一种用于极端黑洞与引力波物理计算的 GPU 加速混合精度 WENO 方法
A GPU-accelerated mixed-precision WENO method for extremal black hole and gravitational wave physics computations
AI总结：
提出 GPU 加速的混合精度 WENO 求解器，用于 Teukolsky 方程及极端黑洞、引力波问题，无需额外耗散并实现 3.3 倍加速。
摘要：
我们开发并使用一种新颖的混合精度加权本质无振荡（WENO）方法来求解 Teukolsky 方程，该方程产生于对 Kerr 黑洞扰动进行建模时。我们表明，WENO 方法优于 Teukolsky 方程离散化中常用的高阶有限差分方法，因为后者需要添加耗散以保证稳定性。特别是，由于 WENO 格式不使用额外耗散，它非常适合需要长时间演化的场景，例如研究 Price 尾以及极端质量比双星的引力波发射。在混合精度方法中，WENO 权重的高成本计算以降低的浮点精度执行，从而带来 3.3 倍的显著加速。此外，我们使用最先进的 Nvidia 通用图形处理单元和集群并行性进一步加速 WENO 计算。我们优化后的 WENO 求解器可用于快速生成在黑洞和引力波物理领域具有重要意义的准确结果。我们应用该求解器研究 Aretakis 荷的行为——这是一种守恒量，如果被 LIGO/Virgo 等引力波天文台探测到，将证明极端黑洞的存在。
英文摘要：
We develop and use a novel mixed-precision weighted essentially non-oscillatory (WENO) method for solving the Teukolsky equation, which arises when modeling perturbations of Kerr black holes. We show that WENO methods outperform higher-order finite-difference methods, standard in the discretization of the Teukolsky equation, due to the need to add dissipation for stability purposes in the latter. In particular, as the WENO scheme uses no additional dissipation it is well-suited for scenarios requiring long-time evolution such as the study of Price tails and gravitational wave emission from extreme mass ratio binaries. In the mixed-precision approach, the expensive computation of the WENO weights is performed in reduced floating-point precision that results in a significant speedup factor of 3.3. In addition, we use state-of-the-art Nvidia general-purpose graphics processing units and cluster parallelism to further accelerate the WENO computations. Our optimized WENO solver can be used to quickly generate accurate results of significance in the field of black hole and gravitational wave physics. We apply our solver to study the behavior of the Aretakis charge -- a conserved quantity, that if detected by a gravitational wave observatory like LIGO/Virgo would prove the existence of extremal black holes.
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