An algorithm for the optimization of finite element integration loops

TL;DR

This paper introduces an algorithm that optimizes finite element integration loops by exploiting mathematical properties, achieving near-global optimal operation counts and significantly improving performance over existing methods.

Contribution

The paper presents a novel algorithm that leverages mathematical properties to optimize finite element loop nests, demonstrating near-global optimality and superior performance.

Findings

Achieves locally optimal operation count for finite element loops

Demonstrates significant performance improvements in numerical experiments

Validates effectiveness and limitations of the proposed algorithm

Abstract

We present an algorithm for the optimization of a class of finite element integration loop nests. This algorithm, which exploits fundamental mathematical properties of finite element operators, is proven to achieve a locally optimal operation count. In specified circumstances the optimum achieved is global. Extensive numerical experiments demonstrate significant performance improvements over the state of the art in finite element code generation in almost all cases. This validates the effectiveness of the algorithm presented here, and illustrates its limitations.