MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite
element methods that features arbitrary high-order finite element meshes and spaces …

We consider the generation of samples of a mean-zero Gaussian random field with Matérn
covariance function. Every sample requires the solution of a differential equation with …

We propose and analyze several multilevel algorithms for the fast simulation of possibly
nonstationary Gaussian random fields (GRFs) indexed, for example, by the closure of a …

When solving stochastic partial differential equations (SPDEs) driven by additive spatial
white noise, the efficient sampling of white noise realizations can be challenging. Here, we …

Gaussian random fields are popular models for spatially varying uncertainties, arising for
instance in geotechnical engineering, hydrology or image processing. A Gaussian random …

In this work we develop a new hierarchical multilevel approach to generate Gaussian
random field realizations in an algorithmically scalable manner that is well suited to …

Geological settings, such as reservoirs, include fractures with different material properties
and geometric features. Hence, numerical simulations in applied geophysics demands for …

This work presents an efficient approach for accelerating multilevel Markov Chain Monte
Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning …

Complex geometries as common in industrial applications consist of multiple patches, if
spline based parametrizations are used. The requirements for the generation of analysis …

Scalable approaches for uncertainty quantification are necessary for characterizing
prediction confidence in large‐scale subsurface flow simulations with uncertain …