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

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Final revised paper (published on 27 Oct 2016)
Preprint (discussion started on 09 Jun 2016)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'A numbering algorithm for finite elements on extruded meshes which avoids the unstructured mesh penalty', Anonymous Referee #1, 06 Jul 2016
- AC1: 'Answers to Reviewer 1', Gheorghe-Teodor Bercea, 15 Sep 2016
RC2: 'Review', Anonymous Referee #2, 22 Aug 2016
- AC2: 'Answers to Reviewer 2', Gheorghe-Teodor Bercea, 15 Sep 2016

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Gheorghe-Teodor Bercea on behalf of the Authors (16 Sep 2016) Author's response Manuscript

ED: Publish as is (26 Sep 2016) by Simon Unterstrasser

AR by Gheorghe-Teodor Bercea on behalf of the Authors (04 Oct 2016)

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.