This paper is a contemporary review of QMC ('quasi-Monte Carlo') methods, that is, equal-
weight rules for the approximate evaluation of high-dimensional integrals over the unit cube …

We consider the numerical solution of elliptic partial differential equations with random
coefficients. Such problems arise, for example, in uncertainty quantification for groundwater …

In this paper quasi-Monte Carlo (QMC) methods are applied to a class of elliptic partial
differential equations (PDEs) with random coefficients, where the random coefficient is …

We consider a finite element approximation of elliptic partial differential equations with
random coefficients. Such equations arise, for example, in uncertainty quantification in …

We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random
coefficients. We focus on models of the random coefficient that lack uniform ellipticity and …

This article provides a survey of recent research efforts on the application of quasi-Monte
Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion …

In this paper we analyze the numerical approximation of diffusion problems over polyhedral
domains in R^ d R d (d= 1, 2, 3 d= 1, 2, 3), with diffusion coefficient a (x, ω) a (x, ω) given as …

This paper is a sequel to our previous work (Kuo et al. in SIAM J Numer Anal, 2012) where
quasi-Monte Carlo (QMC) methods (specifically, randomly shifted lattice rules) are applied to …

In this paper we present a rigorous cost and error analysis of a multilevel estimator based on
randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems …

A probabilistic approach to phase-field brittle and ductile fracture with random material and
geometric properties is proposed within this work. In the macroscopic failure mechanics …