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


Swirydowicz K., Chalmers N., Karakus A., Warburton T.

INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS, vol.33, no.4, pp.735-757, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.1177/1094342018816368
  • Journal Name: INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.735-757
  • Keywords: Finite element method, elliptic problem, hexahedral elements, matrix-vector product, GPU tensor operations, NVIDIA Tesla P100, LEVEL, MODEL

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.