A compiler for variational forms

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 of 1000. Categories and Subject Descriptors: G.4 [Mathematies of Computing]: Mathematical Software--Algorithm design and analysis; efficiency; G.1.8 [Numerical Analysis]: Partial Differential Equations Finite element methods General Terms: Algorithms, Performance Additional Key Words and Phrases: Variational form, compiler, finite element, automation