AuthorsM. S. Alnæs and K. Mardal
TitleOn the Efficiency of Symbolic Computations Combined With Code Generation for Finite Element Methods
AfilliationScientific Computing, Center for Biomedical Computing (SFF), Scientific Computing
Project(s)Center for Biomedical Computing (SFF)
StatusPublished
Publication TypeJournal Article
Year of Publication2010
JournalACM Transactions on Mathematical Software
Volume37
Number1
Abstract

Efficient and easy implementation of variational forms for finite element discretization can be accomplished with meta-programming. Using a high-level language like Python and symbolic mathematics makes an abstract problem definition possible, but the use of a low-level compiled language is vital for run-time efficiency. By generating low-level C++ code based on symbolic expressions for the discrete weak form, it is possible to accomplish a high degree of abstraction in the problem definition while surpassing the run-time efficiency of traditional hand written C++ codes. We provide several examples where we demonstrate orders of magnitude in speed-up.

Citation KeySimula.SC.110