In this paper, we propose two mixed precision algorithms for Block-Jacobi preconditioner(BJAC): a fixed low precision strategy and an adaptive precision strategy. We evaluate the performance improvement of the proposed mixed precision BJAC preconditioners combined with the preconditioned conjugate gradient algorithm using problems including diffusion equations and radiation hydrodynamics equations. Numerical results show that, compared to the uniform high precision PCG algorithm, the mixed precision preconditioners can achieve speedups from 1.3 to 1.8 without sacrificing accuracy. Furthermore, we observe the phenomenon of convergence delay in some test cases for the mixed precision preconditioners, and further analyse the matrix features associate with the convergence delay behavior.

翻译：本文针对块雅可比预条件子提出了两种混合精度算法：固定低精度策略与自适应精度策略。我们结合预条件共轭梯度算法，通过扩散方程与辐射流体力学方程等算例评估了所提混合精度块雅可比预条件子的性能提升效果。数值结果表明，相较于统一高精度预条件共轭梯度算法，混合精度预条件子可在不损失精度的前提下获得1.3至1.8倍的加速比。此外，我们在部分测试案例中观察到混合精度预条件子存在收敛延迟现象，并进一步分析了与收敛延迟行为相关的矩阵特征。