Acceleration of tensor-product operations for high-order finite element methods. (July 2019)

• Record Type: Journal Article
• Authors: Świrydowicz, Kasia; Chalmers, Noel; Karakus, Ali; Warburton, Tim
• Is Part Of: International journal of high performance computing applications. Volume 33:Number 4(2019)
• Page Start: 735
• Page End: 757
• Publication Date: 2019-07
• Subjects: Finite element method -- elliptic problem -- hexahedral elements -- matrix–vector product -- GPU tensor operations -- NVIDIA Tesla P100; High performance computing -- Periodicals; Supercomputers -- Periodicals; 004.1105
• DOI: 10.1177/1094342018816368
• Languages: English
• ISSNs: 1094-3420

Abstract

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.