This paper introduces a generalized 3rd-order Spectral Representation Method for the simulation of multi-dimensional random fields and ergodic multi-variate stochastic processes with asymmetric non-linearities. The formula for the simulation of general $d$-dimensional random fields is presented and the method is applied to simulate 2D and 3D random fields. The differences between samples generated by the proposed methodology and the existing classical Spectral Representation Method are analysed. The formula for the simulation of multi-variate random processes is subsequently developed. An important feature of the methodologies is that they can be implemented efficiently with the Fast Fourier Transform (FFT), details of which are presented. Computational savings are shown to grow exponentially with dimensionality as a testament of the scalability of the simulation methodology. Examples highlighting the salient features of these methodologies are also presented.

本文介绍了一种通用的三阶频谱表示方法，用于模拟具有非对称非线性的多维随机场和遍历多变量随机过程。通用模拟公式$d$提出了三维随机场，并将该方法应用于2D和3D随机场的仿真。分析了所提出的方法与现有经典谱表示方法所产生的样本之间的差异。随后开发了用于模拟多元随机过程的公式。该方法的一个重要特征是可以使用快速傅立叶变换（FFT）有效地实现这些方法，并给出了详细信息。事实证明，计算节省量随维数呈指数增长，证明了仿真方法的可扩展性。还提供了突出这些方法的突出特征的示例。