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

This article is devoted to graphics processing unit (GPU) kernel optimization and performance analysis of three tensor-product operations arising in finite element methods. We provide a mathematical background to these operations and implementation details. Achieving close to 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 during the kernel execution. 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.