneous Mantle, edited by: Khan, A.
and Deschamps, F., Springer International Publishing, 441–477,
https://doi.org/10.1007/978-3-319-15627-9_14, 2015a. a, b
Davies, D. R., Goes, S., and Sambridge, M.: On the relationship between
volcanic hotspot locations, the reconstructed eruption sites of large igneous
provinces and deep mantle seismic structure, Earth Planet. Sc. Lett., 411,
121–130, https://doi.org/10.1016/j.epsl.2014.11.052, 2015b. a
Davies, D. R., Le Voci, G., Goes, S., Kramer, S. C., and Wilson, C. R.: The
mantle wedge's transient 3-D flow regime and thermal structure, Geochem.
Geophy. Geosy., 17, 78–100, https://doi.org/10.1002/2015GC006125, 2016. a
Davies, D. R., Kramer, S., Ghelichkhan, S., and Gibson, A.: g-adopt/g-adopt: v1.2.0 (v1.2.0), Zenodo [code], https://doi.org/10.5281/zenodo.6762752, 2022. a
Davies, G. F.: Dynamic Earth: plates, plumes and mantle convection, Cambridge
University Press, https://doi.org/10.1017/CBO9780511605802, 1999. a
Donea, J. and Huerta, A.: Finite element methods for flow problems, John Wiley
& Sons, Ltd, https://doi.org/10.1002/0470013826, 2003. a
Elman, H. C., Silvester, D. J., and Wathen, A. J.: Finite elements and fast
iterative solvers: with applications in incompressible fluid dynamics, Oxford
University Press, https://doi.org/10.1093/acprof:oso/9780199678792.001.0001, 2005. a
Farrell, P. E., Ham, D. A., Funke, S. W., and Rognes, M. E.: Automated
derivation of the adjoint of high-level transient finite element programs,
SIAM J. Sci. Comput., 35, C369–C393, 2013. a
firedrake-zenodo: Software used in “Towards Automatic Finite Element Methods for Geodynamics via Firedrake” (Firedrake_20220506.0), Zenodo [code], https://doi.org/10.5281/zenodo.6522930, 2022. a
Flament, N., Bodur, Ö. F., Williams, S. E., and Merdith, A. S.: Assembly
of the basal mantle structure beneath Africa, Nature, 603, 846–851, 2022. a
French, S. W. and Romanowicz, B.: Broad plumes rooted at the base of the
Earth's mantle beneath major hotspots, Nature, 525, 95–99,
https://doi.org/10.1038/nature14876, 2015. a
Garel, F., Goes, S., Davies, D. R., Davies, J. H., Kramer, S. C., and Wilson,
C. R.: Interaction of subducted slabs with the mantle transition-zone: A
regime diagram from 2-D thermo-mechanical models with a mobile trench and
an overriding plate, Geochem. Geophy. Geosy., 15, 1739–1765,
https://doi.org/10.1002/2014GC005257, 2014. a
Gassmoller, R., Dannberg, J., Bangerth, W., Heister, T., and Myhill, R.: On
formulations of compressible mantle convection, Geophys. J. Int., 221,
1264–1280, https://doi.org/10.1093/gji/ggaa078, 2020. a
Ghelichkhan, S. and Bunge, H.: The adjoint equations for thermochemical
compressible mantle convection: derivation and verification by twin
experiments, Proc. Roy. Soc. A, 474, 20180329,
https://doi.org/10.1098/rspa.2018.0329, 2018. a
Ghelichkhan, S., Murbock, M., Colli, L., Pail, R., and Bunge, H.: On the
observability of epeirogenic movement in current and future gravity missions,
Gondwana Res., 53, 273–284, https://doi.org/10.1016/j.gr.2017.04.016, 2018. a
Ghelichkhan, S., Bunge, H., and Oeser, J.: Global mantle flow retrodictions for
the early Cenozoic using an adjoint method: evolving dynamic topographies,
deep mantle structures, flow trajectories and sublithospheric stresses,
Geophys. J. Int., 226, 1432–1460, https://doi.org/10.1093/gji/ggab108, 2020. a
Gibson, T. H., McRae, A. T. T., Cotter, C. J., Mitchell, L., and Ham, D. A.:
