发表机构
Charles University; University of Padova; University of Trieste（查理大学; 帕多瓦大学; 的里雅斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究热方程Runge--Kutta时间离散的全耦合线性系统的混合精度预处理迭代求解，证明鲁棒性并实现并行环境CPU时间最高50%的缩减。
AI 中文摘要
我们研究了混合精度对热方程在时间上采用Runge--Kutta方法离散后的数值积分的影响。应用了全时空离散化，这导致需要求解一个非常大且稀疏的线性系统，以获取所有时间步的数值近似和Runge--Kutta阶段。该线性系统通过应用合适的可并行运行的预处理迭代方法来求解。为了加速求解过程，预处理矩阵采用混合精度框架进行应用。顺序计算结果表明，即使在混合精度下应用，预处理矩阵也具有鲁棒性。最后，我们提供了数值证据，表明在并行环境中应用混合精度策略时性能得到提升，CPU时间最多减少50%。
英文摘要
We study the effect of mixed precision on the numerical integration of the heat equation discretized with a Runge--Kutta method in time. A full space-time discretization is applied, which results in a very large and sparse linear system to be solved for the numerical approximations and the Runge--Kutta stages of all time steps. The linear system is solved by applying a suitable preconditioned iterative method that can be run in parallel. In order to speed up the solution process, the preconditioner is applied using a mixed precision framework. Sequential results show the robustness of the preconditioner, even when applied in mixed precision. Finally, we present numerical evidence of the improved performance of the mixed precision strategy when applied in a parallel environment, achieving up to a 50% reduction in CPU time.
