In this thesis, the solution of large-scale uncertainty quantification problems is considered. Uncertainty quantification aims to extract stochastic (moment) information from processes with uncertain input data. These ...

We present an adaptive algorithm for the computation of quantities of interest involving the solution of a stochastic elliptic PDE where the diffusion coefficient is parametrized by means of a Karhunen-Loève expansion. The ...

In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier–Stokes equations. Our approach is nonintrusive and ...

Peridynamics is an accepted method in engineering for modeling crack propagation on a macroscopic scale. However, the sensitivity of the method to two important model parameters – elasticity and the particle density – has ...

This thesis considers the uncertainty quantification of elliptic eigenvalue problems (EVPs) with a special focus on degenerate eigenvalues. Elliptic EVPs are problems to find a pair of eigenvalues and eigenfunctions of an ...

Scientific machine learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques to uncover the governing equations of complex processes. Among the available ...