Articles | Volume 13, issue 2
https://doi.org/10.5194/gmd-13-735-2020
© Author(s) 2020. 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-13-735-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond
Thomas H. Gibson
CORRESPONDING AUTHOR
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
Lawrence Mitchell
Department of Computer Science, Durham University, Durham, DH1 3LE, UK
David A. Ham
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
Colin J. Cotter
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
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Cited
17 citations as recorded by crossref.
- Hybridization and postprocessing in finite element exterior calculus G. Awanou et al. 10.1090/mcom/3743
- Helmholtz preconditioning for the compressible Euler equations using mixed finite elements with Lorenz staggering D. Lee et al. 10.1002/qj.4887
- Fireshape: a shape optimization toolbox for Firedrake A. Paganini & F. Wechsung 10.1007/s00158-020-02813-y
- Energy conserving SUPG methods for compatible finite element schemes in numerical weather prediction G. Wimmer et al. 10.5802/smai-jcm.77
- Multigrid preconditioners for the mixed finite element dynamical core of the LFRic atmospheric model C. Maynard et al. 10.1002/qj.3880
- Robust Multigrid Techniques for Augmented Lagrangian Preconditioning of Incompressible Stokes Equations with Extreme Viscosity Variations Y. Shih et al. 10.1137/21M1430698
- Stationary Stokes solver for single-phase flow in porous media: A blastingly fast solution based on Algebraic Multigrid Method using GPU N. Evstigneev et al. 10.1016/j.advwatres.2022.104340
- A Hybridized Mixed Approach for Efficient Stress Prediction in a Layerwise Plate Model L. Salha et al. 10.3390/math10101711
- Accelerating linear solvers for Stokes problems with C++ metaprogramming D. Demidov et al. 10.1016/j.jocs.2020.101285
- Finite element hybridization of port-Hamiltonian systems A. Brugnoli et al. 10.1016/j.amc.2025.129377
- A linearly-implicit energy-momentum preserving scheme for geometrically nonlinear mechanics based on non-canonical Hamiltonian formulations A. Brugnoli et al. 10.1007/s11071-025-11601-6
- Exploring forms of the moist shallow‐water equations using a new compatible finite‐element discretisation N. Hartney et al. 10.1002/qj.70018
- Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements T. Bendall & G. Wimmer 10.1016/j.jcp.2022.111834
- A nonconforming primal hybrid finite element method for the two-dimensional vector Laplacian M. Barker et al. 10.5802/smai-jcm.107
- Improving the Accuracy of Discretisations of the Vector Transport Equation on the Lowest-Order Quadrilateral Raviart-Thomas Finite Elements T. Bendall & G. Wimmer 10.2139/ssrn.4166560
- A compatible finite‐element discretisation for the moist compressible Euler equations T. Bendall et al. 10.1002/qj.3841
- asQ: parallel-in-time finite element simulations using ParaDiag for geoscientific models and beyond J. Hope-Collins et al. 10.5194/gmd-18-4535-2025
17 citations as recorded by crossref.
- Hybridization and postprocessing in finite element exterior calculus G. Awanou et al. 10.1090/mcom/3743
- Helmholtz preconditioning for the compressible Euler equations using mixed finite elements with Lorenz staggering D. Lee et al. 10.1002/qj.4887
- Fireshape: a shape optimization toolbox for Firedrake A. Paganini & F. Wechsung 10.1007/s00158-020-02813-y
- Energy conserving SUPG methods for compatible finite element schemes in numerical weather prediction G. Wimmer et al. 10.5802/smai-jcm.77
- Multigrid preconditioners for the mixed finite element dynamical core of the LFRic atmospheric model C. Maynard et al. 10.1002/qj.3880
- Robust Multigrid Techniques for Augmented Lagrangian Preconditioning of Incompressible Stokes Equations with Extreme Viscosity Variations Y. Shih et al. 10.1137/21M1430698
- Stationary Stokes solver for single-phase flow in porous media: A blastingly fast solution based on Algebraic Multigrid Method using GPU N. Evstigneev et al. 10.1016/j.advwatres.2022.104340
- A Hybridized Mixed Approach for Efficient Stress Prediction in a Layerwise Plate Model L. Salha et al. 10.3390/math10101711
- Accelerating linear solvers for Stokes problems with C++ metaprogramming D. Demidov et al. 10.1016/j.jocs.2020.101285
- Finite element hybridization of port-Hamiltonian systems A. Brugnoli et al. 10.1016/j.amc.2025.129377
- A linearly-implicit energy-momentum preserving scheme for geometrically nonlinear mechanics based on non-canonical Hamiltonian formulations A. Brugnoli et al. 10.1007/s11071-025-11601-6
- Exploring forms of the moist shallow‐water equations using a new compatible finite‐element discretisation N. Hartney et al. 10.1002/qj.70018
- Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements T. Bendall & G. Wimmer 10.1016/j.jcp.2022.111834
- A nonconforming primal hybrid finite element method for the two-dimensional vector Laplacian M. Barker et al. 10.5802/smai-jcm.107
- Improving the Accuracy of Discretisations of the Vector Transport Equation on the Lowest-Order Quadrilateral Raviart-Thomas Finite Elements T. Bendall & G. Wimmer 10.2139/ssrn.4166560
- A compatible finite‐element discretisation for the moist compressible Euler equations T. Bendall et al. 10.1002/qj.3841
- asQ: parallel-in-time finite element simulations using ParaDiag for geoscientific models and beyond J. Hope-Collins et al. 10.5194/gmd-18-4535-2025
Latest update: 08 Oct 2025
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.
Galerkin finite element discretizations for atmospheric modeling often require the solution of...
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