As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the FEniCS Form Compiler FFC. We present benchmark results for a series of standard variational forms, including the incompressible Navier-Stokes equations and linear elasticity. The speedup compared to the standard quadrature-based approach is impressive; in some cases the speedup is as large as a factor 1000.
@article{arxiv.1112.0402,
title = {A compiler for variational forms},
author = {Robert C. Kirby and Anders Logg},
journal= {arXiv preprint arXiv:1112.0402},
year = {2011}
}