High-Performance Evaluation of Finite Element Variational Forms via Commuting Diagrams and Duality
Article No.: 25, Pages 1 - 24
Abstract
We revisit the question of optimizing the construction and application of finite element matrices. By using commuting properties of the reference mappings and duality, we reorganize stiffness matrix construction and matrix-free application so that the bulk of the work can be done by optimized matrix multiplication libraries. We provide examples, including numerical experiments, with the Laplace and curl-curl operators as well as develop a general framework. Our techniques are applicable in general geometry and are not restricted to constant coefficient operators.
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- High-Performance Evaluation of Finite Element Variational Forms via Commuting Diagrams and Duality
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June 2014
154 pages
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Association for Computing Machinery
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Publication History
Published: 08 July 2014
Accepted: 01 December 2013
Revised: 01 August 2013
Received: 01 December 2012
Published in TOMS Volume 40, Issue 4
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