An algorithm for the optimization of finite element integration loops
File(s)
Accepted version
Author(s)
Luporini, F
Ham, DA
Kelly, PHJ
Type
Journal Article
Abstract
We present an algorithm for the optimization of a class of finite element integration loop nests. This algo-
rithm, which exploits fundamental mathematical properties of finite element operators, is proven to achieve
a locally optimal operation count. In specified circumstances the optimum achieved is global. Extensive nu-
merical experiments demonstrate significant performance improvements over the state of the art in finite
element code generation in almost all cases. This validates the effectiveness of the algorithm presented here,
and illustrates its limitations.
rithm, which exploits fundamental mathematical properties of finite element operators, is proven to achieve
a locally optimal operation count. In specified circumstances the optimum achieved is global. Extensive nu-
merical experiments demonstrate significant performance improvements over the state of the art in finite
element code generation in almost all cases. This validates the effectiveness of the algorithm presented here,
and illustrates its limitations.
Date Issued
2017-07-24
Date Acceptance
2017-02-06
Citation
ACM Transactions on Mathematical Software, 2017, 44 (1)
ISSN
0098-3500
Publisher
Association for Computing Machinery (ACM)
Journal / Book Title
ACM Transactions on Mathematical Software
Volume
44
Issue
1
Copyright Statement
© 2017 ACM. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Mathematical Software (TOMS), http://dl.acm.org/citation.cfm?doid=3071076.3054944
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Natural Environment Research Council (NERC)
Natural Environment Research Council (NERC)
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/I00677X/1
NE/K008951/1
NE/K006789/1
EP/L000407/1
Subjects
Science & Technology
Technology
Physical Sciences
Computer Science, Software Engineering
Mathematics, Applied
Computer Science
Mathematics
Design
Performance
Finite element integration
local assembly
compilers
performance optimization
VARIATIONAL FORMS
cs.MS
G.1.8; G.4
0802 Computation Theory And Mathematics
0806 Information Systems
Numerical & Computational Mathematics
Publication Status
Published
Article Number
3