Compatible Finite Element Methods for Geophysical Flows: Automation and
Implementation using Firedrake, Springer International Publishing,
https://doi.org/10.1007/978-3-030-23957-2, 2019. a, b, c, d
Glatzmaier, G. A.: Numerical simulations of mantle convection-time dependent,
3-dimensional, compressible, spherical-shell, Geophys. Astro. Fluid,
43, 223–264, 1988. a
Gurnis, M., Yang, T., Cannon, J., Turner, M., Williams, S., Flament, N., and
Müller, R. D.: Global tectonic reconstructions with continuously
deforming and evolving rigid plates, Comput. Geosci., 116, 32–41,
https://doi.org/10.1016/j.cageo.2018.04.007, 2012. a
Ham, D. A., Farrell, P. E., Gorman, G. J., Maddison, J. R., Wilson, C. R., Kramer, S. C., Shipton, J., Collins, G. S., Cotter, C. J., and Piggott, M. D.: Spud 1.0: generalising and automating the user interfaces of scientific computer models, Geosci. Model Dev., 2, 33–42, https://doi.org/10.5194/gmd-2-33-2009, 2009. a
Hassan, R., Flament, N., Gurnis, M., Bowe, D. J., and Müller, R. D.:
Provenance of plumes in global convection models, Geochem. Geophy. Geosy.,
16, 1465–1489, https://doi.org/10.1002/2015GC005751, 2015. a
Heister, T., Dannberg, J., Gassmoller, R., and Bangerth, W.: High accuracy
mantle convection simulation through modern numerical methods – II:
Realistic models and problems, Geophys. J. Int., 210, 833–851,
https://doi.org/10.1093/gji/ggx195, 2017. a
Heroux, M. A., Bartlett, R. A., Howle, V. E., Hoekstra, R. J., Hu, J. J.,
Kolda, T. G., Lehoucq, R. B., Long, K. R., Pawlowski, R. P., Phipps, E. T.,
Salinger, A. G., Thornquist, H. K., Tuminaro, R. S., Willenbring, J. M.,
Williams, A., and Stanlet, K. S.: An overview of the Trilinos project, ACM
T. Math. Software, 31, 397–423, https://doi.org/10.1145/1089014.1089021, 2005. a
Hillebrand, B., Thieulot, C., Geenen, T., van den Berg, A. P., and Spakman, W.: Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface, Solid Earth, 5, 1087–1098, https://doi.org/10.5194/se-5-1087-2014, 2014. a
Hillewaert, K.: Development of the discontinuous Galerkin method for
high-resolution, large scale CFD and acoustics in industrial geometries, PhD
Thesis, Université de Louvain, 2013. a
Homolya, M., Mitchell, L., Luporini, F., and Ham, D.: Tsfc: a
structure-preserving form compiler, SIAM J. Sci. Comput., 40, 401–428,
https://doi.org/10.1137/17M1130642, 2018. a, b, c
Hunt, S. A., Davies, D. R., Walker, A. M., McCormack, R. J., Wills, A. S.,
Dobson, D. P., and Li, L.: On the increase in thermal diffusivity caused by
the perovskite to post-perovskite phase transition and its implications for
mantle dynamics, Earth Planet. Sc. Lett., 319, 96–103,
https://doi.org/10.1016/j.epsl.2011.12.009, 2012. a
Jadamec, M. A.: Insights on slab-driven mantle flow from advances in
three-dimensional modelling, J. Geodynam., 100, 51–70, 2016. a
Jadamec, M. A. and Billen, M. I.: Reconciling surface plate motions with rapid
three-dimensional mantle flow around a slab edge, Nature, 465, 338–341,
2010. a
Jarvis, G. T.: Effects of curvature on two–dimensional models of mantle
convection: cylindrical polar coordinates, J. Geophys. Res., 98, 4477–4485,
1993. a
Jarvis, G. T. and McKenzie, D. P.: Convection in a compressible fluid with
infinite Prandtl number, J. Fluid Mech., 96, 515–583,
https://doi.org/10.1017/S002211208000225X, 1980. a
Katz, R. F. and Weatherley, S. M.: Consequences of mantle heterogeneity for
melt extraction at mid-ocean ridges, Earth Planet. Sc. Lett., 335, 226–237,
