Simulation of Gaussian random fields on surfaces using the isogeometric finite element method
For researchers needing efficient simulation of Gaussian random fields on surfaces, this method offers a fast solver, though it is an incremental combination of existing techniques.
The paper develops a fast simulation method for Matérn random fields on closed surfaces by solving a fractional SPDE using isogeometric FEM and a geometric multigrid solver. Numerical results demonstrate the approach's effectiveness.
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.