Numerical Approximation of Gaussian random fields on Closed Surfaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910448624861184 |
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| author | Bonito, Andrea Guignard, Diane Lei, Wenyu |
| author_facet | Bonito, Andrea Guignard, Diane Lei, Wenyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_13739 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Numerical Approximation of Gaussian random fields on Closed Surfaces Bonito, Andrea Guignard, Diane Lei, Wenyu Numerical Analysis 65M12, 65M15, 65M60, 35S11, 65R20 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. |
| title | Numerical Approximation of Gaussian random fields on Closed Surfaces |
| topic | Numerical Analysis 65M12, 65M15, 65M60, 35S11, 65R20 |
| url | https://arxiv.org/abs/2211.13739 |