A multi-GPU enabled solver in Kronecker product form for multiphysics problems

Abstract

Modern engineering and scientific computing often requires solving sparse linear systems containing point-block matrix to model multiphysics problems. The space-time parallel method is popular and attractive in fluid dynamics, fitting parallel computers very well. In this paper, we design and implement a parallel, multi-GPU enabled GMRES solver for solving linear systems in the Kronecker product form arising from the domain decomposition based space-time parallel methods. To improve the efficiency of the solver, we also design a set of optimization strategies for Sparse Matrix-Vector Multiplication (SpMV) in Kronecker product form. These include: (1) enhancing the Compute-to-Memory Access Ratio (CMAR) to fully utilize the high bandwidth nature of the GPU during the computation phase and (2) introducing a parallel buffering scheme and a pre-mapping algorithm to enable the use of GPU-Direct for accelerating the communication phase. We conducted experiments on 1, 2, 4, and 8 GPUs and compared the performance of OKP-Solver with the cuSPARSE based implementation. On the V100 platform, the Kronecker product based SpMV computation ([Formula: see text]) achieves speedups of [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] on 1, 2, 4, and 8 GPUs, respectively, while the communication time ([Formula: see text]) achieves [Formula: see text], [Formula: see text], and [Formula: see text] on 2, 4, and 8 GPUs, respectively. On the A100 platform, [Formula: see text] achieves speedups of [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], while [Formula: see text] achieves [Formula: see text], [Formula: see text], and [Formula: see text]. The overall solver runtime ([Formula: see text]) achieves speedups of [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] on V100, and [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] on A100, for 1, 2, 4, and 8 GPUs, respectively.

Keywords

Affiliated Institutions

• Chinese Academy of Sciences CN
• Computer Network Information Center CN
• Xinyang Normal University CN

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