Multilevel QMC with Product Weights for Affine-Parametric, Elliptic PDEs

DOI10.1007/978-3-319-72456-0_18zbMath1405.65008OpenAlexW2803351718MaRDI QIDQ4611809

Christoph Schwab, Lukas Herrmann, Robert Nicholas Gantner

Publication date: 22 January 2019

Published in: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-72456-0_18

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical integration (65D30) Second-order elliptic systems (35J47)

Related Items (10)

Higher-Order Quasi-Monte Carlo for Bayesian Shape Inversion ⋮ Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification ⋮ Quasi--Monte Carlo Integration for Affine-Parametric, Elliptic PDEs: Local Supports and Product Weights ⋮ Multilevel Quasi-Monte Carlo Uncertainty Quantification for Advection-Diffusion-Reaction ⋮ Strong convergence analysis of iterative solvers for random operator equations ⋮ MDFEM: multivariate decomposition finite element method for elliptic PDEs with uniform random diffusion coefficients using higher-order QMC and FEM ⋮ Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients ⋮ Uncertainty Quantification Using Periodic Random Variables ⋮ Uncertainty Quantification for Spectral Fractional Diffusion: Sparsity Analysis of Parametric Solutions ⋮ The uniform sparse FFT with application to PDEs with random coefficients

Uses Software

• deal.ii
• gMLQMC
• QMC4PDE

Cites Work

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