Articles | Volume 13, issue 3
https://doi.org/10.5194/gmd-13-955-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-13-955-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Modelling thermomechanical ice deformation using an implicit pseudo-transient method (FastICE v1.0) based on graphical processing units (GPUs)
Stanford University, Geophysics Department, 397 Panama Mall, Stanford, CA 94305, USA
now at: Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zurich, Zurich, Switzerland
now at: Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf, Switzerland
Aleksandar Licul
Institute of Earth Surface Dynamics, University of Lausanne, 1015 Lausanne, Switzerland
Swiss Geocomputing Centre, University of Lausanne, 1015 Lausanne, Switzerland
Frédéric Herman
Institute of Earth Surface Dynamics, University of Lausanne, 1015 Lausanne, Switzerland
Swiss Geocomputing Centre, University of Lausanne, 1015 Lausanne, Switzerland
Yury Y. Podladchikov
Swiss Geocomputing Centre, University of Lausanne, 1015 Lausanne, Switzerland
Institute of Earth Sciences, University of Lausanne, 1015 Lausanne, Switzerland
Jenny Suckale
Stanford University, Geophysics Department, 397 Panama Mall, Stanford, CA 94305, USA
Related authors
Thibault Duretz, Albert de Monserrat, Rubén Sevilla, Ludovic Räss, Ivan Utkin, and Arne Spang
EGUsphere, https://doi.org/10.5194/egusphere-2025-5641, https://doi.org/10.5194/egusphere-2025-5641, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
Geodynamic modeling helps scientists understand how the Earth deforms. New computer methods make these simulations faster and more efficient, especially on powerful computers. They automatically adjust settings for better performance and can handle complex materials and flow types. This approach makes it easier to study large, detailed models of Earth processes.
Thibault Duretz, Albert de Monserrat, Rubén Sevilla, Ludovic Räss, Ivan Utkin, and Arne Spang
EGUsphere, https://doi.org/10.5194/egusphere-2025-5641, https://doi.org/10.5194/egusphere-2025-5641, 2025
Short summary
Short summary
Geodynamic modeling helps scientists understand how the Earth deforms. New computer methods make these simulations faster and more efficient, especially on powerful computers. They automatically adjust settings for better performance and can handle complex materials and flow types. This approach makes it easier to study large, detailed models of Earth processes.
Arne Spang, Marcel Thielmann, Casper Pranger, Albert de Montserrat, and Ludovic Räss
EGUsphere, https://doi.org/10.5194/egusphere-2025-2417, https://doi.org/10.5194/egusphere-2025-2417, 2025
Short summary
Short summary
Concentration of deformation is difficult to capture accurately in computer simulations. We present a number of challenges associated with concentrated viscous deformation and demonstrate strategies to overcome them. These strategies include automatic selection of appropriate time steps to react to rapid changes in model behavior, automatic rescaling to avoid rounding errors, and two methods to prevent model instability. This way, we are able to accurately capture very fast viscous deformation.
Anjali Sandip, Ludovic Räss, and Mathieu Morlighem
Geosci. Model Dev., 17, 899–909, https://doi.org/10.5194/gmd-17-899-2024, https://doi.org/10.5194/gmd-17-899-2024, 2024
Short summary
Short summary
We solve momentum balance for unstructured meshes to predict ice flow for real glaciers using a pseudo-transient method on graphics processing units (GPUs) and compare it to a standard central processing unit (CPU) implementation. We justify the GPU implementation by applying the price-to-performance metric for up to million-grid-point spatial resolutions. This study represents a first step toward leveraging GPU processing power, enabling more accurate polar ice discharge predictions.
Ludovic Räss, Ivan Utkin, Thibault Duretz, Samuel Omlin, and Yuri Y. Podladchikov
Geosci. Model Dev., 15, 5757–5786, https://doi.org/10.5194/gmd-15-5757-2022, https://doi.org/10.5194/gmd-15-5757-2022, 2022
Short summary
Short summary
Continuum mechanics-based modelling of physical processes at large scale requires huge computational resources provided by massively parallel hardware such as graphical processing units. We present a suite of numerical algorithms, implemented using the Julia language, that efficiently leverages the parallelism. We demonstrate that our implementation is efficient, scalable and robust and showcase applications to various geophysical problems.
