Articles | Volume 6, issue 6
https://doi.org/10.5194/gmd-6-2099-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/gmd-6-2099-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Development and technical paper
| 
17 Dec 2013
Development and technical paper |
| 17 Dec 2013
Automating the solution of PDEs on the sphere and other manifolds in FEniCS 1.2
M. E. Rognes
Center for Biomedical Computing, Simula Research Laboratory, P.O. Box 134, 1325 Lysaker, Norway
D. A. Ham
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Department of Computing, Imperial College London, London SW7 2AZ, UK
C. J. Cotter
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
A. T. T. McRae
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
The Grantham Institute for Climate Change, Imperial College London, London SW7 2AZ, UK
Viewed
Total article views: 11,932 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 05 Jul 2013)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 4,249 | 7,356 | 327 | 11,932 | 240 | 162 |
- HTML: 4,249
- PDF: 7,356
- XML: 327
- Total: 11,932
- BibTeX: 240
- EndNote: 162
Total article views: 10,266 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 17 Dec 2013)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 3,754 | 6,237 | 275 | 10,266 | 209 | 155 |
- HTML: 3,754
- PDF: 6,237
- XML: 275
- Total: 10,266
- BibTeX: 209
- EndNote: 155
Total article views: 1,666 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 05 Jul 2013)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 495 | 1,119 | 52 | 1,666 | 31 | 7 |
- HTML: 495
- PDF: 1,119
- XML: 52
- Total: 1,666
- BibTeX: 31
- EndNote: 7
Cited
26 citations as recorded by crossref.
- A reduced-dimensional model for near-wall transport in cardiovascular flows K. Hansen & S. Shadden 10.1007/s10237-015-0719-4
- The scaling and skewness of optimally transported meshes on the sphere C. Budd et al. 10.1016/j.jcp.2018.08.028
- Boundary-aware hodge decompositions for piecewise constant vector fields K. Poelke & K. Polthier 10.1016/j.cad.2016.05.004
- A Shape Newton Scheme for Deforming Shells with Application to Capillary Bridges S. Schmidt et al. 10.1137/20M1389054
- ConvPDE-UQ: Convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains N. Winovich et al. 10.1016/j.jcp.2019.05.026
- GridapDistributed: a massively parallel finite element toolbox in Julia S. Badia et al. 10.21105/joss.04157
- A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere D. Lee & A. Palha 10.1016/j.jcp.2018.08.042
- Firedrake-Fluids v0.1: numerical modelling of shallow water flows using an automated solution framework C. Jacobs & M. Piggott 10.5194/gmd-8-533-2015
- A quasi-Hamiltonian discretization of the thermal shallow water equations C. Eldred et al. 10.1016/j.jcp.2018.10.038
- Code Generation for Generally Mapped Finite Elements R. Kirby & L. Mitchell 10.1145/3361745
- Bayesian estimations of orientation distribution functions from small-angle scattering enable direct prediction of mechanical stress in anisotropic materials P. Corona et al. 10.1103/PhysRevMaterials.5.065601
- Compatible finite element spaces for geophysical fluid dynamics A. Natale et al. 10.1093/climsys/dzw005
- Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds V. Nguyen et al. 10.1016/j.jmr.2019.01.002
- Firedrake F. Rathgeber et al. 10.1145/2998441
- A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations D. Lee et al. 10.1016/j.camwa.2024.04.016
- Divergence‐free tangential finite element methods for incompressible flows on surfaces P. Lederer et al. 10.1002/nme.6317
- Fourth-Order Time-Stepping For Stiff PDEs On The Sphere H. Montanelli & Y. Nakatsukasa 10.1137/17M1112728
- 3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries C. Lee et al. 10.1371/journal.pcbi.1007756
- Gradient-enhanced damage modeling in Kirchhoff–Love shells: Application to isogeometric analysis of composite laminates M. Pigazzini et al. 10.1016/j.cma.2018.10.042
- Simple and extensible plate and shell finite element models through automatic code generation tools J. Hale et al. 10.1016/j.compstruc.2018.08.001
- Transient structures in rupturing thin films: Marangoni-induced symmetry-breaking pattern formation in viscous fluids L. Shen et al. 10.1126/sciadv.abb0597
- Hierarchical high order finite element bases forH(div)spaces based on curved meshes for two-dimensional regions or manifolds D. Castro et al. 10.1016/j.cam.2016.01.053
- Abstractions and Automated Algorithms for Mixed Domain Finite Element Methods C. Daversin-Catty et al. 10.1145/3471138
- Higher-order compatible finite element schemes for the nonlinear rotating shallow water equations on the sphere J. Shipton et al. 10.1016/j.jcp.2018.08.027
- Mixed finite elements for global tide models C. Cotter & R. Kirby 10.1007/s00211-015-0748-z
- Mixed finite elements for global tide models with nonlinear damping C. Cotter et al. 10.1007/s00211-018-0980-4
23 citations as recorded by crossref.
