Simulation of Gaussian random fields on surfaces using the isogeometric finite element method
数值分析
2026-05-26 v1 数值分析
摘要
We are concerned with the fast simulation of random fields on closed surfaces in which are generated by the (Whittle-) Mat\'ern class of covariance functions. To this end, we solve the underlying fractional stochastic partial differential equation with additive white noise by using an isogeometric finite element method on the surface in combination with the Balakrishnan integral representation of the solution. The solution of the underlying linear system of equations is performed by means of a geometric multigrid method that naturally underlies the isogeometric approach. Numerical results are presented to demonstrate the approach.
引用
@article{arxiv.2605.24882,
title = {Simulation of Gaussian random fields on surfaces using the isogeometric finite element method},
author = {Helmut Harbrecht and Florian Sonderegger and Remo von Rickenbach},
journal= {arXiv preprint arXiv:2605.24882},
year = {2026}
}