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GaussianRandomFields

A package for Gaussian random field generation in Julia

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GaussianRandomFields

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A Julia package to compute and sample from Gaussian random fields.

Key Features

  • Support for stationary (isotropic and anisotropic) and separable non-stationary covariance functions.
  • We provide most standard covariance functions such as Gaussian, Exponential and Matérn covariances. Adding a user-defined covariance function is very easy.
  • Implementation of most common methods to generate Gaussian random fields: Cholesky factorization, Karhunen-Loève expansion and circulant embedding.
  • Easy generation of Gaussian random fields defined on a Finite Element mesh.
  • Versatile plotting features for easy visualisation of Gaussian random fields.

Examples

Read the tutorial for details and examples on how to use this package. The tutorial is currently under construction...

References

[1] Lord, G. J., Powell, C. E. and Shardlow, T. An introduction to computational stochastic PDEs. No. 50. Cambridge University Press, 2014.

[2] Graham, I. G., Kuo, F. Y., Nuyens, D., Scheichl, R. and Sloan, I.H. Analysis of circulant embedding methods for sampling stationary random fields. ArXiv preprint, 2017.

[3] Le Maître, O. and Knio, M. O. Spectral methods for uncertainty quantification: with applications to computational fluid dynamics. Springer Science & Business Media, 2010.

[4] Baker, C. T. The numerical treatment of integral equations. Clarendon Press, 1977.

[5] Betz, W., Papaioannou I. and Straub, D. Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion. Computer Methods in Applied Mechanics and Engineering 271, pp. 109-129, 2014.

First Commit

01/04/2018

Last Touched

3 days ago

Commits

63 commits