An algorithm for the optimization of finite element integration loops

Abstract

We present an algorithm for the optimization of a class of finite element integration loop nests. This algo- rithm, 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 nu- merical 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.