5 papers
A higher order lattice-based method for high-dimensional numerical integration using periodization
Felix Bartel, Alexander D. Gilbert, Michael Griebel +2
We present a novel numerical integration method for non-periodic functions over the high-dimensional unit cube by a specially crafted (unequally-)weighted quadrature rule…
Quasi-Monte Carlo methods for uncertainty quantification of tumor growth modeled by a parametric semi-linear parabolic reaction-diffusion equation
Alexander D. Gilbert, Frances Y. Kuo, Dirk Nuyens +3
We study the application of a quasi-Monte Carlo (QMC) method to a class of semi-linear parabolic reaction-diffusion partial differential equations used to model tumor growth. Mathe…
Minimal Subsampled Rank-1 Lattices for Multivariate Approximation with Optimal Convergence Rate
Felix Bartel, Alexander D. Gilbert, Frances Y. Kuo +1
In this paper we show error bounds for randomly subsampled rank-1 lattices. We pay particular attention to the ratio of the size of the subset to the size of the initial lattice, w…
Multilevel lattice-based kernel approximation for elliptic PDEs with random coefficients
Alexander D. Gilbert, Michael B. Giles, Frances Y. Kuo +2
This paper introduces a multilevel kernel-based approximation method to estimate efficiently solutions to elliptic partial differential equations (PDEs) with periodic random coeffi…
Density estimation for elliptic PDE with random input by preintegration and quasi-Monte Carlo methods
Alexander D. Gilbert, Frances Y. Kuo, Abirami Srikumar
In this paper, we apply quasi-Monte Carlo (QMC) methods with an initial preintegration step to estimate cumulative distribution functions and probability density functions in uncer…