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 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.

References in corpus (3)

• Firedrake: automating the finite element method by composing abstractions
• Optimisations for quadrature representations of finite element tensors through automated code generation
• A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake

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