https://doi.org/10.1016/j.epsl.2012.04.042, 2012. a
Kirby, R. C.: Algorithm 839: FIAT, a new paradigm for computing finite
element basis functions, ACM T. Math. Software, 30, 502–516, 2004. a
Kirby, R. C. and Mitchell, L.: Solver Composition Across the PDE/Linear
Algebra Barrier, SIAM J. Sci. Comput., 40, 76–98, https://doi.org/10.1137/17M1133208,
2018. a, b
Knepley, M. G. and Karpeev, D. A.: Mesh Algorithms for PDE with Sieve I: Mesh
Distribution, Sci. Program., 17, 215–230, 2009. a
Koelemeijer, P. J., Schuberth, B. S. A., Davies, D. R., Deuss, A., and Ritsema,
J.: Constraints on the presence of post-perovskite in Earth's lowermost
mantle from tomographic-geodynamic model comparisons, Geophys. J. Int., 494,
226–238, 2018. a
Kramer, S. C., Cotter, C. J., and Pain, C. C.: Solving the Poisson equation on
small aspect ratio domains using unstructured meshes, Ocean Model., 35,
253–263, 2010. a
Kramer, S. C., Wilson, C. R., and Davies, D. R.: An implicit free-surface
algorithm for geodynamical simulations, Phys. Earth Planet. In., 194,
25–37, https://doi.org/10.1016/j.pepi.2012.01.001, 2012. a, b
Kramer, S. C., Wilson, C., Davies, D. R., Mathews, C., Gibson, A., Dubernay,
T., Greaves, T., Candy, A., Cotter, C. J., Percival, J., Mouradian, S.,
Bhutani, G., Avdis, A., Gorman, G., Piggott, M., and Ham, D.:
FluidityProject/fluidity: Zenodo release, Zenodo [code], https://doi.org/10.5281/zenodo.3924604,
2021b. a
Kronbichler, M., Heister, T., and Bangerth, W.: High accuracy mantle convection
simulation through modern numerical methods, Geophys. J. Int., 191, 12–29,
https://doi.org/10.1111/j.1365-246X.2012.05609.x, 2012. a, b
Kärnä, T., Kramer, S. C., Mitchell, L., Ham, D. A., Piggott, M. D., and Baptista, A. M.: Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations, Geosci. Model Dev., 11, 4359–4382, https://doi.org/10.5194/gmd-11-4359-2018, 2018. a
Lange, M., Mitchell, L., Knepley, M. G., and Gorman, G. J.: Efficient mesh
management in Firedrake using PETSc-DMPlex, SIAM J. Sci.
Comput., 38, S143–S155, https://doi.org/10.1137/15M1026092, 2016. a
Le Voci, G., Davies, D. R., Goes, S., Kramer, S. C., and Wilson, C. R.: A
systematic 2-D investigation into the mantle wedge's transient flow regime
and thermal structure: complexities arising from a hydrated rheology and
thermal buoyancy, Geochem. Geophy. Geosy., 15, 28–51,
https://doi.org/10.1002/2013GC005022, 2014. a
Leng, W. and Zhong, S.: Viscous heating, adiabatic heating and energetic
consistency in compressible mantle convection, Geophys. J. Int., 173,
693–702, 2008. a
Li, D., Gurnis, M., and Stadler, G.: Towards adjoint-based inversion of
time-dependent mantle convection with nonlinear viscosity, Geophys. J. Int.,
209, 86–105, https://doi.org/10.1093/gji/ggw493, 2017. a
Liu, L., Spasojevic, S., and Gurnis, M.: Reconstructing Farallon Plate
Subduction Beneath North America Back to the Late Cretaceous, Science,
322, 934–938, https://doi.org/10.1126/science.1162921, 2008. a
Maljaars, J. M., Richardson, C. N., and Sime, N.: LEoPart: A particle library
for FEniCS, Comp. Math. Appl., 81, 289–315, 2021. a
Markall, G. R., Rathgeber, F., Mitchell, L., Loriant, N., Bertolli, C., Ham,
D. A., and Kelly, P. H. J.: Performance-Portable Finite Element Assembly
Using PyOP2 and FEniCS, in: 28th International Supercomputing Conference,
ISC, Proceedings, edited by: Kunkel, J. M., Ludwig, T., and Meuer, H. W., vol.
