An Efficient Multivariate Multidimensional Random Field Generator Using the Fast Fourier Transform

The direct Fast Fourier Transform method is very attractive for its simplicity and speed in generating multidimensional random fields. This thesis describes an efficient FFT method for generating multivariate multidimensional random fields based on the alternative spectral representation. Generation of a multivariate random field is simplified by the use of the spectral factorization function. The new method generates two statistically uncorrelated random fields in a single transform by taking advantage of the complex algebra of the FFT. Details of discrete implementation and parameter selection are discussed. The multivariate random field generator is used to generate a pair of cross-correlated random velocity fields in a porous medium. These fields conserve mass and reproduce the correct ensemble covariance and cross-covariance functions determined from a linerized theoretical analysis. A number of examples are used to show the flexibility of the current method which is also useful in many other applications. Thesis Supervisor: Dennis McLaughlin Title: Associate Professor