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Mathematics > Numerical Analysis

arXiv:2211.13739 (math)
[Submitted on 24 Nov 2022 (v1), last revised 16 May 2024 (this version, v3)]

Title:Numerical Approximation of Gaussian random fields on Closed Surfaces

Authors:Andrea Bonito, Diane Guignard, Wenyu Lei
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Abstract:We consider the numerical approximation of Gaussian random fields on closed surfaces defined as the solution to a fractional stochastic partial differential equation (SPDE) with additive white noise. The SPDE involves two parameters controlling the smoothness and the correlation length of the Gaussian random field. The proposed numerical method relies on the Balakrishnan integral representation of the solution and does not require the approximation of eigenpairs. Rather, it consists of a sinc quadrature coupled with a standard surface finite element method. We provide a complete error analysis of the method and illustrate its performances by several numerical experiments.
Comments: 36 pages, 5 figures, 5 tables
Subjects: Numerical Analysis (math.NA)
MSC classes: 65M12, 65M15, 65M60, 35S11, 65R20
Cite as: arXiv:2211.13739 [math.NA]
  (or arXiv:2211.13739v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2211.13739

Submission history

From: Wenyu Lei [view email]
[v1] Thu, 24 Nov 2022 18:02:38 UTC (2,964 KB)
[v2] Sun, 3 Dec 2023 16:09:09 UTC (3,550 KB)
[v3] Thu, 16 May 2024 15:30:24 UTC (3,549 KB)
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