Title: Accelerating the discontinuous Galerkin cell-vertex scheme solver on GPU-powered systems

Authors: Xiaoqi Hu; Mengshen Zhao; Shuang Z. Tu; Byunghyun Jang

Addresses: Department of Computer and Information Science, University of Mississippi, University, MS 38677, USA ' Department of Computer and Information Science, University of Mississippi, University, MS 38677, USA ' Department of Electrical and Computer Engineering, Jackson State University, Jackson, MS 39217, USA ' Department of Computer and Information Science, University of Mississippi, University, MS 38677, USA

Abstract: The discontinuous Galerkin cell-vertex scheme (DG-CVS) is a high-order space-time Riemann-solver-free numerical solver for general hyperbolic conservation laws. It fuses the discontinuous Galerkin (DG) method and the conservation element/solution element (CE/SE) method to take advantage of the best features of both methods. In DG-CVS, the time derivatives of the solution are treated as independent unknowns together with spatial derivatives of the solution, which is amendable to a GPU's parallel execution style. In a GPU environment, this type of scientific application poses challenges, such as high thread divergence, low kernel occupancy, and hardware-unfriendly memory access patterns. This paper presents various optimisations that address those issues. Our proposed optimisations include thread remapping, register pressure reduction as well as software-managed cache memory utilisation. DG-CVS is accelerated by up to 54% on AMD HD7970 GPU, when compared to CPU only execution.

Keywords: numerical solver; discontinuous Galerkin method; high performance computing; GPGPU; OpenCL.

DOI: 10.1504/IJCSE.2019.103824

International Journal of Computational Science and Engineering, 2019 Vol.20 No.2, pp.209 - 224

Received: 21 Mar 2018
Accepted: 16 Dec 2018

Published online: 27 Nov 2019 *

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