封闭曲面上高斯随机场的数值逼近

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2024-01-04 DOI:10.1515/cmam-2022-0237

Andrea Bonito, Diane Guignard, Wenyu Lei

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引用次数: 0

摘要

我们考虑了封闭表面上高斯随机场的数值近似，其定义为带有加性白噪声的分数随机偏微分方程（SPDE）的解。SPDE 涉及两个参数，分别控制高斯随机场的平滑度和相关长度。所提出的数值方法依赖于解的 Balakrishnan 积分表示法，不需要对特征对进行近似。相反，它由 sinc 正交法和标准曲面有限元法组成。我们对该方法进行了完整的误差分析，并在几个数值实验中对其性能进行了说明。

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Numerical Approximation of Gaussian Random Fields on Closed Surfaces

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 in several numerical experiments.

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.