Articles | Volume 13, issue 2
https://doi.org/10.5194/gmd-13-735-2020
https://doi.org/10.5194/gmd-13-735-2020
Development and technical paper
 | 
25 Feb 2020
Development and technical paper |  | 25 Feb 2020

Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond

Thomas H. Gibson, Lawrence Mitchell, David A. Ham, and Colin J. Cotter

Related authors

asQ: parallel-in-time finite element simulations using ParaDiag for geoscientific models and beyond
Joshua Hope-Collins, Abdalaziz Hamdan, Werner Bauer, Lawrence Mitchell, and Colin Cotter
EGUsphere, https://doi.org/https://doi.org/10.48550/arXiv.2409.18792,https://doi.org/https://doi.org/10.48550/arXiv.2409.18792, 2024
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Consistent point data assimilation in Firedrake and Icepack
Reuben W. Nixon-Hill, Daniel Shapero, Colin J. Cotter, and David A. Ham
Geosci. Model Dev., 17, 5369–5386, https://doi.org/10.5194/gmd-17-5369-2024,https://doi.org/10.5194/gmd-17-5369-2024, 2024
Short summary
Automatic adjoint-based inversion schemes for geodynamics: reconstructing the evolution of Earth's mantle in space and time
Sia Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
Geosci. Model Dev., 17, 5057–5086, https://doi.org/10.5194/gmd-17-5057-2024,https://doi.org/10.5194/gmd-17-5057-2024, 2024
Short summary
Multilevel multifidelity Monte Carlo methods for assessing uncertainty in coastal flooding
Mariana C. A. Clare, Tim W. B. Leijnse, Robert T. McCall, Ferdinand L. M. Diermanse, Colin J. Cotter, and Matthew D. Piggott
Nat. Hazards Earth Syst. Sci., 22, 2491–2515, https://doi.org/10.5194/nhess-22-2491-2022,https://doi.org/10.5194/nhess-22-2491-2022, 2022
Short summary
Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations
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
Short summary

Related subject area

Numerical methods
A joint reconstruction and model selection approach for large-scale linear inverse modeling (msHyBR v2)
Malena Sabaté Landman, Julianne Chung, Jiahua Jiang, Scot M. Miller, and Arvind K. Saibaba
Geosci. Model Dev., 17, 8853–8872, https://doi.org/10.5194/gmd-17-8853-2024,https://doi.org/10.5194/gmd-17-8853-2024, 2024
Short summary
Assimilation of snow water equivalent from AMSR2 and IMS satellite data utilizing the local ensemble transform Kalman filter
Joonlee Lee, Myong-In Lee, Sunlae Tak, Eunkyo Seo, and Yong-Keun Lee
Geosci. Model Dev., 17, 8799–8816, https://doi.org/10.5194/gmd-17-8799-2024,https://doi.org/10.5194/gmd-17-8799-2024, 2024
Short summary
The Paleochrono-1.1 probabilistic model to derive a common age model for several paleoclimatic sites using absolute and relative dating constraints
Frédéric Parrenin, Marie Bouchet, Christo Buizert, Emilie Capron, Ellen Corrick, Russell Drysdale, Kenji Kawamura, Amaëlle Landais, Robert Mulvaney, Ikumi Oyabu, and Sune Olander Rasmussen
Geosci. Model Dev., 17, 8735–8750, https://doi.org/10.5194/gmd-17-8735-2024,https://doi.org/10.5194/gmd-17-8735-2024, 2024
Short summary
Explicit stochastic advection algorithms for the regional-scale particle-resolved atmospheric aerosol model WRF-PartMC (v1.0)
Jeffrey H. Curtis, Nicole Riemer, and Matthew West
Geosci. Model Dev., 17, 8399–8420, https://doi.org/10.5194/gmd-17-8399-2024,https://doi.org/10.5194/gmd-17-8399-2024, 2024
Short summary
Enhancing Single-Precision with Quasi Double-Precision: Achieving Double-Precision Accuracy in the Model for Prediction Across Scales-Atmosphere (MPAS-A) version 8.2.1
Jiayi Lai, Lanning Wang, Qizhong Wu, Yizhou Yang, and Fang Wang
EGUsphere, https://doi.org/10.5194/egusphere-2024-2986,https://doi.org/10.5194/egusphere-2024-2986, 2024
Short summary

Cited articles

Alnæs, M. S., Logg, A., Ølgaard, K. B., Rognes, M. E., and Wells, G. N.: Unified form language: A domain-specific language for weak formulations of partial differential equations, ACM Trans. Mathe. Softw. (TOMS), 40, 1–37, 2014. a, b, c, d, e
Arnold, D. N. and Brezzi, F.: Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, ESAIM: Mathe. Modell. Num. Anal., 19, 7–32, 1985. a, b, c, d
Arnold, D. N., Falk, R. S., and Winther, R.: Multigrid in H(div) and H(curl), Num. Mathe., 85, 197–217, https://doi.org/10.1007/s002110000137, 2000. a
Balay, S., Gropp, W. D., McInnes, L. C., and Smith, B. F.: Efficient management of parallelism in object-oriented numerical software libraries, in: Modern software tools for scientific computing, 163–202, Springer, 1997. a
Balay, S., Abhyankar, S., Adams, M. F., Brown, J., Brune, P., Buschelman, K., Dalcin, L., 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 3.11, Argonne National Laboratory, 2019. a, b
Download
Short summary
Galerkin finite element discretizations for atmospheric modeling often require the solution of ill-conditioned, saddle point equations which can be efficiently solved using a hybridized method. By extending Firedrake's domain-specific abstraction, we provide a mechanism for the rapid implementation of hybridization methods for a wide class of methods. In this paper, we show that hybridization is an effective alternative to traditional block solvers for simulating geophysical flows.