Computer Methods in Applied Mechanics and Engineering· 2026Q1
Simulation of Gaussian random fields on surfaces using the isogeometric finite element method
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- Q1SCImago
- 2026year
Short summary
A novel isogeometric finite element method combined with the Balakrishnan integral representation enables fast simulation of Gaussian random fields on closed surfaces, outperforming traditional methods.
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Key points
- Developed an isogeometric finite element method for simulating Gaussian random fields on closed surfaces.
- Utilized the Balakrishnan integral representation to solve fractional stochastic partial differential equations.
- Employed a geometric multigrid method for efficient solution of linear systems.
- The method is designed for (Whittle-) Matérn class covariance functions.
AI-generated from the title and abstract; the full text is not read.
Abstract
We are concerned with the fast simulation of random fields on closed surfaces in $\mathbb{R}^3$ which are generated by the (Whittle-) Matérn 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.
The authors' abstract, as published at the source. Computer Methods in Applied Mechanics and Engineering, 2026 · DOI ↗
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Statistics, Probability and UncertaintyDecision Sciences