6 papers · 1 filter
Finite element analysis of density estimation using preintegration for elliptic PDE with random input
Alexander D. Gilbert
This paper analyses the finite element component of the error when using preintegration to approximate the cdf and pdf for uncertainty quantification (UQ) problems involving ellipt…
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…
A complex-projected Rayleigh quotient iteration for targeting interior eigenvalues
Nils Friess, Alexander D. Gilbert, Robert Scheichl
We introduce a new Projected Rayleigh Quotient Iteration aimed at improving the convergence behaviour of classic Rayleigh Quotient iteration (RQI) by incorporating approximate info…