论文标题
封闭表面上高斯随机场的数值近似
Numerical Approximation of Gaussian random fields on Closed Surfaces
论文作者
论文摘要
我们考虑封闭表面上高斯随机场的数值近似，该封闭表面定义为具有加性白噪声的分数随机部分微分方程（SPDE）的解决方案。 SPDE涉及两个参数，以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溶液的Balakrishnan积分表示，并且不需要特征的近似。相反，它由SINC正交正交和标准表面有限元法组成。我们提供了该方法的完整误差分析，并通过几个数值实验说明了其性能。
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.
