@Article{Alnaes:2009:OES,
  author =       "M. S. Aln{\ae}s and K-A. Mardal",
  title =        "On the Efficiency of Symbolic Computations Combined with
                  Code Generation for Finite Element Methods",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "37",
  number =       "1",
  accepted =     "15 June 2009",
  upcoming =     "true", 
  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.",
}