A compiler for variational forms

TL;DR

This paper introduces FFC, a compiler that automates and accelerates the evaluation of multilinear variational forms in finite element methods, achieving speedups up to 1000 times over traditional methods.

Contribution

It presents a novel algorithm and compiler for automatic, efficient evaluation of variational forms, significantly improving computational performance in finite element analysis.

Findings

Speedup up to 1000 times compared to quadrature-based methods

Effective handling of standard variational forms like Navier-Stokes and elasticity

Demonstrated efficiency in benchmark tests

Abstract

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.