86 citations · 301 across the 37 of their papers we have counts for
7 papers · 1 filter
Fast component-by-component construction of lattice algorithms for multivariate approximation with POD and SPOD weights
Ronald Cools, Frances Y. Kuo, Dirk Nuyens +1
In a recent paper by the same authors, we provided a theoretical foundation for the component-by-component (CBC) construction of lattice algorithms for multivariate approxima…
Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters
Ronald Cools, Frances Y. Kuo, Dirk Nuyens +1
This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate approximation in the worst case setting, for functions in a periodi…
Function integration, reconstruction and approximation using rank-1 lattices
Frances Y. Kuo, Giovanni Migliorati, Fabio Nobile +1
We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fo…
Enhanced Multi-Index Monte Carlo by means of Multiple Semi-Coarsened Multigrid for Anisotropic Diffusion Problems
Pieterjan Robbe, Dirk Nuyens, Stefan Vandewalle
In many models used in engineering and science, material properties are uncertain or spatially varying. For example, in geophysics, and porous media flow in particular, the uncerta…
Rank-1 lattices and higher-order exponential splitting for the time-dependent Schrödinger equation
Yuya Suzuki, Dirk Nuyens
In this paper, we propose a numerical method to approximate the solution of the time-dependent Schrödinger equation with periodic boundary condition in a high-dimensional setting.…
MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM
Dong T. P. Nguyen, Dirk Nuyens
We introduce the multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficient where is a Gaussian random field defined by…
Constructing QMC finite element methods for elliptic PDEs with random coefficients by a reduced CBC construction
Adrian Ebert, Peter Kritzer, Dirk Nuyens
In the analysis of using quasi-Monte Carlo (QMC) methods to approximate expectations of a linear functional of the solution of an elliptic PDE with random diffusion coefficient the…