In this work, we present a parallel MPI software, called GENFIELD, to generate stationary Gaussian random fields, based on the circulant embedding method [7, 1, 4].
The advantage of the circulant embedding method over existing methods (Cholesky factorization of the covariance matrix, Karhunen Loève series expansion) is its computational efficiency. It relies on Discrete Fourier Transform that can be computed efficiently with a Fast Fourier Transform algorithm. In GENFIELD, we use the FFTW3 library , which performs MPI parallel one-dimensional transforms. To ensure reproducibility and independence between the generated fields, we take benefit of the streams and substreams structure offered by the Rngstream library .
GENFIELD is used in hydrogeology to model natural fields, like hydraulic conductivity or porosity fields [3, 6]. Such fields are a pre-requisite for uncertainty quantification studies .
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