Articles | Volume 9, issue 10
https://doi.org/10.5194/gmd-9-3803-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Special issue:
https://doi.org/10.5194/gmd-9-3803-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Development and technical paper
| 
27 Oct 2016
Development and technical paper |
| 27 Oct 2016
A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake
Gheorghe-Teodor Bercea
CORRESPONDING AUTHOR
Department of Computing, Imperial College London, London, SW7 2AZ, UK
Andrew T. T. McRae
The Grantham Institute, Imperial College London, London, SW7 2AZ, UK
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK
David A. Ham
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
Lawrence Mitchell
Department of Computing, Imperial College London, London, SW7 2AZ, UK
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
Florian Rathgeber
Department of Computing, Imperial College London, London, SW7 2AZ, UK
European Centre for Medium-Range Weather Forecasts (ECMWF), Reading, RG2 9AX, UK
Luigi Nardi
Department of Computing, Imperial College London, London, SW7 2AZ, UK
Fabio Luporini
Department of Computing, Imperial College London, London, SW7 2AZ, UK
Paul H. J. Kelly
Department of Computing, Imperial College London, London, SW7 2AZ, UK
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- Variational inequality approach to enforcing the non-negative constraint for advection–diffusion equations J. Chang & K. Nakshatrala https://doi.org/10.1016/j.cma.2017.03.022
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- A compatible finite element discretisation for the nonhydrostatic vertical slice equations C. Cotter & J. Shipton https://doi.org/10.1007/s13137-023-00236-7
- A compatible finite‐element discretisation for the moist compressible Euler equations T. Bendall et al. https://doi.org/10.1002/qj.3841
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- Composable block solvers for the four-field double porosity/permeability model M. Joshaghani et al. https://doi.org/10.1016/j.jcp.2019.02.020
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25 citations as recorded by crossref.
- Towards a fully unstructured ocean model for ice shelf cavity environments: Model development and verification using the Firedrake finite element framework W. Scott et al. https://doi.org/10.1016/j.ocemod.2023.102178
- A MATLAB Script for Solving 2D/3D Minimum Compliance Problems using Anisotropic Mesh Adaptation K. Jensen https://doi.org/10.1016/j.proeng.2017.09.792
- An Algorithm for the Optimization of Finite Element Integration Loops F. Luporini et al. https://doi.org/10.1145/3054944
- A scalable DG solver for the electroneutral Nernst-Planck equations T. Roy et al. https://doi.org/10.1016/j.jcp.2022.111859
- Variational inequality approach to enforcing the non-negative constraint for advection–diffusion equations J. Chang & K. Nakshatrala https://doi.org/10.1016/j.cma.2017.03.022
- tIGAr: Automating isogeometric analysis with FEniCS D. Kamensky & Y. Bazilevs https://doi.org/10.1016/j.cma.2018.10.002
- The Dune framework: Basic concepts and recent developments P. Bastian et al. https://doi.org/10.1016/j.camwa.2020.06.007
- Firedrake F. Rathgeber et al. https://doi.org/10.1145/2998441
- A compatible finite element discretisation for the nonhydrostatic vertical slice equations C. Cotter & J. Shipton https://doi.org/10.1007/s13137-023-00236-7
- A compatible finite‐element discretisation for the moist compressible Euler equations T. Bendall et al. https://doi.org/10.1002/qj.3841
- FNPF-SEM: A parallel spectral element model in Firedrake for fully nonlinear water wave simulations J. Visbech et al. https://doi.org/10.1177/10943420261462394
- Composable block solvers for the four-field double porosity/permeability model M. Joshaghani et al. https://doi.org/10.1016/j.jcp.2019.02.020
- asQ: parallel-in-time finite element simulations using ParaDiag for geoscientific models and beyond J. Hope-Collins et al. https://doi.org/10.5194/gmd-18-4535-2025
- Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations T. Kärnä et al. https://doi.org/10.5194/gmd-11-4359-2018
- A Mixed Finite Element Discretization of Dynamical Optimal Transport A. Natale & G. Todeschi https://doi.org/10.1007/s10915-022-01821-y
- Energy conserving SUPG methods for compatible finite element schemes in numerical weather prediction G. Wimmer et al. https://doi.org/10.5802/smai-jcm.77
- Comparative Study of Finite Element Methods Using the Time-Accuracy-Size(TAS) Spectrum Analysis J. Chang et al. https://doi.org/10.1137/18M1172260
- hyper.deal: An Efficient, Matrix-free Finite-element Library for High-dimensional Partial Differential Equations P. Munch et al. https://doi.org/10.1145/3469720
- A 3D battery model incorporating Si particle expansion induced electrolyte motion L. Boveleth et al. https://doi.org/10.1016/j.est.2025.119206
- The scaling and skewness of optimally transported meshes on the sphere C. Budd et al. https://doi.org/10.1016/j.jcp.2018.08.028
- Structure matters: A scale-resolved numerical operando approach for Lithium–Sulfur batteries M. Okraschevski et al. https://doi.org/10.1016/j.est.2026.122529
- Robust Multigrid Techniques for Augmented Lagrangian Preconditioning of Incompressible Stokes Equations with Extreme Viscosity Variations Y. Shih et al. https://doi.org/10.1137/21M1430698
- Open-source immersogeometric analysis of fluid–structure interaction using FEniCS and tIGAr D. Kamensky https://doi.org/10.1016/j.camwa.2020.01.023
- Demystifying asynchronous I/O Interference in HPC applications S. Tseng et al. https://doi.org/10.1177/10943420211016511
- Automated forward and adjoint modelling of viscoelastic deformation of the solid Earth W. Scott et al. https://doi.org/10.5194/gmd-19-2717-2026
Saved (final revised paper)
Latest update: 27 Jul 2026
Short summary
Unstructured meshes offer flexibility but are perceived as slow. Some applications, including atmosphere or ocean simulations, admit an extruded mesh: the horizontal mesh may be unstructured, but the vertical dimension can be traversed in a structured way. By extending the Firedrake automated simulation framework to this case, we show that an extruded mesh can be traversed as fast as a structured mesh. This paves the way for highly efficient unstructured mesh models of the ocean and atmosphere.
Unstructured meshes offer flexibility but are perceived as slow. Some applications, including...
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