Fast generation of isotropic Gaussian random fields on the sphere

Creasey Peter E. () and Lang Annika ()
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Creasey Peter E.: Department of Physics and Astronomy, University of California, Riverside, CA 92507, USA
Lang Annika: Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg, 412 96 Göteborg, Sweden

Monte Carlo Methods and Applications, 2018, vol. 24, issue 1, 1-11

Abstract: The efficient simulation of isotropic Gaussian random fields on the unit sphere is a task encountered frequently in numerical applications. A fast algorithm based on Markov properties and fast Fourier transforms in 1d is presented that generates samples on an n × n {n\times n} grid in O ⁡ ( n 2 ⁢ log ⁡ n ) {\operatorname{O}(n^{2}\log n)} . Furthermore, an efficient method to set up the necessary conditional covariance matrices is derived and simulations demonstrate the performance of the algorithm. An open source implementation of the code has been made available at https://github.com/pec27/smerfs.

Keywords: Gaussian random fields; isotropic random fields; Gaussian Markov random fields; fast Fourier transform; efficient simulation (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1515/mcma-2018-0001

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