Random Fields Generation on the GPU with the Spectral Turning Bands Method

Lars Hunger, Biagio Cosenza, Stefan Kimeswenger, Thomas Fahringer
Institute for Astro- and Particle Physics, University of Innsbruck, Austria
European Conference on Parallel Processing (Euro-Par), 2014


   title={Random Fields Generation on the GPU with the Spectral Turning Bands Method},

   author={Hunger, Lars and Cosenza, Biagio and Kimeswenger, Stefan and Fahringer, Thomas},



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Random Field (RF) generation algorithms are of paramount importance for many scientific domains, such as astrophysics, geostatistics, computer graphics and many others. Some examples are the generation of initial conditions for cosmological simulations or hydrodynamical turbulence driving. In the latter a new random field is needed every time-step. Current approaches commonly make use of 3D FFT (Fast Fourier Transform) and require the whole generated field to be stored in memory. Moreover, they are limited to regular rectilinear meshes and need an extra processing step to support non-regular meshes. In this paper, we introduce TBARF (Turning BAnd Random Fields), a RF generation algorithm based on the turning band method that is optimized for massively parallel hardware such as GPUs. Our algorithm replaces the 3D FFT with a lower order, one-dimensional FFT followed by a projection step, and is further optimized with loop unrolling and blocking. We show that TBARF can easily generate RF on non-regular (non uniform) meshes and can afford mesh sizes bigger than the available GPU memory by using a streaming, out-of-core approach. TBARF is 2 to 5 times faster than the traditional methods when generating RFs with more than 16M cells. It can also generate RF on non-regular meshes, and has been successfully applied to two real case scenarios: planetary nebulae and cosmological simulations.
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