Simulation of Fractional Brownian Surfaces via Spectral Synthesis on Manifolds

03/26/2013 ∙ by Zachary Gelbaum, et al. ∙ 0 ∙ share

Using the spectral decomposition of the Laplace-Beltrami operator we simulate fractal surfaces as random series of eigenfunctions. This approach allows us to generate random fields over smooth manifolds of arbitrary dimension, generalizing previous work with fractional Brownian motion with multi-dimensional parameter. We give examples of surfaces with and without boundary and discuss implementation.

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Approximation of the spectral fractional powers of the Laplace-Beltrami Operator

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01/13/2021 ∙ by Andrea Bonito, et al. ∙ 0 ∙ share

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Three representations of the fractional p-Laplacian: semigroup, extension and Balakrishnan formulas

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10/14/2020 ∙ by Félix del Teso, et al. ∙ 0 ∙ share

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3rd-order Spectral Representation Method: Part I – Multi-dimensional random fields with fast Fourier transform implementation

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10/14/2019 ∙ by Lohit Vandanapu, et al. ∙ 0 ∙ share

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Characterization of Multi-scale Invariant Random Fields

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10/04/2017 ∙ by H. Ghasemi, et al. ∙ 0 ∙ share

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On the numerical solution of the Laplace-Beltrami problem on piecewise-smooth surfaces

The Laplace-Beltrami problem on closed surfaces embedded in three dimens...
08/20/2021 ∙ by Tristan Goodwill, et al. ∙ 0 ∙ share

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Galerkin–Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds

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Discrete Geodesic Nets for Modeling Developable Surfaces

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07/26/2017 ∙ by Michael Rabinovich, et al. ∙ 0 ∙ share

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Simulation of Fractional Brownian Surfaces via Spectral Synthesis on Manifolds

Authors

Approximation of the spectral fractional powers of the Laplace-Beltrami Operator

Three representations of the fractional p-Laplacian: semigroup, extension and Balakrishnan formulas

3rd-order Spectral Representation Method: Part I – Multi-dimensional random fields with fast Fourier transform implementation

Characterization of Multi-scale Invariant Random Fields

On the numerical solution of the Laplace-Beltrami problem on piecewise-smooth surfaces

Galerkin–Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds

Discrete Geodesic Nets for Modeling Developable Surfaces

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