7905 of Lecture Notes in Computer Science, Springer, 279–289,
https://doi.org/10.1007/978-3-642-38750-0_21, 2013. a
McKenzie, D.: Speculations on consequences and causes of plate motions,
Geophys. J. Roy. Astr. S., 18, 1–18, 1969. a
McKenzie, D. P., Roberts, J. M., and Weiss, N. O.: Numerical models of
convection in the Earth's mantle, Tectonophys., 19, 89–103,
https://doi.org/10.1016/0040-1951(73)90034-6, 1973. a, b
Minear, J. and Toksoz, M.: Thermal regime of a downgoing slab and new global
tectonics, J. Geophys. Res., 75, 1397–1419, 1970. a
Mitush, S. K., Funke, S. W., and Dokken, J. S.: dolfin-adjoint 2018.1:
automated adjoints for FEniCS and Firedrake, J. Open Source Softw., 4, 1292, https://doi.org/10.21105/joss.01292,
2019. a
Moresi, L., Dufour, F., and Muhlhaus, H.: Mantle convection modeling with
viscoelastic/brittle lithosphere: Numerical methodology and plate tectonic
modeling, Pure Appl. Geophys., 159, 2335–2356, 2002. a
Moresi, L., Quenette, S., Lemiale, V., Meriaux, C., Appelbe, B., and Muhlhaus,
H.-B.: Computational approaches to studying non-linear dynamics of the crust
and mantle, Phys. Earth Planet. In., 163, 69–82,
https://doi.org/10.1016/j.pepi.2007.06.009, 2007. a
Moresi, L. N. and Solomatov, V. S.: Numerical investigations of 2D convection
with extremely large viscosity variations, Phys. Fluid, 7, 2154–2162,
https://doi.org/10.1063/1.868465, 1995. a
Müller, R. D., Seton, M., Zahirovic, S., Williams, S. E., Matthews, K. J.,
Wright, N. M., Shephard, G. E., Maloney, K. T., Barnett-Moore, N.,
Hosseinpour, M., Bower, D. J., and Cannon, J.: Ocean Basin Evolution and
Global-Scale Plate Reorganization Events Since Pangea Breakup, Annu. Rev.
Earth Pl. Sc., 44, 107–138, https://doi.org/10.1146/annurev-earth-060115-012211,
2016. a, b, c, d
Müller, R. D., Cannon, J., Qin, X., Watson, R. J., Gurnis, M., Williams,
S., Pfaffelmoser, T., Seton, M., Russell, S. H. J., and Zahirovic, S.:
GPlates: Building a Virtual Earth Through Deep Time, Geochem. Geophy.
Geosy., 19, 2243–2261, https://doi.org/10.1029/2018GC007584, 2018. a
Nakagawa, T., Tackley, P. J., Deschamps, F., and Connolly, J. A. D.:
Incorporating self–consistently calculated mineral physics into
thermo–chemical mantle convection simulations in a 3-D spherical shell and
its influence on seismic anomalies in Earth's mantle, Geochem. Geophy.
Geosy., 10, Q3304, https://doi.org/10.1029/2008GC002280, 2009. a
Nerlich, R., Colli, L., Ghelichkhan, S., Schuberth, B., and Bunge, H.-P.:
Constraining entral Neo-Tethys Ocean reconstructions with mantle convection
models, Geophys. Res. Lett., 43, 9595–9603, https://doi.org/10.1002/2016GL070524,
2016. a
Nitsche, J.: Über ein Variationsprinzip zur Lösung von
Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen
Randbedingungen unterworfen sind, in: Abhandlungen aus dem mathematischen
Seminar der Universität Hamburg, Springer, vol. 36, 9–15,
https://doi.org/10.1007/BF02995904, 1971. a
Quenette, S., Moresi, L., Appelbe, B. F., and Sunter, P. D.: Explaining
StGermain: an aspect oriented environment for building extensible
computational mechanics modeling software, IEEE International Parallel and
Distributed Processing Symposium, IEEE New York, 210 pp.,
https://doi.org/10.1109/IPDPS.2007.370400, 2007. a
Ratcliff, J. T., Schubert, G., and Zebib, A.: Steady tetrahedral and cubic
patterns of spherical shell convection with temperature-dependent viscosity,
J. Geophys. Res., 101, 25473–25484, https://doi.org/10.1029/96JB02097, 1996. a, b, c
Rathgeber, F., Markall, G. R., Mitchell, L., Loriant, N., Ham, D. A., Bertolli,
C., and Kelly, P. H. J.: PyOP2: A High-Level Framework for
Performance-Portable Simulations on Unstructured Meshes, in: High Performance
Computing, Networking Storage and Analysis, SC Companion,
IEEE Computer Society, Los Alamitos, CA, USA, 1116–1123,
https://doi.org/10.1109/SC.Companion.2012.134, 2012. a
Rathgeber, F., Ham, D. A., Mitchell, L., Lange, M., Luporini, F., Mcrae, A.
