Power-law noises over general spatial domains and on nonstandard meshes

Hans Werner Van Wyk; Max Gunzburger; John Burkhardt; Miroslav Stoyanov

doi:10.1137/140985433

Power-law noises over general spatial domains and on nonstandard meshes

Hans Werner Van Wyk, Max Gunzburger, John Burkhardt, Miroslav Stoyanov

Multiscale Methods

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Power-law noises abound in nature and have been observed extensively in both time series and spatially varying environmental parameters. Although recent years have seen the extension of traditional stochastic partial differential equations to include systems driven by fractional Brownian motion, spatially distributed scale-invariance has received comparatively little attention, especially for parameters defined over nonstandard spatial domains. This paper discusses the extension of power-law noises to general spatial domains by outlining their theoretical underpinnings as well as addressing their numerical simulation on arbitrary meshes. Three computational algorithms are presented for efficiently generating their sample paths, accompanied by numerous numerical illustrations.

Original language	English
Pages (from-to)	296-319
Number of pages	24
Journal	SIAM-ASA Journal on Uncertainty Quantification
Volume	3
Issue number	1
DOIs	https://doi.org/10.1137/140985433
State	Published - 2015

Funding

∗Received by the editors September 4, 2014; accepted for publication (in revised form) February 10, 2015; published electronically April 21, 2015. This research was partially supported by the U.S. Department of Energy Advance Simulation Computing Research (ASCR) program under grant DE-SC0010678. http://www.siam.org/journals/juq/3/98543.html †Department of Scientific Computing, Florida State University, Tallahassee, FL 32306 ([email protected], [email protected], [email protected]). ‡Computational and Applied Mathematics Group, Oak Ridge National Laboratory, Oak Ridge, TN 37831 ([email protected]). This research was partially supported by the U.S. Department of Energy Advance Simulation Computing Research (ASCR) program under grant DE-SC0010678.

Funders	Funder number
U.S. Department of Energy Advance Simulation Computing Research
U.S. Department of Energy
Advanced Scientific Computing Research	DE-SC0010678

Keywords

Fractional brownian surfaces
Fractional laplacian
Gaussian random fields
Power laws
Self-similarity

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Power-law noises over general spatial domains and on nonstandard meshes

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