OpenACC-based GPU Acceleration of a p-multigrid Discontinuous Galerkin Method for Compressible Flows on 3D Unstructured Grids

Abstract

A GPU accelerated p-multigrid discontinuous Galerkin (DG) method based on the OpenACC directives is presented for compressible flows on 3-D unstructured grids. The present design is aimed to utilize the power of high-performance GPU computing with very little intrusion and algorithm alteration to a well-developed CPU-based code. Due to the fact that the GPU memory is still far from abundant for high-order DG methods even on a top-rank model, a p-multigrid technique is therefore preferred for convergence acceleration rather than an implicit algorithm that requires huge memory for storing high-order Jacobian matrices. In this study, a multi-stage explicit time stepping scheme is used for advancing the higher-order approximation in time, with a first-order matrix-free implicit backward Euler scheme applied to accelerate the lower-order approximation. A variety of inviscid flow problems are computed on an NVIDIA Tesla K20c GPU to assess the performance of the developed GPU-accelerated code using a strong scaling test. The numerical results indicate that the p-multigrid discontinuous Galerkin method can be effectively accelerated on GPU in comparison with two eight-core AMD Opteron-6128 CPUs for its CPU-based counterpart.