Thibault Duretz, Albert de Monserrat, Rubén Sevilla, Ludovic Räss, Ivan Utkin, and Arne Spang
EGUsphere, https://doi.org/10.5194/egusphere-2025-5641, https://doi.org/10.5194/egusphere-2025-5641, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
Geodynamic modeling helps scientists understand how the Earth deforms. New computer methods make these simulations faster and more efficient, especially on powerful computers. They automatically adjust settings for better performance and can handle complex materials and flow types. This approach makes it easier to study large, detailed models of Earth processes.
Thibault Duretz, Albert de Monserrat, Rubén Sevilla, Ludovic Räss, Ivan Utkin, and Arne Spang
EGUsphere, https://doi.org/10.5194/egusphere-2025-5641, https://doi.org/10.5194/egusphere-2025-5641, 2025
Short summary
Short summary
Geodynamic modeling helps scientists understand how the Earth deforms. New computer methods make these simulations faster and more efficient, especially on powerful computers. They automatically adjust settings for better performance and can handle complex materials and flow types. This approach makes it easier to study large, detailed models of Earth processes.
Chloé Bouscary, Georgina E. King, Melanie Kranz-Bartz, Maxime Bernard, Rabiul H. Biswas, Lily Bossin, Arnaud Duverger, Benny Guralnik, Frédéric Herman, Ugo Nanni, Nadja Stalder, Pierre G. Valla, Vjeran Visnjevic, and Xiaoxia Wen
EGUsphere, https://doi.org/10.5194/egusphere-2025-5474, https://doi.org/10.5194/egusphere-2025-5474, 2025
This preprint is open for discussion and under review for Geochronology (GChron).
Short summary
Short summary
The OSLThermo and ESRThermo MATLAB libraries simulate how luminescence signals in feldspar and electron spin resonance signals in quartz minerals accumulate and fade over time, enabling reconstruction of recent rock cooling and surface temperature changes. By sharing these tools openly, we hope to promote collaboration, reproducibility, and broader use and development of these ultra-low-temperature thermochronology methods.
Yury Alkhimenkov, Lyudmila Khakimova, and Yury Y. Podladchikov
Solid Earth, 16, 1335–1350, https://doi.org/10.5194/se-16-1335-2025, https://doi.org/10.5194/se-16-1335-2025, 2025
Short summary
Short summary
This study examines stress drops sequences in elasto-plastic media using 2D simulations, highlighting the importance of high temporal and spatial resolutions in capturing stress evolution and strain fields. Stress drops reflect fault rupture mechanics and emulate earthquake behavior. The non-Gaussian distribution of stress drop amplitudes resembles "solid turbulence." Elasto-plastic models simulate key earthquake processes and could improve seismic hazard assessment.
Yury Alkhimenkov and Yury Y. Podladchikov
Solid Earth, 16, 1227–1247, https://doi.org/10.5194/se-16-1227-2025, https://doi.org/10.5194/se-16-1227-2025, 2025
Short summary
Short summary
We present a thermodynamically consistent derivation of extended Biot poroelasticity, showing that Gassmann, Brown–Korringa, and related models emerge as special cases. Our formulation clarifies the conditions under which Gassmann’s relation holds and extends it by incorporating off-diagonal Hessian terms. Symbolic Maple code with consistency checks ensures full transparency, reproducibility, and accessibility for further research.
Fien De Doncker, Frédéric Herman, Bruno Belotti, and Thierry Adatte
EGUsphere, https://doi.org/10.5194/egusphere-2025-4695, https://doi.org/10.5194/egusphere-2025-4695, 2025
This preprint is open for discussion and under review for Earth Surface Dynamics (ESurf).
Short summary
Short summary
Sediments carried by rivers can damage infrastructure, affect ecosystems, and alter landscapes, yet it is often unclear where these sediments come from, especially in regions hidden beneath ice. We developed a simple way to trace their origins by shining X-rays on crushed rocks and sediments. The resulting X-ray signals act like fingerprints that can be matched to source rocks, revealing where sediments come from and allowing us to map erosion across landscapes.
