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  5. A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake
 
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A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake
OA Location
http://www.geosci-model-dev.net/9/3803/2016/
Author(s)
Bercea, G
McRae, ATT
Ham, DA
Mitchell, L
Rathgeber, F
more
Type
Journal Article
Abstract
We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of prismatic cells. Applications of extruded meshes include, but are not limited to, the representation of 3D high aspect ratio domains employed by geophysical finite element simulations. These meshes are structured in the extruded direction. The algorithm presented here exploits this structure to avoid the performance penalty traditionally associated with unstructured meshes. We evaluate the implementation of this algorithm in the Firedrake finite element system on a range of low compute intensity operations which constitute worst cases for data layout performance exploration. The experiments show that having structure along the extruded direction enables the cost of the indirect data accesses to be amortized after 10-20 layers as long as the underlying mesh is well-ordered. We characterise the resulting spatial and temporal reuse in a representative set of both continuous-Galerkin and discontinuous-Galerkin discretisations. On meshes with realistic numbers of layers the performance achieved is between 70% and 90% of a theoretical hardware-specific limit.
Date Issued
2016-10-27
Date Acceptance
2016-09-26
Citation
Geoscientific Model Development, 2016, 9 (10), pp.3803-3815
URI
http://hdl.handle.net/10044/1/53366
URL
http://www.geoscientific-model-development.net/
DOI
https://www.dx.doi.org/10.5194/gmd-9-3803-2016
ISSN
1991-9603
Publisher
European Geosciences Union (EGU)
Start Page
3803
End Page
3815
Journal / Book Title
Geoscientific Model Development
Volume
9
Issue
10
Replaces
http://hdl.handle.net/10044/1/40836
10044/1/40836
Copyright Statement
© Author(s) 2016. This work is distributed
under the Creative Commons Attribution 3.0 License (https://creativecommons.org/licenses/by/3.0/)
License URL
http://creativecommons.org/licenses/by/4.0/
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Natural Environment Research Council (NERC)
Natural Environment Research Council (NERC)
Engineering & Physical Science Research Council (E
Identifier
http://www.geoscientific-model-development.net/
Grant Number
EP/I00677X/1
NE/K008951/1
NE/K006789/1
EP/L000407/1
Subjects
extruded meshes
code generation
locality optimisation
Publication Status
Published
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