Simulation of homogeneous nonGaussian stochastic vector fields

A spectral representation-based simulation methodology is proposed to generate sample functions of a multi-variate, multi-dimensional, nonGaussian stochastic vector field, according to a prescribed cross-spectral density matrix and prescribed (nonGaussian) marginal probability distribution functions. The proposed methodology starts by generating a Gaussian vector field that is then transformed into the desired nonGaussian one using a memoryless nonlinear transformation in conjunction with an iterative scheme. The generation of the Gaussian vector field is performed taking advantage of the Fast Fourier Transform technique for great computational efficiency. The special case of simulation of nonGaussian vector fields modeling material properties is examined, mainly from the point of view of certain simplifying assumptions that can be made for such random media. Finally, a numerical example involving a tri-variate, two-dimensional, nonGaussian stochastic vector field is presented in order to demonstrate the capabilities and the efficiency of the proposed methodology.