T. T., Bercea, G.-T., Markall, G. R., and Kelly, P. H. J.: Firedrake:
Automating the Finite Element Method by Composing Abstractions, ACM T.
Math. Softw., 43, 1–27, https://doi.org/10.1145/2998441, 2016. a, b, c, d, e, f, g, h, i, j
Ritsema, J., Deuss, A., van Heijst, H. J., and Woodhouse, J. H.: S40RTS: a
degree-40 shear-velocity model for the mantle from new Rayleigh wave
dispersion, teleseismic traveltime and normal-mode splitting function
measurements, Geophys. J. Int., 184, 1223–1236,
https://doi.org/10.1111/j.1365-246X.2010.04884.x, 2011. a
Rubey, M., Brune, S., Heine, C., Davies, D. R., Williams, S. E., and Müller, R. D.: Global patterns in Earth's dynamic topography since the Jurassic: the role of subducted slabs, Solid Earth, 8, 899–919, https://doi.org/10.5194/se-8-899-2017, 2017. a
Saad, Y.: A flexible inner-outer preconditioned GMRES algorithm, SIAM J.
Sci. Comput., 14, 461–469, 1993. a
Schuberth, B. S. A., H.-P. Bunge, Steinle-Neumann, G., Moder, C., and
Oeser, J.: Thermal versus elastic heterogeneity in high-resolution mantle
circulation models with pyrolite composition: high plume excess temperatures
in the lowermost mantle, Geochem. Geophy. Geosy., 10, Q01W01,
https://doi.org/10.1029/2008GC002235, 2009. a
Shahbazi, K.: An explicit expression for the penalty parameter of the interior
penalty method, J. Comput. Phys., 205, 401–407, 2005. a
Shapero, D. R., Badgeley, J. A., Hoffman, A. O., and Joughin, I. R.: icepack: a new glacier flow modeling package in Python, version 1.0, Geosci. Model Dev., 14, 4593–4616, https://doi.org/10.5194/gmd-14-4593-2021, 2021. a
Shih, Y., Stadler, G., and Wechsung, F.: Robust multigrid techniques for
augmented Lagrangian preconditioning of incompressible Stokes equations with
extreme viscosity variations, arXiv [preprint], arXiv:2107.00820, 2021. a
Shipton, J., Gibson, T., and Cotter, C.: Higher-order compatible finite element
schemes for the nonlinear rotating shallow water equations on the sphere, J. Comput. Phys.,
375, 1121–1137, https://doi.org/10.1016/j.jcp.2018.08.027, 2018. a
Spiegelman, M., May, D. A., and Wilson, C. R.: On the solvability of
incompressible Stokes with viscoplastic rheologies in geodynamics,
Geochem. Geophy. Geosy., 17, 2213–2238,
https://doi.org/10.1002/2015GC006228, 2016. a, b, c
Stadler, G., Gurnis, M., Burstedde, C., Wilcox, L. C., Alisic, L., and Ghattas,
O.: The dynamics of plate tectonics and mantle flow: from local to global
scales, Science, 329, 1033–1038, https://doi.org/10.1126/science.1191223, 2010. a, b
Stemmer, K., Harder, H., and Hansen, U.: A new method to simulate convection
with strongly temperature- and pressure-dependent viscosity in a spherical
shell: Applications to the Earth's mantle, Phys. Earth Planet. In., 157,
223–249, https://doi.org/10.1016/j.pepi.2006.04.007, 2006. a, b
Styles, E., Davies, D. R., and Goes, S.: Mapping spherical seismic into
physical structure: biases from 3-D phase-transition and thermal
boundary-layer heterogeneity, Geophys. J. Int., 184, 1371–1378,
https://doi.org/10.1111/j.1365-246X.2010.04914.x, 2011. a
Tackley, P. J.: Effects of strongly variable viscosity on three–dimensional
compressible convection in planetary mantles, J. Geophys. Res., 101,
3311–3332, https://doi.org/10.1029/95JB03211, 1996. a
Tackley, P. J.: Mantle convection and plate tectonics: towards and integrated
physical and chemical theory, Science, 288, 2002–2007, 2000. a
Tackley, P. J.: Modelling compressible mantle convection with large viscosity
contrasts in a three-dimensional spherical shell using the Yin-Yang grid,
Phys. Earth Planet. In., 171, 7–18, https://doi.org/10.1016/j.pepi.2008.08.005, 2008. a, b, c
Tackley, P. J. and Xie, S.: The thermo-chemical structure and evolution of
Earth's mantle: constraints and numerical models, Philos. T. R. Soc.
