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MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM - MaRDI portal

MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM (Q5074378)

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scientific article; zbMATH DE number 7523505

Language	Label	Description	Also known as
English	MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM	scientific article; zbMATH DE number 7523505

Statements

scholarly article

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MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM (English)

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Dong T. P. Nguyen

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ESAIM: Mathematical Modelling and Numerical Analysis

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publication date

9 May 2022

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full work available at URL

https://arxiv.org/abs/1904.13327

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zbMATH Keywords

elliptic PDE

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stochastic diffusion coefficient

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lognormal case

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infinite-dimensional integration

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multivariate decomposition method

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finite element method

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higher-order quasi-Monte Carlo

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high-dimensional quadrature

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cubature

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complexity bounds

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients

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Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs

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Representations of Gaussian random fields and approximation of elliptic PDEs with lognormal coefficients

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QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach

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Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules

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Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence

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Construction algorithms for polynomial lattice rules for multivariate integration

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Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs

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On the Optimal Order of Integration in Hermite Spaces with Finite Smoothness

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Efficient Implementations of the Multivariate Decomposition Method for Approximating Infinite-Variate Integrals

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On weighted Hilbert spaces and integration of functions of infinitely many variables

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Embeddings of weighted Hilbert spaces and applications to multivariate and infinite-dimensional integration

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Good interlaced polynomial lattice rules for numerical integration in weighted Walsh spaces

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Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients

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Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients

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Strong convergence analysis of iterative solvers for random operator equations

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Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients

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QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights

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High-dimensional integration on \(\mathbb{R}^d\), weighted Hermite spaces, and orthogonal transforms

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Integration in Hermite spaces of analytic functions

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Quasi–Monte Carlo integration with product weights for elliptic PDEs with log-normal coefficients

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Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation

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Randomly shifted lattice rules with the optimal rate of convergence for unbounded integrands

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Liberating the dimension

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On decompositions of multivariate functions

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Infinite-dimensional integration and the multivariate decomposition method

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Multivariate integration over \(\mathbb{R}^s\) with exponential rate of convergence

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MDFEM: multivariate decomposition finite element method for elliptic PDEs with uniform random diffusion coefficients using higher-order QMC and FEM

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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

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Tractability of multivariate problems. Volume II: Standard information for functionals.

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Tractability of infinite-dimensional integration in the worst case and randomized settings

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1051/M2AN/2021029

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Sitelinks

Mathematics(1 entry)

mardi Publication:5074378

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