@article{11186, author = {Martin Aln{\ae}s and Kent-Andre Mardal}, title = {On the Efficiency of Symbolic Computations Combined With Code Generation for Finite Element Methods}, 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.}, year = {2010}, journal = {ACM Transactions on Mathematical Software}, volume = {37}, number = {1}, }