A GPU-Accelerated Mixed-Precision WENO Method for Extremal Black Hole and Gravitational Wave Physics Computations
A GPU-Accelerated Mixed-Precision WENO Method for Extremal Black Hole and Gravitational Wave Physics Computations
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DOI：
10.1007/s42967-021-00129-2
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发表时间：
2020-10
影响因子：
1.6
通讯作者：
Scott E. Field;S. Gottlieb;Zachary J. Grant;Leah Isherwood;G. Khanna
中科院分区：
文献类型：
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作者：
Scott E. Field;S. Gottlieb;Zachary J. Grant;Leah Isherwood;G. Khanna
我们发展并使用了一种新的混合精度加权基本无振荡(WENO)方法来求解Teukolsky方程，该方程是在模拟Kerr黑洞的微扰时产生的。我们证明了WENO方法优于高阶有限差分方法，后者是离散Teukolsky方程的标准方法，因为后者需要增加耗散以达到稳定的目的。特别是，由于WENO方案不使用额外的耗散，它非常适合于需要长期演化的场景，如研究价格尾巴和极端质量比双星的引力波发射。在混合精度方法中，WENO权重的昂贵计算是以降低的浮点精度执行的，这导致了显著的加速比。此外，我们使用最先进的NVIDIA通用图形处理器和集群并行来进一步加速WENO计算。我们优化的WENO求解器可以用来快速产生在黑洞和引力波物理领域有重要意义的准确结果。我们应用我们的解算器来研究Aretakis电荷的行为-一个守恒量，如果被LIGO/Virgo这样的引力波观测站探测到，将证明极端黑洞的存在。
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. 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.