Analysis of continuous spectral method for sampling stationary Gaussian random fields

Jocelyne Erhel 1 Mestapha Oumouni 2 Géraldine Pichot 3 Franck Schoefs 2
1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
2 TRUST - Contrôle de santé fiabilité et calcul des structures
GeM - Institut de Recherche en Génie Civil et Mécanique
Abstract : Problems of uncertainty quantification usually involve large number realiza-tions of a stationary spatial Gaussian random field over a regular grid points. This paper analyzes the convergence of the continuous spectral method for generating a stationary Gaussian random field. The continuous spectral method is the classical approach which discretizes the spectral representation integral to construct an approximation of the field within the Fast Fourier Transform algorithm. The method can be used as an alternative of circulant embedding approach when the discrete covariance matrix is not valid. We demonstrate that the method is computationally attractive when the spectral is a smooth function and decreases rapidly to zero at infinity. In such case, The spectral method is a very versatile approach for generating Gaussian stochastic fields. A simulation results are realized using pseudo-random data based on Monte-Carlo simulations to illustrate the theoretical bound of the method regarding the regularity of the random field and its spectral density.
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Jocelyne Erhel, Mestapha Oumouni, Géraldine Pichot, Franck Schoefs. Analysis of continuous spectral method for sampling stationary Gaussian random fields. 2019. ⟨hal-02109037⟩

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