We investigate variational phase-field formulations of anisotropic brittle fracture to model
zigzag crack patterns in cubic materials. Our objective is twofold:(i) to analytically derive and …

In this paper, the potential benefits of quasi-Monte Carlo (QMC) methods for uncertainty
propagation are assessed via two applications: a numerical case study and a realistic and …

The Bayesian approach to inverse problems provides a rigorous framework for the
incorporation and quantification of uncertainties in measurements, parameters and models …

We study an optimal control problem under uncertainty, where the target function is the
solution of an elliptic partial differential equation with random coefficients, steered by a …

Nowadays, much of the world has a regional air pollution strategy to limit and decrease the
pollution levels across governmental borders and control their impact on human health and …

Abstract Quasi-Monte Carlo (QMC) points are a substitute for plain Monte Carlo (MC) points
that greatly improve integration accuracy under mild assumptions on the problem. Because …

We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal
control problems subject to parabolic partial differential equation (PDE) constraints under …

Quantifying uncertainty associated with the microstructure variation of a material can be a
computationally daunting task, especially when dealing with advanced constitutive models …

High order perturbation theory has seen an unexpected recent revival for controlled
calculations of quantum many-body systems, even at strong coupling. We adapt integration …

We propose an approximation method for high-dimensional 1-periodic functions based on
the multivariate ANOVA decomposition. We provide analysis of classical ANOVA …