86 citations · 301 across the 37 of their papers we have counts for
9 papers · 1 filter
Efficient implementations of the Multivariate Decomposition Method for approximating infinite-variate integrals
Alexander D. Gilbert, Frances Y. Kuo, Dirk Nuyens +1
In this paper we focus on efficient implementations of the Multivariate Decomposition Method (MDM) for approximating integrals of -variate functions. Such -variate…
Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial
Frances Y. Kuo, Dirk Nuyens
This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth…
Hot new directions for quasi-Monte Carlo research in step with applications
Frances Y. Kuo, Dirk Nuyens
This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first orde…
Circulant embedding with QMC -- analysis for elliptic PDE with lognormal coefficients
Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens +2
In a previous paper (J. Comp. Phys. 230 (2011), 3668--3694), the authors proposed a new practical method for computing expected values of functionals of solutions for certain class…
Analysis of circulant embedding methods for sampling stationary random fields
Ivan G. Graham, Frances Y. Kuo, Dirk Nuyens +2
In this paper we prove, under mild conditions, that the positive definiteness of the circulant matrix appearing in the circulant embedding method is always guaranteed, provided the…
The analysis of vertex modified lattice rules in a non-periodic Sobolev space
Dirk Nuyens, Ronald Cools
In a series of papers, in 1993, 1994 & 1996, Sloan & Niederreiter introduced a modification of lattice rules for non-periodic functions, called "vertex modified lattice rules"', an…
A Dimension-Adaptive Multi-Index Monte Carlo Method Applied to a Model of a Heat Exchanger
Pieterjan Robbe, Dirk Nuyens, Stefan Vandewalle
We present an adaptive version of the Multi-Index Monte Carlo method, introduced by Haji-Ali, Nobile and Tempone (2016), for simulating PDEs with coefficients that are random field…
Lattice rules with random achieve nearly the optimal error independently of the dimension
Peter Kritzer, Frances Y. Kuo, Dirk Nuyens +1
We analyze a new random algorithm for numerical integration of -variate functions over from a weighted Sobolev space with dominating mixed smoothness and prod…
Successive Coordinate Search and Component-by-Component Construction of Rank-1 Lattice Rules
Adrian Ebert, Hernan Leövey, Dirk Nuyens
The (fast) component-by-component (CBC) algorithm is an efficient tool for the construction of generating vectors for quasi-Monte Carlo rank-1 lattice rules in weighted reproducing…