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

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Title: A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake
Authors: Bercea, G
McRae, ATT
Ham, DA
Mitchell, L
Rathgeber, F
Nardi, L
Luporini, F
Kelly, PHJ
Item 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.
Issue Date: 27-Oct-2016
Date of Acceptance: 26-Sep-2016
URI: http://hdl.handle.net/10044/1/53366
DOI: https://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/)
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Natural Environment Research Council (NERC)
Natural Environment Research Council (NERC)
Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/I00677X/1
NE/K008951/1
NE/K006789/1
EP/L000407/1
Keywords: extruded meshes
code generation
locality optimisation
04 Earth Sciences
Publication Status: Published
Open Access location: http://www.geosci-model-dev.net/9/3803/2016/
Appears in Collections:Faculty of Engineering
Mathematics
Computing
Centre for Environmental Policy
Faculty of Natural Sciences



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