Arne Spang, Marcel Thielmann, Casper Pranger, Albert de Montserrat, and Ludovic Räss
EGUsphere, https://doi.org/10.5194/egusphere-2025-2417, https://doi.org/10.5194/egusphere-2025-2417, 2025
Short summary
Short summary
Concentration of deformation is difficult to capture accurately in computer simulations. We present a number of challenges associated with concentrated viscous deformation and demonstrate strategies to overcome them. These strategies include automatic selection of appropriate time steps to react to rapid changes in model behavior, automatic rescaling to avoid rounding errors, and two methods to prevent model instability. This way, we are able to accurately capture very fast viscous deformation.
Andrew O. Hoffman, Paul T. Summers, Jenny Suckale, Knut Christianson, Ginny Catania, and Howard Conway
EGUsphere, https://doi.org/10.5194/egusphere-2025-1239, https://doi.org/10.5194/egusphere-2025-1239, 2025
Short summary
Short summary
In Antarctica, fast-flowing ice streams drive most ice loss. Radar data from Conway Ice Ridge reveal that the van der Veen and Mercer Ice Streams were wider ~3000 years ago and narrowed progressively. Numerical modeling demonstrates that small thickness changes can rapidly alter shear-margin locations. These findings offer crucial insights into Late Holocene Ice Sheet readvance.
Yury Alkhimenkov and Yury Y. Podladchikov
Geosci. Model Dev., 18, 563–583, https://doi.org/10.5194/gmd-18-563-2025, https://doi.org/10.5194/gmd-18-563-2025, 2025
Short summary
Short summary
The accelerated pseudo-transient (APT) method is an efficient way to solve partial differential equations, particularly well-suited for parallel computing. This paper explores the APT method's effectiveness in solving elastic, viscoelastic, and hydromechanical problems, focusing on quasi-static conditions in 1D, 2D, and 3D. The study examines the best numerical settings for fast and accurate solutions. The paper shows how the APT method can handle complex problems in high-resolution models.
Anjali Sandip, Ludovic Räss, and Mathieu Morlighem
Geosci. Model Dev., 17, 899–909, https://doi.org/10.5194/gmd-17-899-2024, https://doi.org/10.5194/gmd-17-899-2024, 2024
Short summary
Short summary
We solve momentum balance for unstructured meshes to predict ice flow for real glaciers using a pseudo-transient method on graphics processing units (GPUs) and compare it to a standard central processing unit (CPU) implementation. We justify the GPU implementation by applying the price-to-performance metric for up to million-grid-point spatial resolutions. This study represents a first step toward leveraging GPU processing power, enabling more accurate polar ice discharge predictions.
Ian Delaney, Leif Anderson, and Frédéric Herman
Earth Surf. Dynam., 11, 663–680, https://doi.org/10.5194/esurf-11-663-2023, https://doi.org/10.5194/esurf-11-663-2023, 2023
Short summary
Short summary
This paper presents a two-dimensional subglacial sediment transport model that evolves a sediment layer in response to subglacial sediment transport conditions. The model captures sediment transport in supply- and transport-limited regimes across a glacier's bed and considers both the creation and transport of sediment. Model outputs show how the spatial distribution of sediment and water below a glacier can impact the glacier's discharge of sediment and erosion of bedrock.
Ian Madden, Simone Marras, and Jenny Suckale
Geosci. Model Dev., 16, 3479–3500, https://doi.org/10.5194/gmd-16-3479-2023, https://doi.org/10.5194/gmd-16-3479-2023, 2023
Short summary
Short summary
To aid risk managers who may wish to rapidly assess tsunami risk but may lack high-performance computing infrastructure, we provide an accessible software package able to rapidly model tsunami inundation over real topography by leveraging Google's Tensor Processing Unit, a high-performance hardware. Minimally trained users can take advantage of the rapid modeling abilities provided by this package via a web browser thanks to the ease of use of Google Cloud Platform.
Ugo Nanni, Dirk Scherler, Francois Ayoub, Romain Millan, Frederic Herman, and Jean-Philippe Avouac
The Cryosphere, 17, 1567–1583, https://doi.org/10.5194/tc-17-1567-2023, https://doi.org/10.5194/tc-17-1567-2023, 2023
Short summary
Short summary
Surface melt is a major factor driving glacier movement. Using satellite images, we have tracked the movements of 38 glaciers in the Pamirs over 7 years, capturing their responses to rapid meteorological changes with unprecedented resolution. We show that in spring, glacier accelerations propagate upglacier, while in autumn, they propagate downglacier – all resulting from changes in meltwater input. This provides critical insights into the interplay between surface melt and glacier movement.
