Multilevel Monte Carlo Approaches for Numerical Homogenization

DOI10.1137/130905836zbMath1328.65010arXiv1301.2798OpenAlexW2144389445MaRDI QIDQ3459648

C. Kronsbein, Frédéric Legoll, Yalchin R. Efendiev

Publication date: 11 January 2016

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.2798

zbMATH Keywords

stochastic homogenizationnumerical homogenizationmulti level Monte Carlo methods

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (10)

A hierarchical finite element Monte Carlo method for stochastic two-scale elliptic equations ⋮ An offline-online strategy for multiscale problems with random defects ⋮ Multilevel Monte Carlo Approaches for Numerical Homogenization ⋮ Asymptotically Compatible Schemes for Stochastic Homogenization ⋮ Quantifying uncertainties in contact mechanics of rough surfaces using the Multilevel Monte Carlo method ⋮ A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems ⋮ Examples of computational approaches for elliptic, possibly multiscale PDEs with random inputs ⋮ A Data-Driven Approach for Multiscale Elliptic PDEs with Random Coefficients Based on Intrinsic Dimension Reduction ⋮ Proper orthogonal decomposition method for multiscale elliptic PDEs with random coefficients ⋮ The choice of representative volumes in the approximation of effective properties of random materials

Uses Software

• DUNE
• DUNE-FEM
• ISTL

Cites Work

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