论文标题
混合精液runge-kutta方法的稳定性分析和绩效评估
Stability Analysis and Performance Evaluation of Mixed-Precision Runge-Kutta Methods
论文作者
论文摘要
提出并在4中分析了用于保留混合精确计算中高度精确解决方案的添加剂runge-kutta方法。这些经过专门设计的方法使用降低的精度来进行隐式计算，并为显式计算提供了完整的精确度。在这项工作中，我们分析了这些方法的稳定性及其对低精度舍入错误的敏感性，并在准确性和效率方面证明了它们的性能。我们开发了Fortran和Julia中的代码，以使用混合精度添加剂Runge-Kutta（MP-ARK）方法求解ODE和PDE的非线性系统。探索了这些方法的收敛，准确性，运行时和能耗。我们表明，对于给定的准确性，适当选择的MP-ARK方法可能会大大减少运行时。
Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed in 4. These specially designed methods use reduced precision for the implicit computations and full precision for the explicit computations. In this work we analyze the stability properties of these methods and their sensitivity to the low precision rounding errors, and demonstrate their performance in terms of accuracy and efficiency. We develop codes in FORTRAN and Julia to solve nonlinear systems of ODEs and PDEs using the mixed precision additive Runge-Kutta (MP-ARK) methods. The convergence, accuracy, runtime, and energy consumption of these methods is explored. We show that for a given level of accuracy, suitably chosen MP-ARK methods may provide significant reductions in runtime.
