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Spectral turning bands for efficient Gaussian random fields generation on GPUs and accelerators

Hunger, Lars; Cosenza, Biagio; Kimeswenger, Stefan; Fahringer, Thomas

FG Architektur eingebetteter Systeme

A random field (RF) is a set of correlated random variables associated with different spatial locations. RF generation algorithms are of crucial importance for many scientific areas, such as astrophysics, geostatistics, computer graphics, and many others. Current approaches commonly make use of 3D fast Fourier transform (FFT), which does not scale well for RF bigger than the available memory; they are also limited to regular rectilinear meshes. We introduce random field generation with the turning band method (RAFT), an RF generation algorithm based on the turning band method that is optimized for massively parallel hardware such as GPUs and accelerators. 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. RAFT can easily generate RF on non‐regular (non‐uniform) meshes and efficiently produce fields with mesh sizes bigger than the available device memory by using a streaming, out‐of‐core approach. Our algorithm generates RF with the correct statistical behavior and is tested on a variety of modern hardware, such as NVIDIA Tesla, AMD FirePro and Intel Phi. RAFT is faster than the traditional methods on regular meshes and has been successfully applied to two real case scenarios: planetary nebulae and cosmological simulations.