GPU上基于SEM的混合精度CFD模拟：Taylor-Green涡案例
Mixed-Precision SEM-Based CFD Simulations on GPUs: A Taylor-Green Vortex case
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中文总结 AI 辅助
针对Taylor-Green涡案例，提出三级分层混合精度控制模型，在GPU上基于SEM的无矩阵CFD模拟中，选定配置较fp64基线降低约34%的求解时间与能耗，同时提升鲁棒性。
中文摘要 AI 辅助
混合精度是降低计算流体动力学（CFD）模拟计算成本和能耗的有前景方法，但其有效性高度依赖于在完整模拟流程中降低精度的位置。本研究使用基于谱元法（SEM）的无矩阵CFD求解器Neko，对Taylor-Green涡案例展开研究。性能分析显示，流体时间步长并非仅由Krylov收敛主导：速度和压力求解器每步仅需少量迭代，而运行时间的很大一部分消耗在其他SEM算子和求解器组件上。基于此结构，我们提出一种三级分层混合精度控制模型。在分别以64位浮点数（fp64）和32位浮点数（fp32）精度为边界的环境中，评估两组配置。以fp64为边界的组识别出精度敏感组件，表明聚焦于SEM的fp32计算是未来优化的有前景方向；以fp32为边界的组则提供主要实际收益。针对所研究的高雷诺数案例，选定配置相较于fp64基线，可将求解时间和能耗均降低约34%，同时相比全局fp32提升了鲁棒性。我们还探索了有针对性的fp16内核覆盖，其在选定操作中展现潜力，但在涡量等基于梯度的量中敏感性增加。总体而言，这些结果表明，基于SEM的无矩阵CFD的混合精度应被视为模拟级控制问题，而非仅作为Krylov求解器优化。
英文摘要
Mixed precision is a promising approach for reducing the computational cost and energy consumption of Computation Fluid Dynamics (CFD) simulations, but its effectiveness depends strongly on where precision is reduced within the full simulation pipeline. In this work, we study Taylor-Green vortex case using Neko, a matrix-free CFD solver based on the spectral element method (SEM). Profiling shows that the fluid time step is not dominated by Krylov convergence alone: the velocity and pressure solvers require only a small number of iterations per step, while a substantial fraction of runtime is spent in other SEM operators and solver components. Motivated by this structure, we propose a three-level hierarchical mixed-precision control model. Two groups of configurations are evaluated in environments bounded by 64-bit floating-point (fp64) and 32-bit floating-point (fp32) precision, respectively. The fp64-bounded group identifies accuracy sensitive components and shows that SEM-focused fp32 computation is a promising direction for future optimization. The fp32-bounded group provides the main practical benefit. For the high Reynolds number case studied, selected configurations reduce both time- and energy-to-solution by about 34% relative to the fp64 baseline, while improving robustness compared with global fp32. Targeted fp16 kernel overrides are also explored, showing potential for selected operations but increased sensitivity in gradient-based quantities such as enstrophy. Overall, these results indicate that mixed-precision for matrix-free SEM-based CFD should be treated as a simulation-level control problem rather than solely as a Krylov-solver optimization.
