Articles | Volume 16, issue 6
https://doi.org/10.5194/se-16-457-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/se-16-457-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
On the choice of finite element for applications in geodynamics – Part 2: A comparison of simplex and hypercube elements
Department of Earth Sciences, Utrecht University, Utrecht, the Netherlands
Wolfgang Bangerth
Department of Mathematics, Department of Geosciences, Colorado State University, Fort Collins, CO, USA
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We developed faster methods for simulating Earth's interior dynamics. Standard iterative algorithms struggle to solve these equations efficiently. We introduced two improvements. First, we reformulated how calculation errors are measured. Second, we added a mass conservation correction. Our method solves the equations much faster while staying accurate. We tested it on multiple benchmark problems, showing significant speed improvements with minimal extra computational cost.
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Several alternative gravity modelling techniques and associated numerical codes with their own advantages and limitations are available for the solid Earth community. With upcoming state-of-the-art lithosphere density models and accurate global gravity field data sets, it is vital to understand the differences of the various approaches. In this paper, we discuss the four widely used techniques: spherical harmonics, tesseroid integration, triangle integration, and hexahedral integration.
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Geodynamic modelling provides a powerful tool to investigate processes in the Earth’s crust, mantle, and core that are not directly observable. In this review, we present a comprehensive yet concise overview of the modelling process with an emphasis on best practices. We also highlight synergies with related fields, such as seismology and geology. Hence, this review is the perfect starting point for anyone wishing to (re)gain a solid understanding of geodynamic modelling as a whole.
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One of the main numerical methods to solve the mass, momentum, and energy conservation equations in geodynamics is the finite-element method. Four main types of elements have been used in the past decades in hundreds of publications. For the first time we compare results obtained with these four elements on a series of geodynamical benchmarks and applications and draw conclusions as to which are the best ones and which are to be preferably avoided.
Deok-Kyu Jang, Kyeong-Min Lee, Cedric Thieulot, Whan-Hyuk Choi, and Byung-Dal So
EGUsphere, https://doi.org/10.5194/egusphere-2025-5480, https://doi.org/10.5194/egusphere-2025-5480, 2025
This preprint is open for discussion and under review for Solid Earth (SE).
Short summary
Short summary
We developed faster methods for simulating Earth's interior dynamics. Standard iterative algorithms struggle to solve these equations efficiently. We introduced two improvements. First, we reformulated how calculation errors are measured. Second, we added a mass conservation correction. Our method solves the equations much faster while staying accurate. We tested it on multiple benchmark problems, showing significant speed improvements with minimal extra computational cost.
Erik van der Wiel, Cedric Thieulot, and Douwe J. J. van Hinsbergen
Solid Earth, 15, 861–875, https://doi.org/10.5194/se-15-861-2024, https://doi.org/10.5194/se-15-861-2024, 2024
Short summary
Short summary
Geodynamic models of mantle convection provide a powerful tool to study the structure and composition of the Earth's mantle. Comparing such models with other datasets is difficult. We explore the use of
configurational entropy, which allows us to quantify mixing in models. The entropy may be used to analyse the mixed state of the mantle as a whole and may also be useful to validate numerical models against anomalies in the mantle that are obtained from seismology and geochemistry.
Rene Gassmöller, Juliane Dannberg, Wolfgang Bangerth, Elbridge Gerry Puckett, and Cedric Thieulot
Geosci. Model Dev., 17, 4115–4134, https://doi.org/10.5194/gmd-17-4115-2024, https://doi.org/10.5194/gmd-17-4115-2024, 2024
Short summary
Short summary
Numerical models that use simulated particles are a powerful tool for investigating flow in the interior of the Earth, but the accuracy of these models is not fully understood. Here we present two new benchmarks that allow measurement of model accuracy. We then document that better accuracy matters for applications like convection beneath an oceanic plate. Our benchmarks and methods are freely available to help the community develop better models.
Iris van Zelst, Cedric Thieulot, and Timothy J. Craig
Solid Earth, 14, 683–707, https://doi.org/10.5194/se-14-683-2023, https://doi.org/10.5194/se-14-683-2023, 2023
Short summary
Short summary
A common simplification in subduction zone models is the use of constant thermal parameters, while experiments have shown that they vary with temperature. We test various formulations of temperature-dependent thermal parameters and show that they change the thermal structure of the subducting slab. We recommend that modelling studies of the thermal structure of subduction zones take the temperature dependence of thermal parameters into account, especially when providing insights into seismicity.
Barend Cornelis Root, Josef Sebera, Wolfgang Szwillus, Cedric Thieulot, Zdeněk Martinec, and Javier Fullea
Solid Earth, 13, 849–873, https://doi.org/10.5194/se-13-849-2022, https://doi.org/10.5194/se-13-849-2022, 2022
Short summary
Short summary
Several alternative gravity modelling techniques and associated numerical codes with their own advantages and limitations are available for the solid Earth community. With upcoming state-of-the-art lithosphere density models and accurate global gravity field data sets, it is vital to understand the differences of the various approaches. In this paper, we discuss the four widely used techniques: spherical harmonics, tesseroid integration, triangle integration, and hexahedral integration.
Iris van Zelst, Fabio Crameri, Adina E. Pusok, Anne Glerum, Juliane Dannberg, and Cedric Thieulot
Solid Earth, 13, 583–637, https://doi.org/10.5194/se-13-583-2022, https://doi.org/10.5194/se-13-583-2022, 2022
Short summary
Short summary
Geodynamic modelling provides a powerful tool to investigate processes in the Earth’s crust, mantle, and core that are not directly observable. In this review, we present a comprehensive yet concise overview of the modelling process with an emphasis on best practices. We also highlight synergies with related fields, such as seismology and geology. Hence, this review is the perfect starting point for anyone wishing to (re)gain a solid understanding of geodynamic modelling as a whole.
Cedric Thieulot and Wolfgang Bangerth
Solid Earth, 13, 229–249, https://doi.org/10.5194/se-13-229-2022, https://doi.org/10.5194/se-13-229-2022, 2022
Short summary
Short summary
One of the main numerical methods to solve the mass, momentum, and energy conservation equations in geodynamics is the finite-element method. Four main types of elements have been used in the past decades in hundreds of publications. For the first time we compare results obtained with these four elements on a series of geodynamical benchmarks and applications and draw conclusions as to which are the best ones and which are to be preferably avoided.
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Short summary
One of the main numerical methods in geodynamics is the finite element method. Many types of elements have been used in the past decades in hundreds of publications. They usually fall under two categories: quadrilaterals and triangles. For the first time we compare results obtained with the most-used elements of each type on a series of geodynamical benchmarks and draw conclusions as to which are the best ones and which are to be preferably avoided.
One of the main numerical methods in geodynamics is the finite element method. Many types of...