Towards a heterogeneous architecture solver for the incompressible Navier–Stokes equations

Abstract

Large-scale supercomputers equipped with GPUs as accelerators are potential to satisfy the future Exascale computing. In this work the solution of large and sparse linear systems of equations by using the Krylov subspace methods, which is crucial for the overall performance of many industrial and scientific applications, is chosen to be accelerated by GPUs’ greatly enlarged computing power. To fulfill this objective on the target hardware with a large amount of heterogeneous computing nodes, two main contributions are included in this work. First we propose a communication avoiding variant of the BICGStab solution method which reduces the global synchronization points per iteration from 3 in the classical BICGStab method to 1 in the improved variant. The superiority in terms of a reduction of the expensive global communications via all computing processes can be expected on a large-scale distributed memory cluster. Second, to handle the host-to-accelerator data transfers, the main challenge encountered in the usage of heterogeneous architecture, a communication overlapped implementation of the sparse matrix–vector multiplication is proposed since this kernel features heavily in the Krylov subspace methods. Linear systems of equations arising from the incompressible Navier–Stokes equations are used to evaluate the proposed solution and optimization methods. Evaluations of the GPU and CPU implementations are conducted on up to 256 GPUs and 4096 CPU cores, respectively. It is revealed that to obtain the same computation time a two times reduction of the number of computing nodes is achieved by using the GPU implementation on the heterogeneous node equipped with 4 GPUs and a 32-core CPU. This result can be seen as the advantage of the heterogeneous architecture from the view point of applications, which motivates a wide utilization in other related areas.