Discrete Filter and Non-Gaussian Noise for Fast Roughness Simulations with Gaussian Processes

Abstract

AbstractRough surface simulations result in tight feedback loops in research procedures, such that they speed up studies for example about roughness’ impact on tribology or fluid dynamics. To model and simulate a broad spectrum of rough surfaces, Gaussian processes (GP) have been suggested recently. However, these models are limited on surfaces with small sizes since computational time-costs and memory-costs of simulations with standard procedures scale cubically and quadratically, respectively. In this paper, we apply the discrete filter approach which is a special case of GPs. We use the discrete filter with the fast Fourier transform (FFT) algorithm to efficiently sample from a high-dimensional Gaussian distribution and we compare its computational costs with the contour integral quadrature algorithm. Our experiments show that GPs benefit from FFT and allow stationary rough surfaces with sizes as large as 30, 000 × 30, 000 to be efficiently sampled. Since this approach is complementary to the GP and noise model approach, we also show simulations of rough surfaces with underlying non-Gaussian noise models that can reduce computational complexity.