17747

Acceleration of tensor-product operations for high-order finite element methods

Kasia Swirydowicz, Noel Chalmers, Ali Karakus, Timothy Warburton
Department of Mathematics, Virginia Tech, McBryde Hall, 24061 Blacksburg, VA, USA
arXiv:1711.00903 [cs.MS], (2 Nov 2017)

@article{swirydowicz2017acceleration,

   title={Acceleration of tensor-product operations for high-order finite element methods},

   author={Swirydowicz, Kasia and Chalmers, Noel and Karakus, Ali and Warburton, Timothy},

   year={2017},

   month={nov},

   archivePrefix={"arXiv"},

   primaryClass={cs.MS}

}

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This paper is devoted to GPU kernel optimization and performance analysis of three tensor-product operators arising in finite element methods. We provide a mathematical background to these operations and implementation details. Achieving close-to-the-peak performance for these operators requires extensive optimization because of the operators’ properties: low arithmetic intensity, tiered structure, and the need to store intermediate results inside the kernel. We give a guided overview of optimization strategies and we present a performance model that allows us to compare the efficacy of these optimizations against an empirically calibrated roofline.
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