Joanne Elkadi, Benjamin Lehmann, Georgina E. King, Olivia Steinemann, Susan Ivy-Ochs, Marcus Christl, and Frédéric Herman
Earth Surf. Dynam., 10, 909–928, https://doi.org/10.5194/esurf-10-909-2022, https://doi.org/10.5194/esurf-10-909-2022, 2022
Short summary
Short summary
Glacial and non-glacial processes have left a strong imprint on the landscape of the European Alps, but further research is needed to better understand their long-term effects. We apply a new technique combining two methods for bedrock surface dating to calculate post-glacier erosion rates next to a Swiss glacier. Interestingly, the results suggest non-glacial erosion rates are higher than previously thought, but glacial erosion remains the most influential on landscape evolution.
Ludovic Räss, Ivan Utkin, Thibault Duretz, Samuel Omlin, and Yuri Y. Podladchikov
Geosci. Model Dev., 15, 5757–5786, https://doi.org/10.5194/gmd-15-5757-2022, https://doi.org/10.5194/gmd-15-5757-2022, 2022
Short summary
Short summary
Continuum mechanics-based modelling of physical processes at large scale requires huge computational resources provided by massively parallel hardware such as graphical processing units. We present a suite of numerical algorithms, implemented using the Julia language, that efficiently leverages the parallelism. We demonstrate that our implementation is efficient, scalable and robust and showcase applications to various geophysical problems.
Emmanuel Wyser, Yury Alkhimenkov, Michel Jaboyedoff, and Yury Y. Podladchikov
Geosci. Model Dev., 14, 7749–7774, https://doi.org/10.5194/gmd-14-7749-2021, https://doi.org/10.5194/gmd-14-7749-2021, 2021
Short summary
Short summary
We propose an implementation of the material point method using graphical processing units (GPUs) to solve elastoplastic problems in three-dimensional configurations, such as the granular collapse or the slumping mechanics, i.e., landslide. The computational power of GPUs promotes fast code executions, compared to a traditional implementation using central processing units (CPUs). This allows us to study complex three-dimensional problems tackling high spatial resolution.
Sean D. Willett, Frédéric Herman, Matthew Fox, Nadja Stalder, Todd A. Ehlers, Ruohong Jiao, and Rong Yang
Earth Surf. Dynam., 9, 1153–1221, https://doi.org/10.5194/esurf-9-1153-2021, https://doi.org/10.5194/esurf-9-1153-2021, 2021
Short summary
Short summary
The cooling climate of the last few million years leading into the ice ages has been linked to increasing erosion rates by glaciers. One of the ways to measure this is through mineral cooling ages. In this paper, we investigate potential bias in these data and the methods used to analyse them. We find that the data are not themselves biased but that appropriate methods must be used. Past studies have used appropriate methods and are sound in methodology.
Martin Franz, Michel Jaboyedoff, Ryan P. Mulligan, Yury Podladchikov, and W. Andy Take
Nat. Hazards Earth Syst. Sci., 21, 1229–1245, https://doi.org/10.5194/nhess-21-1229-2021, https://doi.org/10.5194/nhess-21-1229-2021, 2021
Short summary
Short summary
A landslide-generated tsunami is a complex phenomenon that involves landslide dynamics, wave dynamics and their interaction. This phenomenon threatens numerous lives and infrastructures around the world. To assess this natural hazard, we developed an efficient numerical model able to simulate the landslide, the momentum transfer and the wave all at once. The good agreement between the numerical simulations and physical experiments validates our model and its novel momentum transfer approach.
Cited articles
Bassis, J.: Hamilton-type principles applied to ice-sheet dynamics: new
approximations for large-scale ice sheet flow, J. Glaciol.,
97, 497–513, 2010. a
Brædstrup, C., Damsgaard, A., and Egholm, D. L.: Ice-sheet modelling
accelerated by graphics cards, Comput. Geosci., 72, 210–220,
2014. a
Brinkerhoff, D. J. and Johnson, J. V.: Data assimilation and prognostic whole ice sheet modelling with the variationally derived, higher order, open source, and fully parallel ice sheet model VarGlaS, The Cryosphere, 7, 1161–1184, https://doi.org/10.5194/tc-7-1161-2013, 2013. a
Brinkerhoff, D. J. and Johnson, J. V.: Dynamics of thermally induced ice
streams simulated with a higher-order flow model, J. Geophys.
