Articles | Volume 13, issue 2
Geosci. Model Dev., 13, 735–761, 2020
https://doi.org/10.5194/gmd-13-735-2020

Special issue: The Firedrake automatic code generation system

Geosci. Model Dev., 13, 735–761, 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 et al.

Related authors

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
A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake
Gheorghe-Teodor Bercea, Andrew T. T. McRae, David A. Ham, Lawrence Mitchell, Florian Rathgeber, Luigi Nardi, Fabio Luporini, and Paul H. J. Kelly
Geosci. Model Dev., 9, 3803–3815, https://doi.org/10.5194/gmd-9-3803-2016,https://doi.org/10.5194/gmd-9-3803-2016, 2016
Short summary
A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids
J. Thuburn, C. J. Cotter, and T. Dubos
Geosci. Model Dev., 7, 909–929, https://doi.org/10.5194/gmd-7-909-2014,https://doi.org/10.5194/gmd-7-909-2014, 2014
Adapting to life: ocean biogeochemical modelling and adaptive remeshing
J. Hill, E. E. Popova, D. A. Ham, M. D. Piggott, and M. Srokosz
Ocean Sci., 10, 323–343, https://doi.org/10.5194/os-10-323-2014,https://doi.org/10.5194/os-10-323-2014, 2014
Automating the solution of PDEs on the sphere and other manifolds in FEniCS 1.2
M. E. Rognes, D. A. Ham, C. J. Cotter, and A. T. T. McRae
Geosci. Model Dev., 6, 2099–2119, https://doi.org/10.5194/gmd-6-2099-2013,https://doi.org/10.5194/gmd-6-2099-2013, 2013

Related subject area

Numerical methods
A nested multi-scale system implemented in the large-eddy simulation model PALM model system 6.0
Antti Hellsten, Klaus Ketelsen, Matthias Sühring, Mikko Auvinen, Björn Maronga, Christoph Knigge, Fotios Barmpas, Georgios Tsegas, Nicolas Moussiopoulos, and Siegfried Raasch
Geosci. Model Dev., 14, 3185–3214, https://doi.org/10.5194/gmd-14-3185-2021,https://doi.org/10.5194/gmd-14-3185-2021, 2021
Short summary
Extending legacy climate models by adaptive mesh refinement for single-component tracer transport: a case study with ECHAM6-HAMMOZ (ECHAM6.3-HAM2.3-MOZ1.0)
Yumeng Chen, Konrad Simon, and Jörn Behrens
Geosci. Model Dev., 14, 2289–2316, https://doi.org/10.5194/gmd-14-2289-2021,https://doi.org/10.5194/gmd-14-2289-2021, 2021
Short summary
Using the Després and Lagoutière (1999) antidiffusive transport scheme: a promising and novel method against excessive vertical diffusion in chemistry-transport models
Sylvain Mailler, Romain Pennel, Laurent Menut, and Mathieu Lachâtre
Geosci. Model Dev., 14, 2221–2233, https://doi.org/10.5194/gmd-14-2221-2021,https://doi.org/10.5194/gmd-14-2221-2021, 2021
Short summary
Porosity and permeability prediction through forward stratigraphic simulations using GPM™ and Petrel™: application in shallow marine depositional settings
Daniel Otoo and David Hodgetts
Geosci. Model Dev., 14, 2075–2095, https://doi.org/10.5194/gmd-14-2075-2021,https://doi.org/10.5194/gmd-14-2075-2021, 2021
Short summary
Effects of transient processes for thermal simulations of the Central European Basin
Denise Degen and Mauro Cacace
Geosci. Model Dev., 14, 1699–1719, https://doi.org/10.5194/gmd-14-1699-2021,https://doi.org/10.5194/gmd-14-1699-2021, 2021
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.