Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients
We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random
coefficients. We focus on models of the random coefficient that lack uniform ellipticity and …
coefficients. We focus on models of the random coefficient that lack uniform ellipticity and …
A hierarchical multilevel Markov chain Monte Carlo algorithm with applications to uncertainty quantification in subsurface flow
In this paper we address the problem of the prohibitively large computational cost of existing
Markov chain Monte Carlo methods for large-scale applications with high-dimensional …
Markov chain Monte Carlo methods for large-scale applications with high-dimensional …
Multilevel markov chain monte carlo
In this paper we address the problem of the prohibitively large computational cost of existing
Markov chain Monte Carlo methods for large-scale applications with high-dimensional …
Markov chain Monte Carlo methods for large-scale applications with high-dimensional …
Multilevel Monte Carlo analysis for optimal control of elliptic PDEs with random coefficients
This work is motivated by the need to study the impact of data uncertainties and material
imperfections on the solution to optimal control problems constrained by partial differential …
imperfections on the solution to optimal control problems constrained by partial differential …
Multilevel estimation of rare events
E Ullmann, I Papaioannou - SIAM/ASA Journal on Uncertainty Quantification, 2015 - SIAM
This work is motivated by the need to estimate the probability of rare events in engineering
systems with random inputs. We introduce a multilevel estimator which is based on and …
systems with random inputs. We introduce a multilevel estimator which is based on and …
Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients
In a previous paper (Graham et al. in J Comput Phys 230: 3668–3694, 2011), the authors
proposed a new practical method for computing expected values of functionals of solutions …
proposed a new practical method for computing expected values of functionals of solutions …
Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing
statistics of the solution of a partial differential equation (PDE) with random data, where the …
statistics of the solution of a partial differential equation (PDE) with random data, where the …
Uncertainty modeling and propagation for groundwater flow: a comparative study of surrogates
We compare sparse grid stochastic collocation and Gaussian process emulation as
surrogates for the parameter-to-observation map of a groundwater flow problem related to …
surrogates for the parameter-to-observation map of a groundwater flow problem related to …
[HTML][HTML] Two guaranteed equilibrated error estimators for harmonic formulations in eddy current problems
E Creusé, Y Le Menach, S Nicaise, F Piriou… - … & Mathematics with …, 2019 - Elsevier
In this paper a guaranteed equilibrated error estimator is developed for the 3D harmonic
magnetodynamic problem of Maxwell's system. This system is recasted in the classical A− φ …
magnetodynamic problem of Maxwell's system. This system is recasted in the classical A− φ …
Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes
This work describes a domain embedding technique between two nonmatching meshes
used for generating realizations of spatially correlated random fields with applications to …
used for generating realizations of spatially correlated random fields with applications to …