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Efficient compilation of a class of variational forms

R.C. Kirby ; Anders Logg (Institutionen för matematiska vetenskaper, matematik)
ACM Transactions on Mathematical Software (0098-3500). Vol. 33 (2007), 3,
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Automation , BLAS , Compiler , Finite element , Granularity , Loop hoisting , Monomials , Variational form



Denna post skapades 2014-01-05. Senast ändrad 2014-09-29.
CPL Pubid: 191163

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik
Beräkningsmatematik

Chalmers infrastruktur