High-precision numerical simulations on a CUDA GPU: Kerr black hole tails

Abstract

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 ∼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 ∼30 decimal digits) or octal (256-bit or ∼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. © 2013 Springer Science+Business Media New York.