High-Precision Numerical Simulations on a CUDA GPU: Kerr Black Hole Tails
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- Khanna, G. J Sci Comput (2013) 56: 366. doi:10.1007/s10915-012-9679-3
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Computational science has advanced significantly over the past decade and has impacted almost every area of science and engineering. Most numerical scientific computation today is performed with double-precision floating-point accuracy (64-bit or \(\sim \)15 decimal digits); however, there are a number of applications that benefit from a higher level of numerical precision. In this paper, we describe such an application in the research area of black hole physics: studying the late-time behavior of decaying fields in Kerr black hole space-time. More specifically, this application involves a hyperbolic partial-differential-equation solver that uses high-order finite-differencing and quadruple (128-bit or \(\sim \)30 decimal digits) or octal (256-bit or \(\sim \)60 decimal digits) floating-point precision. Given the computational demands of this high-order and high-precision solver, in addition to the rather long evolutions required for these studies, we accelerate the solver using a many-core Nvidia graphics-processing-unit and obtain an order-of-magnitude speed-up over a high-end multi-core processor. We thus demonstrate a practical solution for demanding problems that utilize high-precision numerics today.