Simulation of Stochastic Fields by Statistical Preconditioning

Abstract

A new stochastic fields simulation technique that can realize prescribed means and covariances with a substantially smaller sample size than that of other existing methods is developed. The method utilizes the modal decomposition of the covariance matrix of the correlated random vector and the spectral representation of random processes. The decreasing feature of the eigenvalues of the covariance matrix and the orthogonality of the trigonometric functions are taken advantage of for generating sets of independent random variables. The generated discretized stochastic field is Gaussian by virtue of the central limit theorem. The sample functions of the discretized stochastic field precisely reproduces, when ensemble-averaged, the prescribed zero-mean and covariance function. Hence, the proposed statistical preconditioning technique will, in general, dramatically reduce the large computational effort that Monte Carlo simulation involving stochastic fields would otherwise entail.