Res.-Earth, 120, 1743–1770, 2015. a
Bueler, E. and Brown, J.: Shallow shelf approximation as a “sliding law” in a
thermomechanically coupled ice sheet model, J. Geophys. Res.,
114, F03008, https://doi.org/10.1029/2008JF001179, 2009. a, b
Bueler, E., Brown, J., and Lingle, C.: Exact solutions to the
thermomechanically coupled shallow-ice approximation: effective tools for
verification, J. Glaciol., 53, 499–516, 2007. a
Chorin, A. J.: The numerical solution of the Navier-Stokes equations for an
incompressible fluid, B. Am. Math. Soc., 73,
928–931, 1967. a
Chorin, A. J.: Numerical solution of the Navier-Stokes equations, Math. Comput., 22, 745–762, 1968. a
Clarke, G. K. C., Nitsan, U., and Paterson, W. S. B.: Strain heating and creep
instability in glaciers and ice sheets, Rev. Geophys. Space
Phys., 15, 235–247, 1977. a
Cook, S.: CUDA Programming, Morgan Kaufmann, Elsevier, 2012. a
Crank, J. and Nicolson, P.: A practical method for numerical evaluation of
solutions of partial differential equations of the heat-conduction type,
Mathe. Proc. Cambridge Philos. Soc., 43, 50–67,
https://doi.org/10.1017/S0305004100023197, 1947. a
Egholm, D., M.F., K., Clark, C., and Lesemann, J.: Modeling the flow of
glaciers in steep terrains: The integrated second-order shallow ice
approximation (iSOSIA), J. Geophys. Res.-Earth, 116,
F02012, https://doi.org/10.1029/2010JF001900, 2011. a
Gagliardini, O. and Zwinger, T.: The ISMIP-HOM benchmark experiments performed using the Finite-Element code Elmer, The Cryosphere, 2, 67–76, https://doi.org/10.5194/tc-2-67-2008, 2008. a, b
Gagliardini, O., Zwinger, T., Gillet-Chaulet, F., Durand, G., Favier, L., de Fleurian, B., Greve, R., Malinen, M., Martín, C., Råback, P., Ruokolainen, J., Sacchettini, M., Schäfer, M., Seddik, H., and Thies, J.: Capabilities and performance of Elmer/Ice, a new-generation ice sheet model, Geosci. Model Dev., 6, 1299–1318, https://doi.org/10.5194/gmd-6-1299-2013, 2013. a, b, c, d
Gerya, T.: Introduction to Numerical Geodynamic Modelling, Cambridge
University Press, Cambridge, United Kingdom, 2009. a
Gerya, T. V. and Yuen, D. A.: Characteristics-based marker-in-cell method with
conservative finite-differences schemes for modeling geological flows with
strongly variable transport properties, Phys. Earth Planet.
Int., 140, 293–318, 2003. a
Gilbert, A., Gagliardini, O., Vincent, C., and Wagnon, P.: A 3-D thermal
regime model suitable for cold accumulation zones of polythermal mountain
glaciers, J. Geophys. Res.-Earth, 119, 876–1893,
2014. a
Glen, J. W.: The flow law of ice from measurements in glacier tunnels,
laboratory experiments and the Jungfraufirn borehole experiment, J. Glaciol., 2, 111–114, 1952. a
Goldberg, D.: A variationally-derived, depth-integrated approximation to the
Blatter Pattyn balance, J. Glaciol., 57, 157–170, 2011. a
Gong, Y., Zwinger, T., Åström, J., Altena, B., Schellenberger, T., Gladstone, R., and Moore, J. C.: Simulating the roles of crevasse routing of surface water and basal friction on the surge evolution of Basin 3, Austfonna ice cap, The Cryosphere, 12, 1563–1577, https://doi.org/10.5194/tc-12-1563-2018, 2018. a
Hindmarsh, R. C. A.: Stress gradient damping of thermoviscous ice flow
instabilities, J. Geophys. Res.-Earth., 111, B12409, https://doi.org/10.1029/2005JB004019,
2006. a
Hindmarsh, R. C. A.: Consistent generation of ice-streams via thermo-viscous
instabilities modulated by membrane stresses, Geophys. Res. Lett.,
36, L06502, https://doi.org/10.1029/2008GL036877, 2009. a
Hutter, K.: Theoretical glaciology: material science of ice and the mechanics
of glaciers and ice sheets, Vol. 1, Springer, 1983. a
Huybrechts, P. and Payne, T.: The EISMINT benchmarks for testing ice-sheet
models, Ann. Glaciol., 23, 1–12, 1996. a
Isaac, T., Stadler, G., and Ghattas, O.: Solution of Nonlinear Stokes
Equations Discretized by High-order Finite Elements on Nonconforming and
Anisotropic Meshes, with Application to Ice Sheet Dynamics, SIAM J.
