A structure-exploiting numbering algorithm for finite elements on
extruded meshes, and its performance evaluation in Firedrake

Bercea, Gheorghe-Teodor; McRae, Andrew T. T.; Ham, David A.; Mitchell, Lawrence; Rathgeber, Florian; Nardi, Luigi; Luporini, Fabio; Kelly, Paul H. J.

doi:https://doi.org/10.5194/gmd-9-3803-2016

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.

Special issue:

The Firedrake automatic code generation system

https://doi.org/10.5194/gmd-9-3803-2016

© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 9, issue 10

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, Andrew T. T. McRae, David A. Ham, Lawrence Mitchell, Florian Rathgeber, Luigi Nardi, Fabio Luporini, and Paul H. J. Kelly

Data sets

An automated finite element system Firedrake https://doi.org/10.5281/zenodo.47717

Portable, Extensible Toolkit for Scientific Computation PETSc https://doi.org/10.5281/zenodo.47718

The Python interface to PETSc petsc4py https://doi.org/10.5281/zenodo.47714

The Finite Element Automated Tabulator FIAT https://doi.org/10.5281/zenodo.47716

The Unified Form Language UFL https://doi.org/10.5281/zenodo.47713

FEniCS Form Compiler FFC https://doi.org/10.5281/zenodo.47761

Framework for performance-portable parallel computations on unstructured meshes PyOP2 https://doi.org/10.5281/zenodo.47712

A Compiler for Fast Expression Evaluation COFFEE https://doi.org/10.5281/zenodo.47715

Data and plot scripts for Sandy Bridge experiments Data and plot scripts for Sandy Bridge experiments G.-T. Bercea https://doi.org/10.5281/zenodo.61920

Data and plot scripts for Haswell experiments G.-T. Bercea https://doi.org/10.5281/zenodo.61919

Unstructured meshes for extrusion article G.-T. Bercea https://doi.org/10.5281/zenodo.61819

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.