Lond. A., 360, 2593–2609, 2002. a
Tackley, P. J., Stevenson, D. J., Glatzmaier, G. A., and Schubert, G.: Effects
of an endothermic phase transition at 670 km depth in a spherical model of
convection in the Earth's mantle, Nature, 361, 699–704,
https://doi.org/10.1038/361699a0, 1993. a
Thieulot, C. and Bangerth, W.: On the choice of finite element for applications in geodynamics, Solid Earth, 13, 229–249, https://doi.org/10.5194/se-13-229-2022, 2022. a, b
Torrance, K. E. and Turcotte, D. L.: Thermal convection with large viscosity
variations, J. Fluid Mech., 47, 113–125, 1971. a
Tosi, N., Stein, C., Noack, L., Hüttig, C., Maierová, P., Samuel, H.,
Davies, D. R., Wilson, C. R., Kramer, S. C., Thieulot, C., Glerum, A.,
Fraters, M., Spakman, W., Rozel, A., and Tackley, P. J.: A community
benchmark for viscoplastic thermal convection in a 2-D square box,
Geochem. Geophy. Geosy., 16, 2175–2196,
https://doi.org/10.1002/2015GC005807, 2015. a, b, c, d, e, f, g, h, i, j, k
Trilinos Project Team, T.: The Trilinos Project Website, https://trilinos.github.io, last access: 22 May 2020. a
Trompert, R. and Hansen, U.: Mantle convection simulations with rheologies that
generate plate-like behaviour, Nature, 395, 686–689, 1998. a
van Keken, P.: Evolution of starting mantle plumes: a comparison between
numerical and laboratory models, Earth Planet. Sc. Lett., 148, 1–11,
https://doi.org/10.1016/S0012-821X(97)00042-3, 1997. a
van Keken, P. E. and Ballentine, C. J.: Whole–mantle versus layered mantle
convection and the role of a high–viscosity lower mantle in terrestrial
volatile evolution, Earth Planet. Sc. Lett., 156, 19–32, 1998. a
Vanek, P., Mandel, J., and Brezina, M.: Algebraic multigrid by smoothed
aggregation for second and fourth order elliptic problems, Computing, 56,
179–196, https://doi.org/10.1007/BF02238511, 1996. a
Vynnytska, L., Rognes, M. E., and Clark, S. R.: Benchmarking FEniCS for
mantle convection simulations, Compu. Geosci., 50, 95–105,
https://doi.org/10.1016/j.cageo.2012.05.012, 2013. a, b
Wilson, C. R., Spiegelman, M., van Keken, P. E., and R., H. B.: Fluid flow in
subduction zones: The role of solid rheology and compaction pressure, Earth
Planet. Sc. Lett., 401, 261–274, https://doi.org/10.1016/j.epsl.2014.05.052, 2014. a
Wolstencroft, M., Davies, J. H., and Davies, D. R.: Nusselt-Rayleigh number
scaling for spherical shell Earth mantle simulation up to a Rayleigh
number of 109, Phys. Earth Planet. In., 176, 132–141,
https://doi.org/10.1016/j.pepi.2009.05.002, 2009.
a
Yoshida, M. and Kageyama, A.: Application of the Yin-Yang grid to a thermal
convection of a Boussinesq fluid with infinite Prandtl number in a
three-dimensional spherical shell, Geophys. Res. Lett., 31, L12609,
https://doi.org/10.1029/2004GL019970, 2004. a, b
Zhong, S., Zuber, M. T., Moresi, L., and Gurnis, M.: Role of
temperature-dependent viscosity and surface plates in spherical shell models
of mantle convection, J. Geophys. Res., 105, 11063–11082,
https://doi.org/10.1029/2000JB900003, 2000. a
Zienkiewicz, O. C., Taylor, R. L., and Zhu, J. Z.: The finite element method: its basis and fundamentals, Elsevier, ISBN 9780080472775, 2005. a
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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