Sci. Comput., 37,
B804–B833, https://doi.org/10.1137/140974407, 2015. a
Jarosch, A.: Icetools: a full Stokes finite element model for glaciers,
Comput. Geosci., 34, 1005–1014, 2008. a
Jouvet, G., Picasso, M., Rappaz, J., and Blatter, H.: A new algorithm to
simulate the dynamics of a glacier: theory and applications, J.
Glaciol., 54, 801–811, 2008. a
Kiss, D., Podladchikov, Y., Duretz, T., and Schmalholz, S. M.: Spontaneous
generation of ductile shear zones by thermal softening: Localization
criterion, 1D to 3D modelling and application to the lithosphere, Earth
Planet. Sci. Lett., 519, 284–296, https://doi.org/10.1016/j.epsl.2019.05.026,
2019. a
Larour, E., Seroussi, H., Morlighem, M., and Rignot, E.: Continental scale,
high order, high spatial resolution, ice sheet modeling using the Ice Sheet
System Model (ISSM), J. Geophys. Res., 117, 1–20, 2012. a
Leng, W., Ju, L., Gunzburger, M., and Ringler, T.: A parallel high- order
accurate finite element nonlinear Stokes ice sheet model and benchmark
experiments, J. Geophys. Res., 117, F01001, https://doi.org/10.1029/2011JF001962, 2012. a
McKee, S., Tomé, M., Ferreira, V., Cuminato, J., Castelo, A., Sousa, F.,
and Mangiavacchi, N.: The MAC method, Comput. Fluid., 37, 907–930,
https://doi.org/10.1016/j.compfluid.2007.10.006, 2008. a
Morland, L.: Thermomechanical balances of ice sheet flows, Geophys.
Astrophys. Fluid Dynam., 29, 237–266, 1984. a
Nye, J. F.: The flow law of ice from measurements in glacier tunnels,
laboratory experiments and the Jungfraufirn borehole experiment, Proc. Royal Soc. A, 219, 477–489, 1953. a
Ogawa, M., Schubert, G., and Zebib, A.: Numerical simulations of
three-dimensional thermal convection in a fluid with strongly temperature
dependent viscosity, J. Fluid Mech., 233, 299–328, 1991. a
Patankar, S.: Numerical Heat Transfer and Fluid Flow, Comput. Methods Mech.
