标题： 高阶方法中的混合精度：浮点精度对ADER-DG算法的影响 显示英文标题

标题： Mixed-Precision in High-Order Methods: the Impact of Floating-Point Precision on the ADER-DG Algorithm

摘要： 我们提出了一种高阶不连续伽辽金方法与ADER时间步进(ADER-DG)的混合精度实现，用于在超偏微分方程引擎ExaHyPE中求解双曲型偏微分方程(PDEs)系统。该实现提供了一个简单的API扩展，用于指定各个内核的数值精度，从而允许测试低精度和混合精度对解的准确性的影响。为了展示这一点，我们研究了精度对方法的整体收敛阶数和实际准确性的影响，针对四个常见的双曲型PDE系统和五个具有解析解的相关场景进行了分析。对于所有场景，我们还评估了ADER-DG算法中的每个内核对使用双精度、单精度甚至半精度的敏感程度。这回答了如何有意识地采用混合精度来减轻低精度对整体模拟的有害影响的问题。 显示英文摘要

摘要： We present a mixed-precision implementation of the high-order discontinuous Galerkin method with ADER time stepping (ADER-DG) for solving hyperbolic systems of partial differential equations (PDEs) in the hyperbolic PDE engine ExaHyPE. The implementation provides a simple API extension for specifying the numerical precision for individual kernels, and thus allows for testing the effect of low and mixed precision on the accuracy of the solution. To showcase this, we study the impact of precision on the overall convergence order and actual accuracy of the method as achieved for four common hyperbolic PDE systems and five relevant scenarios that feature an analytic solution. For all scenarios, we also assess how sensitive each kernel of the ADER-DG algorithm is to using double, single or even half precision. This addresses the question where thoughtful adoption of mixed precision can mitigate hurtful effects of low precision on the overall simulation.