Simple and Efficient Method to Simulate Homogenous Multidimensional Non-Gaussian Vector Fields by the Spectral Representation Method

Abstract

A simple and efficient simulation method is proposed to generate multidimensional non-Gaussian vector fields based on the spectral representation method, according to the target cross spectral density matrix and the prescribed non-Gaussian marginal probability density functions. The proposed method starts by estimating the underlying Gaussian cross spectral density matrix through sample-function–free iterative scheme. Then, the resulting underlying Gaussian cross spectral density matrix can be applied to simulate a multidimensional Gaussian vector field, which is then mapped to the desired multidimensional non-Gaussian vector field through nonlinear memoryless translation. Finally, a numerical example involving a trivariate, two-dimensional, non-Gaussian vector field is presented to demonstrate the capabilities of the proposed method.