MIST: Efficient Mixed-Precision Preconditioning Through Iterative Sparse- Triangular Solver Design
Haoyuan Zhang, Yidong Chen, Wenpeng Ma, Wu Yuan, Jian Zhang, Zhonghua Lu · 2024
Exact sparse-triangular solvers are highly sequential and difficult to implement efficiently on GPUs with ILU preconditioning. Lower precision is crucial for reducing data movement and storage demands in memory-bound problems. However, current mixed-precision systems struggle to achieve performance gains for ILU preconditioning on multi-GPU platforms due to challenges in (1) utilizing two levels of parallelism and (2) minimizing off-chip memory bandwidth while maintaining accuracy. Additionally, these systems focus on scalar operations and lack support for point-block matrices, which arise naturally in multiphysics problems and require tailored algorithm designs. To address these challenges, we propose MIST, a novel Mixed-precision Iterative Sparse-Triangular solver optimized for GPUs to accelerate preconditioning in Krylov methods. We (1) implement an efficient mixed-precision Jacobi iterative local solver to harness single-GPU parallelism and scale it to multi- GPU via domain decomposition, and (2) design a BSpMVA kernel to reduce bandwidth while achieving high double-precision accuracy. Integrated into a widely-used numerical library, MIST offers end-to-end support for solving sparse linear systems, balancing efficiency and convergence. Experimental results show that MIST provides a 3.38× average speedup over cuSPARSE�s exact sparse-triangular solver, with an additional 1.37× speedup when using low-precision, while maintaining robustness