79 citations · 258 across the 61 of their papers we have counts for
6 papers · 2 filters
Multilevel Monte Carlo Simulations of Composite Structures with Uncertain Manufacturing Defects
T. J. Dodwell, S. Kinston, R. Butler +3
By adopting a Multilevel Monte Carlo (MLMC) framework, we show that only a handful of costly fine scale computations are needed to accurately estimate statistics of the failure of…
Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances
Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen +1
The periodization of a stationary Gaussian random field on a sufficiently large torus comprising the spatial domain of interest is the basis of various efficient computational meth…
Full Error Analysis and Uncertainty Quantification for the Heterogeneous Transport Equation in Slab Geometry
Ivan G. Graham, Matthew J. Parkinson, Robert Scheichl
We present an analysis of multilevel Monte Carlo techniques for the forward problem of uncertainty quantification for the radiative transport equation, when the coefficients ({\em…
A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data
Jens Lang, Robert Scheichl, David Silvester
We propose and analyse a fully adaptive strategy for solving elliptic PDEs with random data in this work. A hierarchical sequence of adaptive mesh refinements for the spatial appro…
Bounding the spectral gap for an elliptic eigenvalue problem with uniformly bounded stochastic coefficients
Alexander D. Gilbert, Ivan G. Graham, Robert Scheichl +1
A key quantity that occurs in the error analysis of several numerical methods for eigenvalue problems is the distance between the eigenvalue of interest and the next nearest eigenv…
High-performance dune modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites
Richard Butler, Tim Dodwell, Anne Reinarz +3
The key innovation in this paper is an open-source, high-performance iterative solver for high contrast, strongly anisotropic elliptic partial differential equations implemented wi…