Benchmarking Domain-Specific Compiler Optimizations for Variational Forms

TL;DR

This paper evaluates the impact of complexity-reducing compiler optimizations on finite element variational form evaluation, demonstrating significant speedups in some cases through a prototype tool integrated with FEniCS.

Contribution

It introduces FErari, a prototype optimization backend for FEniCS, and benchmarks its effectiveness in reducing operation counts and improving assembly times.

Findings

Speedups of up to 7.9 in local operation counts

Global matrix assembly speedups of up to 2.8

Variable effectiveness depending on the form complexity

Abstract

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.