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

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.