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Efficient compilation of a class of variational forms

Journal article
Authors R.C. Kirby
Anders Logg
Published in ACM Transactions on Mathematical Software
Volume 33
Issue 3
ISSN 0098-3500
Publication year 2007
Published at Department of Mathematical Sciences, Mathematics
Language en
Links dx.doi.org/10.1145/1268769.1268771
Keywords Automation , BLAS , Compiler , Finite element , Granularity , Loop hoisting , Monomials , Variational form
Subject categories Mathematics, Computational Mathematics

Abstract

We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant reference tensor and a geometry tensor that accounts for geometry and variable coefficients. Based on this representation theorem, we design an algorithm for efficient pretabulation of the reference tensor. The new algorithm has been implemented in the FEniCS Form Compiler (FFC) and improves on a previous loop-based implementation by several orders of magnitude, thus shortening compile-times and development cycles for users of FFC. © 2007 ACM.

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