Thermal Sci. Ser., CRC Press, Boca Raton,Fla, 1980. a
Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson, G. H., Hindmarsh, R. C. A., Hubbard, A., Johnson, J. V., Kleiner, T., Konovalov, Y., Martin, C., Payne, A. J., Pollard, D., Price, S., Rückamp, M., Saito, F., Souček, O., Sugiyama, S., and Zwinger, T.: Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP-HOM), The Cryosphere, 2, 95–108, https://doi.org/10.5194/tc-2-95-2008, 2008. a, b, c, d, e
Payne, T. and Baldwin, D.: Analysis of ice-flow instabilities identified in
the EISMINT intercomparison exercise, Ann. Glaciol., 30, 204–210,
2000. a
Payne, T., Huybrechts, P., Abe-Ouchi, A., Calov, R., Fastook, J., Greve, R.,
Marshall, S., Marsiat, I., Ritz, C., Tarasov, L., and Thomassen, M.: Results
from the EISMINT model intercomparison: the effects of thermomechanical
coupling, J. Glaciol., 46, 227–238, 2000. a
Perego, M., Gunzburger, M., and Burkardt, J.: Parallel finite element
implementation for higher order ice-sheet models, J. Glaciol.,
58, 76–88, 2012. a
Poliakov, A. N. B., Cundall, P. A., Podladchikov, Y. Y., and Lyakhovsky, V. A.:
An explicit inertial method for the simulation of viscoelastic flow: An
evaluation of elastic effects on diapiric flow in two- and three-layers
models, Flow and Creep in the Solar Systems: Observations, Modeling and
Theory, 175–195, 1993. a, b
Pollard, D. and DeConto, R. M.: Description of a hybrid ice sheet-shelf model, and application to Antarctica, Geosci. Model Dev., 5, 1273–1295, https://doi.org/10.5194/gmd-5-1273-2012, 2012. a
Räss, L., Simon, N., and Podladchikov, Y.: Spontaneous formation of
fluid escape pipes from subsurface reservoirs, Sci. Rep., 8, 11116, https://doi.org/10.1038/s41598-018-29485-5, 2018. a, b, c
Räss, L., Licul, A., Herman, F., Podladchikov, Y., and Suckale, J.:
FastICE, https://doi.org/10.5281/zenodo.3461171, 2019b. a, b
Robin, G. D. Q.: Ice movement and temperature distribution in glaciers and ice
sheets, J. Glaciol., 2, 523–532, 1955. a
Saito, F., Abe-Ouchi, A., and Blatter, H.: European Ice Sheet Modelling
Initiative (EISMINT) model intercomparison experiments with first-order
mechanics, J. Geophys. Res., 111, F02012, https://doi.org/10.1029/2004JF000273, 2006. a
Schäfer, M., Gillet-Chaulet, F., Gladstone, R., Pettersson, R., A. Pohjola, V., Strozzi, T., and Zwinger, T.: Assessment of heat sources on the control of fast flow of Vestfonna ice cap, Svalbard, The Cryosphere, 8, 1951–1973, https://doi.org/10.5194/tc-8-1951-2014, 2014.
a
Schoof, C. and Hindmarsh, R.: Thin film flows with wall slip: an asymptotic
analysis of higher order glacier flow models, Q. J.
Mechan. Appl. Mathe., 63, 73–114, 2010. a
Shin, D. and Strikwerda, J. C.: Inf-Sup conditions for finite-difference
approximations of the Stokes equations, J. Aust.
Mathe. Soc. B, 39, 121–134, 1997. a
Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K., Tignor,
M., and Miller, H.: The physical science basis, 235–337, IPCC report AR4, New York and Cambridge, Cambridge University Press, 2007. a
Tezaur, I. K., Perego, M., Salinger, A. G., Tuminaro, R. S., and Price, S. F.: Albany/FELIX: a parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis, Geosci. Model Dev., 8, 1197–1220, https://doi.org/10.5194/gmd-8-1197-2015, 2015. a, b
Virieux, J.: P-SV wave propagation in heterogeneous media: Velocity‐stress
finite‐difference method, Geophysics, 51, 889–901,
https://doi.org/10.1190/1.1442147, 1986. a
Watkins, J., Tezaur, I., and Demeshko, I.: A study on the performance
portability of the finite element assembly process within the Albany Land Ice solver, Elsevier, 2019. a
Weinan, E. and Liu, J.-G.: Projection method I: convergence and numerical
boundary layers, SIAM J. Num. Anal., 1017–1057, 1995. a
Zwinger, T., Greve, R., Gagliardini, O., Shiraiwa, T., and Lyly, M.: A full
Stokes-flow thermo-mechanical model for firn and ice applied to the Gorshkov
crater glacier, Kamchatka, Ann. Glaciol., 45, 29–37, 2007. a
Short summary
Accurate predictions of future sea level rise require numerical models that predict rapidly deforming ice. Localised ice deformation can be captured numerically only with high temporal and spatial resolution. This paper’s goal is to propose a parallel FastICE solver for modelling ice deformation. Our model is particularly useful for improving our process-based understanding of localised ice deformation. Our solver reaches a parallel efficiency of 99 % on GPU-based supercomputers.
Accurate predictions of future sea level rise require numerical models that predict rapidly...