An Algorithm for the Optimization of Finite Element Integration Loops

Fabio Luporini, David A. Ham, Paul H. J. Kelly
2017 ACM Transactions on Mathematical Software  
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
more » ... ess of the algorithm presented here, and illustrates its limitations.
doi:10.1145/3054944 fatcat:kitpmlah4nbpxc2dxqt6x6y6jq