Benchmarking Domain-Specific Compiler Optimizations for Variational Forms

We examine the effect of using complexity-reducing relations to generate optimized code for the evaluation of finite element variational forms. The optimizations are implemented in a prototype code named FErari, which has been integrated as an optimizing backend to the FEniCS Form Compiler, FFC. In some cases, FErari provides very little speedup, while in other cases, we obtain reduced local operation counts of a factor of as much as 7.9 and speedups for the assembly of the global sparse matrix of as much as a factor of 2.8.