Constructing QMC Finite Element Methods for Elliptic PDEs with Random Coefficients by a Reduced CBC Construction

DOI10.1007/978-3-030-43465-6_9OpenAlexW3028477142MaRDI QIDQ5117928

Adrian Ebert, Dirk Nuyens, Peter Kritzer

Publication date: 26 August 2020

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.11068

zbMATH Keywords

quasi-Monte Carlo methodselliptic partial differential equations with random coefficientsinfinite-dimensional integrationcomponent-by-component constructions

Mathematics Subject Classification ID

Monte Carlo methods (65C05)

Related Items (2)

A note on concatenation of quasi-Monte Carlo and plain Monte Carlo rules in high dimensions ⋮ Digit-by-digit and component-by-component constructions of lattice rules for periodic functions with unknown smoothness

Uses Software

• QMC4PDE

Cites Work

• A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights
• Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation
• Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
• Tractability of multivariate integration for weighted Korobov classes
• QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights
• Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points
• Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients
• Quasi--Monte Carlo Integration for Affine-Parametric, Elliptic PDEs: Local Supports and Product Weights
• Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients
• Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs
• High-dimensional integration: The quasi-Monte Carlo way
• Constructing Embedded Lattice Rules for Multivariate Integration
• Quasi–Monte Carlo integration with product weights for elliptic PDEs with log-normal coefficients

This page was built for publication: Constructing QMC Finite Element Methods for Elliptic PDEs with Random Coefficients by a Reduced CBC Construction