- A reduced-dimensional model for near-wall transport in cardiovascular flows K. Hansen & S. Shadden 10.1007/s10237-015-0719-4
- The scaling and skewness of optimally transported meshes on the sphere C. Budd et al. 10.1016/j.jcp.2018.08.028
- Boundary-aware hodge decompositions for piecewise constant vector fields K. Poelke & K. Polthier 10.1016/j.cad.2016.05.004
- A Shape Newton Scheme for Deforming Shells with Application to Capillary Bridges S. Schmidt et al. 10.1137/20M1389054
- ConvPDE-UQ: Convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains N. Winovich et al. 10.1016/j.jcp.2019.05.026
- GridapDistributed: a massively parallel finite element toolbox in Julia S. Badia et al. 10.21105/joss.04157
- A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere D. Lee & A. Palha 10.1016/j.jcp.2018.08.042
- Firedrake-Fluids v0.1: numerical modelling of shallow water flows using an automated solution framework C. Jacobs & M. Piggott 10.5194/gmd-8-533-2015
- A quasi-Hamiltonian discretization of the thermal shallow water equations C. Eldred et al. 10.1016/j.jcp.2018.10.038
- Code Generation for Generally Mapped Finite Elements R. Kirby & L. Mitchell 10.1145/3361745
- Bayesian estimations of orientation distribution functions from small-angle scattering enable direct prediction of mechanical stress in anisotropic materials P. Corona et al. 10.1103/PhysRevMaterials.5.065601
- Compatible finite element spaces for geophysical fluid dynamics A. Natale et al. 10.1093/climsys/dzw005
- Diffusion MRI simulation in thin-layer and thin-tube media using a discretization on manifolds V. Nguyen et al. 10.1016/j.jmr.2019.01.002
- Firedrake F. Rathgeber et al. 10.1145/2998441
- A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations D. Lee et al. 10.1016/j.camwa.2024.04.016
- Divergence‐free tangential finite element methods for incompressible flows on surfaces P. Lederer et al. 10.1002/nme.6317
- Fourth-Order Time-Stepping For Stiff PDEs On The Sphere H. Montanelli & Y. Nakatsukasa 10.1137/17M1112728
- 3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries C. Lee et al. 10.1371/journal.pcbi.1007756
- Gradient-enhanced damage modeling in Kirchhoff–Love shells: Application to isogeometric analysis of composite laminates M. Pigazzini et al. 10.1016/j.cma.2018.10.042
- Simple and extensible plate and shell finite element models through automatic code generation tools J. Hale et al. 10.1016/j.compstruc.2018.08.001
- Transient structures in rupturing thin films: Marangoni-induced symmetry-breaking pattern formation in viscous fluids L. Shen et al. 10.1126/sciadv.abb0597
- Hierarchical high order finite element bases forH(div)spaces based on curved meshes for two-dimensional regions or manifolds D. Castro et al. 10.1016/j.cam.2016.01.053
- Abstractions and Automated Algorithms for Mixed Domain Finite Element Methods C. Daversin-Catty et al. 10.1145/3471138
3 citations as recorded by crossref.
- Higher-order compatible finite element schemes for the nonlinear rotating shallow water equations on the sphere J. Shipton et al. 10.1016/j.jcp.2018.08.027
- Mixed finite elements for global tide models C. Cotter & R. Kirby 10.1007/s00211-015-0748-z
- Mixed finite elements for global tide models with nonlinear damping C. Cotter et al. 10.1007/s00211-018-0980-4
Saved (final revised paper)
Saved (final revised paper)
Saved (preprint)
Latest update: 16 Jul 2024
