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This paper introduces a generalised 3rd-order Spectral Representation Methodfor the simulation of multi-dimensional stochastic fields with asymmetricnon-linearities. The simulated random fields satisfy a prescribed PowerSpectrum and Bispectrum. The general d-dimensional simulation equations arepresented and the method is applied to simulate 2D and 3D random fields. Thedifferences between samples generated by the proposed methodology and theexisting classical Spectral Representation Method are analysed. An importantfeature of this methodology is that the formula can be implemented efficientlywith the Fast Fourier Transform, details of which are presented. Computationalsavings are shown to grow exponentially with dimensionality as a testament ofthe scalability of the simulation methodology.

3rd-order Spectral Representation Method: Part I -- Multi-dimensional random fields with fast Fourier transform implementation