A compiler for variational forms
This work addresses the computational bottleneck of variational form evaluation in finite element analysis, offering dramatic speedups for practitioners.
The paper presents a new algorithm for automatic evaluation of multilinear variational forms, implemented as the FEniCS Form Compiler (FFC), achieving up to 1000x speedup over standard quadrature-based approaches for finite element methods.
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.