High-Precision Numerical Simulations of Rotating Black Holes Accelerated by CUDA

Hardware accelerators (such as Nvidia's CUDA GPUs) have tremendous promise for computational science, because they can deliver large gains in performance at relatively low cost. In this work, we focus on the use of Nvidia's Tesla GPU for high-precision (double, quadruple and octal precision) numerical simulations in the area of black hole physics -- more specifically, solving a partial-differential-equation using finite-differencing. We describe our approach in detail and present the final performance results as compared with a single-core desktop processor and also the Cell BE. We obtain mixed results -- order-of-magnitude gains in overall performance in some cases and negligible gains in others.

[1]  Gaurav Khanna,et al.  Late-time Kerr tails revisited , 2007, 0711.0960.

[2]  David A. Bader,et al.  Financial modeling on the cell broadband engine , 2008, 2008 IEEE International Symposium on Parallel and Distributed Processing.

[3]  Stuart L. Shapiro,et al.  Numerical relativity and compact binaries , 2003 .

[4]  Saul A. Teukolsky,et al.  Perturbations of a rotating black hole , 1974 .

[5]  C. Gundlach,et al.  Introduction to 3+1 Numerical Relativity , 2008 .

[6]  Luis Lehner,et al.  Numerical relativity: a review , 2001 .

[7]  Gaurav Khanna,et al.  An exploration of CUDA and CBEA for a gravitational wave source-modelling application , 2009 .

[8]  Jens Breitbart,et al.  An exploration of CUDA and CBEA for a gravitational wave data-analysis application (Einstein@Home) , 2009 .

[9]  Gaurav Khanna,et al.  Late-time Kerr tails: generic and non-generic initial data sets, ‘up’ modes, and superposition , 2010, 1001.0541.

[10]  Peter Messmer,et al.  Accelerating Stencil-Based Computations by Increased Temporal Locality on Modern Multi- and Many-Core Architectures , 2008 .

[11]  Lior M. Burko,et al.  Universality of massive scalar field late-time tails in black-hole spacetimes , 2004 .

[12]  P. Laguna,et al.  Dynamics of perturbations of rotating black holes , 1997 .

[13]  Gaurav Khanna,et al.  Radiative falloff in the background of rotating black holes , 2002, gr-qc/0209107.

[14]  Samuel Williams,et al.  Scientific computing Kernels on the cell processor , 2007 .

[15]  Gaurav Khanna.  The CBE Hardware Accelerator for numerical Relativity: a Simple Approach , 2010, Int. J. Model. Simul. Sci. Comput..