[图书][B] Numerical methods for stochastic partial differential equations with white noise
Z Zhang, GE Karniadakis - 2017 - Springer
In his forward-looking paper [374] at the conference “Mathematics Towards the Third
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …
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 multilevel stochastic collocation method for partial differential equations with random input data
Stochastic collocation methods for approximating the solution of partial differential equations
with random input data (eg, coefficients and forcing terms) suffer from the curse of …
with random input data (eg, coefficients and forcing terms) suffer from the curse of …
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 …
Complexity analysis of accelerated MCMC methods for Bayesian inversion
The Bayesian approach to inverse problems, in which the posterior probability distribution
on an unknown field is sampled for the purposes of computing posterior expectations of …
on an unknown field is sampled for the purposes of computing posterior expectations of …
Stochastic stable node-based smoothed finite element method for uncertainty and reliability analysis of thermo-mechanical problems
This thesis herein proposes a stochastic stable node-based smoothed finite element method
for uncertainty and reliability analysis of thermo-mechanical problems. First, the deterministic …
for uncertainty and reliability analysis of thermo-mechanical problems. First, the deterministic …
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 …
An adaptive multilevel Monte Carlo method with stochastic bounds for quantities of interest with uncertain data
The focus of this work is the introduction of some computable a posteriori error control to the
popular multilevel Monte Carlo sampling for PDE with stochastic data. We are especially …
popular multilevel Monte Carlo sampling for PDE with stochastic data. We are especially …
Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs
We establish sparsity and summability results for coefficient sequences of Wiener-Hermite
polynomial chaos expansions of countably-parametric solutions of linear elliptic and …
polynomial chaos expansions of countably-parametric solutions of linear elliptic and …
Accelerated multilevel Monte Carlo with kernel‐based smoothing and Latinized stratification
S Taverniers, SBM Bosma… - Water resources …, 2020 - Wiley Online Library
Heterogeneity and a paucity of measurements of key material properties undermine the
veracity of quantitative predictions of subsurface flow and transport. For such model …
veracity of quantitative predictions of subsurface flow and transport. For such model …