A Multi-Index Quasi--Monte Carlo Algorithm for Lognormal Diffusion Problems

DOI10.1137/16M1082561zbMath1386.60225arXiv1608.03157MaRDI QIDQ5372657

Stefan Vandewalle, Pieterjan Robbe, Dirk Nuyens

Publication date: 27 October 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.03157

zbMATH Keywords

elliptic PDEsquasi-Monte Carlouncertainty quantificationmultilevel Monte Carlomulti-index Monte Carlo

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items

Multilevel asymptotic-preserving Monte Carlo for kinetic-diffusive particle simulations of the Boltzmann-BGK equation ⋮ A Multi-Index Quasi--Monte Carlo Algorithm for Lognormal Diffusion Problems ⋮ Robust Optimization of PDEs with Random Coefficients Using a Multilevel Monte Carlo Method ⋮ Recycling Samples in the Multigrid Multilevel (Quasi-)Monte Carlo Method

Uses Software

• HSL_MI20
• Magic Point Shop
• QMC4PDE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multi-index Monte Carlo: when sparsity meets sampling
• Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: Application to random elliptic PDEs
• High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs
• Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
• Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients
• Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity
• Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation
• Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
• Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
• Multilevel Monte Carlo for the Feynman-Kac formula for the Laplace equation
• Dimension-adaptive tensor-product quadrature
• Fast random field generation with \(H\)-matrices
• Representations of Gaussian random fields and approximation of elliptic PDEs with lognormal coefficients
• Fast CBC construction of randomly shifted lattice rules achieving \(\mathcal{O}(n^{- 1 + \delta})\) convergence for unbounded integrands over \(\mathbb{R}^s\) in weighted spaces with POD weights
• A continuation multilevel Monte Carlo algorithm
• Karhunen-Loève approximation of random fields by generalized fast multipole methods
• Multilevel Monte Carlo Methods
• Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces
• Multilevel Monte Carlo Path Simulation
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs
• Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems
• Sparse grids
• HSL_MI20 : An efficient AMG preconditioner for finite element problems in 3D
• A Multi-Index Quasi--Monte Carlo Algorithm for Lognormal Diffusion Problems
• High-dimensional integration: The quasi-Monte Carlo way