Some variance reduction methods for numerical stochastic homogenization

DOI10.1098/rsta.2015.0168zbMath1353.82006arXiv1509.02389OpenAlexW3099442271WikidataQ39609767 ScholiaQ39609767MaRDI QIDQ2955851

Frédéric Legoll, Claude Le Bris, Xavier Blanc

Publication date: 13 January 2017

Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.02389

Mathematics Subject Classification ID

Related Items (6)

An offline-online strategy for multiscale problems with random defects ⋮ A variance reduction strategy for numerical random homogenization based on the equivalent inclusion method ⋮ Examples of computational approaches for elliptic, possibly multiscale PDEs with random inputs ⋮ Computing homogenized coefficientsviamultiscale representation and hierarchical hybrid grids ⋮ The choice of representative volumes in the approximation of effective properties of random materials ⋮ A Priori Error Analysis of a Numerical Stochastic Homogenization Method

Cites Work

• Unnamed Item
• Special quasirandom structures: a selection approach for stochastic homogenization
• Analyticity of homogenized coefficients under Bernoulli perturbations and the Clausius-Mossotti formulas
• First-order expansion of homogenized coefficients under Bernoulli perturbations
• Variance reduction using antithetic variables for a nonlinear convex stochastic homogenization problem
• An optimal variance estimate in stochastic homogenization of discrete elliptic equations
• Homogenization of a weakly randomly perturbed periodic material
• Approximations of effective coefficients in stochastic homogenization
• A reduced basis approach for some weakly stochastic multiscale problems
• Variance Reduction in Stochastic Homogenization: The Technique of Antithetic Variables
• Variance reduction in stochastic homogenization: proof of concept, using antithetic variables
• A Numerical Approach Related to Defect-Type Theories for Some Weakly Random Problems in Homogenization
• Homogenization theory and multiscale numerical approaches for disordered media: some recent contributions
• Elements of Mathematical Foundations for Numerical Approaches for Weakly Random Homogenization Problems
• A Control Variate Approach Based on a Defect-Type Theory for Variance Reduction in Stochastic Homogenization

This page was built for publication: Some variance reduction methods for numerical stochastic homogenization